Zeroing the function (30) for the system with Ca(OH)2 precipitate introduced into pure water (copy of a fragment of display).
\\n\\n
Dr. Pletser’s experience includes 30 years of working with the European Space Agency as a Senior Physicist/Engineer and coordinating their parabolic flight campaigns, and he is the Guinness World Record holder for the most number of aircraft flown (12) in parabolas, personally logging more than 7,300 parabolas.
\\n\\nSeeing the 5,000th book published makes us at the same time proud, happy, humble, and grateful. This is a great opportunity to stop and celebrate what we have done so far, but is also an opportunity to engage even more, grow, and succeed. It wouldn't be possible to get here without the synergy of team members’ hard work and authors and editors who devote time and their expertise into Open Access book publishing with us.
\\n\\nOver these years, we have gone from pioneering the scientific Open Access book publishing field to being the world’s largest Open Access book publisher. Nonetheless, our vision has remained the same: to meet the challenges of making relevant knowledge available to the worldwide community under the Open Access model.
\\n\\nWe are excited about the present, and we look forward to sharing many more successes in the future.
\\n\\nThank you all for being part of the journey. 5,000 times thank you!
\\n\\nNow with 5,000 titles available Open Access, which one will you read next?
\\n\\nRead, share and download for free: https://www.intechopen.com/books
\\n\\n\\n\\n
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'
Preparation of Space Experiments edited by international leading expert Dr. Vladimir Pletser, Director of Space Training Operations at Blue Abyss is the 5,000th Open Access book published by IntechOpen and our milestone publication!
\n\n"This book presents some of the current trends in space microgravity research. The eleven chapters introduce various facets of space research in physical sciences, human physiology and technology developed using the microgravity environment not only to improve our fundamental understanding in these domains but also to adapt this new knowledge for application on earth." says the editor. Listen what else Dr. Pletser has to say...
\n\n\n\nDr. Pletser’s experience includes 30 years of working with the European Space Agency as a Senior Physicist/Engineer and coordinating their parabolic flight campaigns, and he is the Guinness World Record holder for the most number of aircraft flown (12) in parabolas, personally logging more than 7,300 parabolas.
\n\nSeeing the 5,000th book published makes us at the same time proud, happy, humble, and grateful. This is a great opportunity to stop and celebrate what we have done so far, but is also an opportunity to engage even more, grow, and succeed. It wouldn't be possible to get here without the synergy of team members’ hard work and authors and editors who devote time and their expertise into Open Access book publishing with us.
\n\nOver these years, we have gone from pioneering the scientific Open Access book publishing field to being the world’s largest Open Access book publisher. Nonetheless, our vision has remained the same: to meet the challenges of making relevant knowledge available to the worldwide community under the Open Access model.
\n\nWe are excited about the present, and we look forward to sharing many more successes in the future.
\n\nThank you all for being part of the journey. 5,000 times thank you!
\n\nNow with 5,000 titles available Open Access, which one will you read next?
\n\nRead, share and download for free: https://www.intechopen.com/books
\n\n\n\n
\n'}],latestNews:[{slug:"stanford-university-identifies-top-2-scientists-over-1-000-are-intechopen-authors-and-editors-20210122",title:"Stanford University Identifies Top 2% Scientists, Over 1,000 are IntechOpen Authors and Editors"},{slug:"intechopen-authors-included-in-the-highly-cited-researchers-list-for-2020-20210121",title:"IntechOpen Authors Included in the Highly Cited Researchers List for 2020"},{slug:"intechopen-maintains-position-as-the-world-s-largest-oa-book-publisher-20201218",title:"IntechOpen Maintains Position as the World’s Largest OA Book Publisher"},{slug:"all-intechopen-books-available-on-perlego-20201215",title:"All IntechOpen Books Available on Perlego"},{slug:"oiv-awards-recognizes-intechopen-s-editors-20201127",title:"OIV Awards Recognizes IntechOpen's Editors"},{slug:"intechopen-joins-crossref-s-initiative-for-open-abstracts-i4oa-to-boost-the-discovery-of-research-20201005",title:"IntechOpen joins Crossref's Initiative for Open Abstracts (I4OA) to Boost the Discovery of Research"},{slug:"intechopen-hits-milestone-5-000-open-access-books-published-20200908",title:"IntechOpen hits milestone: 5,000 Open Access books published!"},{slug:"intechopen-books-hosted-on-the-mathworks-book-program-20200819",title:"IntechOpen Books Hosted on the MathWorks Book Program"}]},book:{item:{type:"book",id:"217",leadTitle:null,fullTitle:"Recent Trends in Processing and Degradation of Aluminium Alloys",title:"Recent Trends in Processing and Degradation of Aluminium Alloys",subtitle:null,reviewType:"peer-reviewed",abstract:"In the recent decade a quantum leap has been made in production of aluminum alloys and new techniques of casting, forming, welding and surface modification have been evolved to improve the structural integrity of aluminum alloys. \nThis book covers the essential need for the industrial and academic communities for update information. It would also be useful for entrepreneurs technocrats and all those interested in the production and the application of aluminum alloys and strategic structures. It would also help the instructors at senior and graduate level to support their text.",isbn:null,printIsbn:"978-953-307-734-5",pdfIsbn:"978-953-51-6077-9",doi:"10.5772/741",price:159,priceEur:175,priceUsd:205,slug:"recent-trends-in-processing-and-degradation-of-aluminium-alloys",numberOfPages:530,isOpenForSubmission:!1,isInWos:1,hash:"6b334709c43320a6e92eb9c574a8d44d",bookSignature:"Zaki Ahmad",publishedDate:"November 21st 2011",coverURL:"https://cdn.intechopen.com/books/images_new/217.jpg",numberOfDownloads:114699,numberOfWosCitations:106,numberOfCrossrefCitations:32,numberOfDimensionsCitations:109,hasAltmetrics:0,numberOfTotalCitations:247,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"October 20th 2010",dateEndSecondStepPublish:"November 17th 2010",dateEndThirdStepPublish:"March 24th 2011",dateEndFourthStepPublish:"April 23rd 2011",dateEndFifthStepPublish:"June 22nd 2011",currentStepOfPublishingProcess:5,indexedIn:"1,2,3,4,5,6,7",editedByType:"Edited by",kuFlag:!1,editors:[{id:"52898",title:"Prof.",name:"Zaki",middleName:null,surname:"Ahmad",slug:"zaki-ahmad",fullName:"Zaki Ahmad",profilePictureURL:"https://mts.intechopen.com/storage/users/52898/images/1942_n.jpg",biography:"Professor Dr. Zaki Ahmad worked at King Fahd University of Petroleum and Minerals for thirty years in rendered distinguished services in teaching and research. He obtained his PhD from LEEDS University, UK. He was a chartered metallurgical engineer (C.Eng) from engineering council UK. He was a fellow of the institute of Materials, Minerals and Mining(FIMMM). He was a member of the European federation of corrosion and a fellow of institute of Metal Finishing. He substantially contributed to the founding activities in material science, corrosion engineering and nanotechnology at KFUPM and in Iran. He worked on international projects on aluminum with Aluminum, Ranshofen, Austria and Forschungzentrum, Geethscht, Germany and with Metallgesselscheft, Germany. He worked on international projects with Ministry of Technology, Germany. He was a founder contributor of center of excellence in corrosion at KFUPM, Dhahran, Saudi Arabia. He worked on the foundation and development of nanotechnology in Saudi Arabia in 2004. He was the author of “Principles of Corrosion Engineering and Corrosion Control” published by Elsevier in 2006. He has written over 95 research papers and international journals and over forty papers in international research conferences. His research activities included development of Al/SC alloys, Nanostructured superhydrophrobic surfaces, Nanocoatings and self-healing techniques. He was nominated for best researcher award in the Middle East by Energy Exchange in 2011. 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This requires extensive analysis of developing trends in scientific research in order to offer our readers relevant content. Creating the book catalogue is also based on keeping track of the most read, downloaded and highly cited chapters and books and relaunching similar topics. I am also responsible for consulting with our Scientific Advisors on which book topics to add to our catalogue and sending possible book proposal topics to them for evaluation. Once the catalogue is complete, I contact leading researchers in their respective fields and ask them to become possible Academic Editors for each book project. Once an editor is appointed, I prepare all necessary information required for them to begin their work, as well as guide them through the editorship process. I also assist editors in inviting suitable authors to contribute to a specific book project and each year, I identify and invite exceptional editors to join IntechOpen as Scientific Advisors. 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Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"72",title:"Ionic Liquids",subtitle:"Theory, Properties, New Approaches",isOpenForSubmission:!1,hash:"d94ffa3cfa10505e3b1d676d46fcd3f5",slug:"ionic-liquids-theory-properties-new-approaches",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/72.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"314",title:"Regenerative Medicine and Tissue Engineering",subtitle:"Cells and Biomaterials",isOpenForSubmission:!1,hash:"bb67e80e480c86bb8315458012d65686",slug:"regenerative-medicine-and-tissue-engineering-cells-and-biomaterials",bookSignature:"Daniel Eberli",coverURL:"https://cdn.intechopen.com/books/images_new/314.jpg",editedByType:"Edited by",editors:[{id:"6495",title:"Dr.",name:"Daniel",surname:"Eberli",slug:"daniel-eberli",fullName:"Daniel Eberli"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"57",title:"Physics and Applications of Graphene",subtitle:"Experiments",isOpenForSubmission:!1,hash:"0e6622a71cf4f02f45bfdd5691e1189a",slug:"physics-and-applications-of-graphene-experiments",bookSignature:"Sergey Mikhailov",coverURL:"https://cdn.intechopen.com/books/images_new/57.jpg",editedByType:"Edited by",editors:[{id:"16042",title:"Dr.",name:"Sergey",surname:"Mikhailov",slug:"sergey-mikhailov",fullName:"Sergey Mikhailov"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1373",title:"Ionic Liquids",subtitle:"Applications and Perspectives",isOpenForSubmission:!1,hash:"5e9ae5ae9167cde4b344e499a792c41c",slug:"ionic-liquids-applications-and-perspectives",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/1373.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"2270",title:"Fourier Transform",subtitle:"Materials Analysis",isOpenForSubmission:!1,hash:"5e094b066da527193e878e160b4772af",slug:"fourier-transform-materials-analysis",bookSignature:"Salih Mohammed Salih",coverURL:"https://cdn.intechopen.com/books/images_new/2270.jpg",editedByType:"Edited by",editors:[{id:"111691",title:"Dr.Ing.",name:"Salih",surname:"Salih",slug:"salih-salih",fullName:"Salih Salih"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"55440",title:"Solubility Products and Solubility Concepts",doi:"10.5772/67840",slug:"solubility-products-and-solubility-concepts",body:'The problem of solubility of various chemical compounds occupies a prominent place in the scientific literature. This stems from the fact that among various properties determining the use of these compounds, the solubility is of the paramount importance. Among others, this issue has been the subject of intense activities initiated in 1979 by the Solubility Data Commission V.8 of the IUPAC Analytical Chemistry Division established and headed by S. Kertes [1], who conceived the IUPAC-NIST Solubility Data Series (SDS) project [2, 3]. Within 1979–2009, the series of 87 volumes, concerning the solubility of gases, liquids, and solids in liquids or solids, were issued [3]; one of the volumes concerns the solubility of various oxides and hydroxides [4]. An extensive compilation of aqueous solubility data provides the Handbook of Aqueous Solubility Data [5].
A remark. Precipitates are marked in bold letters; soluble species/complexes are marked in normal letters.
The distinguishing feature of a chemical compound sparingly soluble in a particular medium is the solubility product Ksp value. In practice, the known Ksp values are referred only to aqueous media. One should note, however, that the expression for the solubility product and then the Ksp value of a precipitate depend on the notation of a reaction in which this precipitate is involved. From this it follows the apparent multiplicity of Ksp’s values referred to a particular precipitate. Moreover, as will be stated below, the expression for Ksp must not necessarily contain ionic species. On the other hand, factual or seeming lack of Ksp’s value for some precipitates is perceived; the latter issue be addressed here to MnO2, taken as an example.
Solubility products refer to a large group of sparingly soluble salts and hydroxides and some oxides, e.g., Ag2O, considered overall as hydroxides. Incidentally, other oxides, such as MnO2, ZrO2, do not belong to this group, in principle. For ZrO2, the solubility measurements showed quite low values even under a strongly acidic condition [6]. The solubility depends on the prior history of these oxides, e.g., prior roasting virtually eliminates the solubility of some oxides. Moderately soluble iodine (I2) dissolves due to reduction or oxidation, or disproportionation in alkaline media [7–12]; for I2, minimal solubility in water is a reference state. For 8-hydroxyquinoline, the solubility of the neutral molecule HL is a reference state; a growth in solubility is caused here by the formation of ionic species: H2L+1 in acidic and L−1 in alkaline media.
The Ksp is the main but not the only parameter used for calculation of solubility s of a precipitate. The simplifications [13] practiced in this respect are unacceptable and lead to incorrect/false results, as stated in [14–18]; more equilibrium constants are also involved with two-phase systems. These objections, formulated in the light of the generalized approach to electrolytic systems (GATES) [8], where s is the “weighed” sum of concentrations of all soluble species formed by the precipitate, are presented also in this chapter, related to nonredox and redox systems.
Calculation of s gives an information of great importance, e.g., from the viewpoint of gravimetry, where the primary step of the analysis is the quantitative transformation of a proper analyte into a sparingly soluble precipitate (salt, hydroxide). Although the precipitation and further analytical operations are usually carried out at temperatures far greater than the room temperature, at which the equilibrium constants were determined, the values of s obtained from the calculations made on the basis of equilibrium data related to room temperature are helpful in the choice of optimal a priori conditions of the analysis, ensuring the minimal, summary concentration of all soluble forms of the analyte, remaining in the solution, in equilibrium with the precipitate obtained after addition of an excess of the precipitating agent; this excess is referred to as relative to the stoichiometric composition of the precipitate. The ability to perform appropriate calculations, based on all available physicochemical knowledge, in accordance with the basic laws of matter conservation, deepens our knowledge of the relevant systems. At the same time, it produces the ability to acquire relevant knowledge in an organized manner—not just imitative, but focused on heuristics. This viewpoint is in accordance with constructivist teaching, based on the belief that learning occurs, as learners are actively involved in a process of meaning and knowledge construction, as opposed to passively receiving information [19].
The Ksp value refers to a two-phase system where the equilibrium solid phase is a sparingly soluble precipitate, whose Ksp value is measured/calculated according to defined expression for the solubility product. This assumption means that the solution with defined species is saturated against this precipitate, at given temperature and composition of the solution. However, often a precipitate, when introduced into aqueous media, is not the equilibrium solid phase, and then this fundamental requirement is not complied, as indicated in examples of the physicochemical analyses of the systems with struvite MgNH4PO4 [20, 21], dolomite CaMg(CO3)2 [22, 23], and Ag2Cr2O7.
The values of solubility products Ksp (usually represented by solubility constant pKsp = −logKsp value) are known for stoichiometric precipitates of AaBb or AaBbCc type, related to dissociation reactions:
where A and B or A, B, and C are the species forming the related precipitate; charges are omitted here, for simplicity of notation. The solubility products for more complex precipitates are unknown in the literature. The precipitates AaBbCc are known as ternary salts [24], e.g., struvite, dolomite, and hydroxyapatite Ca5(PO4)3OH.
The solubility products for precipitates of AaBb type are most frequently met in the literature. In these cases, for A are usually put simple cations of metals, or oxycations [25]; e.g., BiO+1 and UO2+2 form the precipitates: BiOCl and (UO2)2(OH)2. As B, simple or more complex anions are considered, e.g., Cl−1, S−2, PO4−3, Fe(CN)6−4, in AgCl, HgS, Zn3(PO4)2, and Zn2Fe(CN)6.
In different textbooks, the solubility products are usually formulated for dissociation reactions, with ions as products, also for HgS
although polar covalent bond exists between its constituent atoms [26]. Very low solubility product value (pKsp = 52.4) for HgS makes the dissociation according to the scheme presented by Eq. (3) impossible, and even verbal formulation of the solubility product is unreasonable. Namely, the ionic product x = [Hg+2][S–2] calculated at [Hg+2] = [S–2] = 1/NA exceeds Ksp, 1/NA2 > Ksp (NA – Avogadro’s number); the concentration 1/NA = 1.66∙10–23 mol/L corresponds to 1 ion in 1 L of the solution. The scheme of dissociation into elemental species [14]
is far more favored from thermodynamic viewpoint; nonetheless, the solubility product (Ksp) for HgS is commonly formulated on the basis of reaction (3). We obtain pKsp1 = pKsp – 2A(E01−E02), where E01 = 0.850 V for Hg+2 + 2e–1 = Hg, E02 = –0.48 V for S + 2e–1 = S–2, 1/A = RT/F⋅ln10, A = 16.92 for 298 K; then pKsp1 = 7.4.
Equilibrium constants are usually formulated for the simplest reaction notations. However, in this respect, Eq. (4) is simpler than Eq. (3). Moreover, we are “accustomed” to apply solubility products with ions (cations and anions) involved, but this custom can easily be overthrown. A similar remark may concern the notation referred to elementary dissociation of mercuric iodide precipitate
where I2 denotes a soluble form of iodine in a system. From
we obtain pKsp1 = pKsp – 2A(E01–E03), where
The species in the expression for solubility products do not predominate in real chemical systems, as a rule. However, the precipitation of HgS from acidified (HCl) solution of mercury salt with H2S solution can be presented in terms of predominating species; we have
Eq. (7) can be applied to formulate the related solubility product, Ksp2, for HgS. To be online with customary requirements put on the solubility product formulation, Eq. (7) should be rewritten into the form
Applying the law of mass action to Eq. (7a), we have
where [HgCl4–2] = 1015.07[Hg+2][Cl–1]4, [H2S] = 1020.0[H+1]2[S–2], Ksp (Eq. (3)).
The solubility product for MgNH4PO4 can be formulated on the basis of reactions:
where K1N = [H+1][NH3]/[NH4+1], K2P = [H+1][HPO4–2]/[H2PO4–1], K3P = [H+1][PO4–3]/[HPO4–2], [MgOH+1] = K1OH[Mg+2][OH–1], KW = [H+1][OH–1].
Note that only uncharged (elemental) species are involved in Eqs. (4) and (5); H2S enters Eq. (8), and NH3 enters Eqs. (10) and (11). This is an extension of the definition/formulation commonly met in the literature, where only charged species were involved in expression for the solubility product. Note also that small/dispersed mercury drops are neutralized with powdered sulfur, according to thermodynamically favored reaction [27]
reverse to Eq. (4). Some precipitates can be optionally considered as the species of AaBb or AaBbCc type. For example, the solubility product for MgHPO4 can be written as Ksp = [Mg+2][HPO4–2] or Ksp1 = [Mg+2][H+1][PO4–3] = KspK3P.
The ferrocyanide ion Fe(CN)6–4 (with evaluated stability constant K6 ca. 1037) can be considered as practically undissociated, i.e., Fe(CN)6–4 is kinetically inert [28], and then it does not give Fe+2 and CN–1 ions. The solubility product of Zn2Fe(CN)6 is Ksp = [Zn+2]2[Fe(CN)6–4]. Therefore, consideration of Zn2Fe(CN)6 as a ternary salt with Ksp1 = [Zn+2]2[Fe2+][CN–1]6 = Ksp/K6 is not acceptable.
In principle, the solubility product values are formulated for stoichiometric compounds, and specified as such in the related tables. However, some precipitates obtained in laboratory have nonstoichiometric composition, e.g., dolomite Ca1+xMg1-x(CO3)2 [22, 23], FexS [29]. In particular, FexS can be rewritten as Fe+2pFe+3qS; from the relations: 2p + 3q − 2 = 0 and p + q = x, we get q/p = 2(1 − x)/(3x − 2).
In this context, some remark needs a formulation of Ksp for some hydroxyoxides (e.g., FeOOH) and oxides (e.g., Ag2O). The related solubility products are formulated after completion of the corresponding reactions with water, e.g., FeOOH + H2O = Fe(OH)3, Fe2O3∙xH2O + (3 − x)H2O = 2Fe(OH)3 ⇒ Fe(OH)3 = Fe+3 + 3OH–1 ⇒ Ksp = [Fe+3][OH–1]3; Ag2O + H2O = 2AgOH ⇒ AgOH = Ag+1 + OH–1 ⇒ Ksp = [Ag+1][OH–1], see it in the context with gcd(a,b) = 1.
The solubility product can be involved not only with dissociation reaction. For example, the dissolution reaction Ca(OH)2 + 2H+1 = Ca+2 + 2H2O [30], characterized by Ksp1 = [Ca+2]/[H+1]2, is involved with Ksp = [Ca+2][OH–1]2 in the relation Ksp1 = Ksp/Kw2. In Ref. [31], the solubility product is associated with formation (not dissociation) of a precipitate.
The scheme presented above cannot be extended to all oxides. For example, one cannot recommend the formulation of this sequence for MnO2, i.e., MnO2 + 2H2O = Mn(OH)4 ⇒ Mn(OH)4 = Mn+4 + 4OH–1 ⇒ Ksp0 = [Mn+4][OH–1]4; Mn+4 ions do not exist in aqueous media, and MnO2 is the sole Mn(+4) species present in such systems. In effect, Ksp0 for MnO2 is not known in the literature, compare with Ref. [32]. However, the Ksp for MnO2 can be formally calculated according to an unconventional approach, based on the disproportionation reaction
reverse to the symproportionation reaction 2MnO4−1 + 3Mn+2 + H2O = 5MnO2 + 4H+1. The Ksp = Ksp1 value can be found there on the basis of E01 and E02 values [33], specified for reactions:
Eqs. (13) and (14) are characterized by the equilibrium constants:
defined on the basis of mass action law (MAL) [14], where logKe1 = 3⋅A⋅E01, logKe2 = 2⋅A⋅E02, A = 16.92. From Eqs. (13) and (14), we get
Assuming [MnO2] = 1 and [H2O] = 1 on the stage of the Ksp1 formulation for reaction (16), equivalent to reaction (12), we have
and then
The solubility products with MnO2 involved can be formulated on the basis of other reactions. For example, addition of
to Eq. (14) gives
Multiplication of Eq. (21) by 3, and then addition to Eq. (13a)
(reverse to Eq. (13)) gives the equation
and its equivalent form, obtained after simplifications,
Eq. (22) and then Eq. (22a) is characterized by the solubility product
where
for Mn+3 + e−1 = Mn+2 (E03 = 1.509 V) (reverse to Eq. (20)), logKe3 = A⋅E03. Then
Formulation of Kspi for other combinations of redox and/or nonredox reactions is also possible. This way, some derivative solubility products are obtained. The choice between the “output” and derivative solubility product values is a matter of choice. Nevertheless, one can choose the Ksp3 value related to the simplest expression for the solubility product Ksp3 = [Mn+2][MnO4−2] involved with reaction 2MnO2 = Mn+2 + MnO4−2.
As results from calculations, the low Kspi (i = 1,2,3) values obtained from the calculations should be crossed, even in acidified solution with the related manganese species presented in Figure 1. In the real conditions of analysis, at Ca = 1.0 mol/L, the system is homogeneous during the titration, also after crossing the equivalence point, at Φ = Φeq > 0.2; this indicates that the corresponding manganese species form a metastable system [34], unable for the symproportionation reactions.
The log[Xi] versus Φ relationships for different manganese species Xi, plotted for titration of V0 = 100 mL solution of FeSO4 (C0 = 0.01 mol/L) + H2SO4 (Ca = 1.0 mol/L) with V mL of C = 0.02 mol/L KMnO4; Φ = C·V/(C0·V0). The species Xi are indicated at the corresponding lines.
In this section, we compare two options applied to the subject in question. The first/criticized option, met commonly in different textbooks, is based on the stoichiometric considerations, resulting from dissociation of a precipitate, characterized by the solubility product Ksp value, and considered a priori as an equilibrium solid phase in the system in question; the solubility value obtained this way will be denoted by s* [mol/L]. The second option, considered as a correct resolution of the problem, is based on full physicochemical knowledge of the system, not limited only to Ksp value (as in the option 1); the solubility value thus obtained is denoted as s [mol/L]. The second option fulfills all requirements expressed in GATES and involved with basic laws of conservation in the systems considered. Within this option, we check, among others, whether the precipitate is really the equilibrium solid phase. The results (s*, s) obtained according to both options (1 and 2) are compared for the systems of different degree of complexity. The unquestionable advantages of GATES will be stressed this way.
The solubility s* will be calculated for a pure precipitate of: (1o) AaBb or (2o) AaBbCc type, when introduced into pure water. Assuming [A] = a∙s* and [B] = b∙s*, from Eq. (1), we have
and assuming [A] = a∙s*, [B] = b∙s*, [C] = c∙s*, from Eq. (2), we have
As a rule, the formulas (26) and (27) are invalid for different reasons, indicated in this chapter. This invalidity results, among others, from inclusion of the simplest/minor species in Eq. (26) or (27) and omission of hydroxo-complexes + other soluble complexes formed by A, and proto-complexes + other soluble complexes, formed by B. In other words, not only the species entering the expression for the related solubility product are present in the solution considered. Then the concentrations: [A], [B] or [A], [B], and [C] are usually minor species relative to the other species included in the respective balances, considered from the viewpoint of GATES [8].
We refer first to the simplest two-phase systems, with insoluble hydroxides as the solid phases. In all instances, s* denotes the solubility obtained from stoichiometric considerations, whereas s relates to the solubility calculated on the basis of full/attainable physicochemical knowledge related to the system in question where, except the solubility product (Ksp), other physicochemical data are also involved.
Applying formula (26) to hydroxides (B = OH−1): Ca(OH)2 (pKsp1 = 5.03) and Fe(OH)3 (pKsp2 = 38.6), we have [35]
respectively. However, Ca+2 and Fe+3 form the related hydroxo-complexes: [CaOH+1] = 101.3·[Ca+2][OH−1] and: [FeOH+2] = 1011.0·[Fe+3][OH−1], [Fe(OH)2+1] = 1021.7·[Fe+3][OH−1]2; [Fe2(OH)2+4] = 1025.1·[Fe+3]2[OH−1]2 [31]. The corrected expression for the solubility of Ca(OH)2 is as follows
Inserting [Ca+2] = Ksp1/[OH−1]2 and [OH−1] = KW/[H+1], [H+1] = 10−pH (pKW = 14.0 for ionic product of water, KW) into the charge balance
we get, by turns,
where
pH | y(pH) | [OH−1] | [Ca+2] | [CaOH+1] |
---|---|---|---|---|
12.451 | 0.000377 | 0.02825 | 0.01169 | 0.006592 |
12.452 | 0.000193 | 0.02831 | 0.01164 | 0.006577 |
12.453 | 8.30E-06 | 0.02838 | 0.01159 | 0.006561 |
12.454 | −0.000176 | 0.02844 | 0.01153 | 0.006546 |
12.455 | −0.000359 | 0.02851 | 0.01148 | 0.006531 |
Zeroing the function (30) for the system with Ca(OH)2 precipitate introduced into pure water (copy of a fragment of display).
The alkaline reaction in the system with Ca(OH)2 results immediately from Eq. (29): [OH−1] – [H+1] =
Analogously, for the system with Fe(OH)3, we have the charge balance
and then
Eq. (32) zeroes at pH0 = 7.0003 (Table 2), where the value
pH | y(pH) | [Fe+3] | [FeOH+2] | [Fe(OH)2+1] | [Fe2(OH)2+4] |
---|---|---|---|---|---|
7.0001 | 7.99E-11 | 2.510E-18 | 2.511E-14 | 1.259E-10 | 7.936E-25 |
7.0002 | 3.38E-11 | 2.508E-18 | 2.510E-14 | 1.258E-10 | 7.929E-25 |
7.0003 | −1.23E-11 | 2.507E-18 | 2.508E-14 | 1.258E-10 | 7.921E-25 |
7.0004 | −5.84E-11 | 2.505E-18 | 2.507E-14 | 1.258E-10 | 7.914E-25 |
7.0005 | −1.04E-10 | 2.503E-18 | 2.506E-14 | 1.257E-10 | 7.907E-25 |
Zeroing the function (32) for the system with Fe(OH)3 precipitate introduced into pure water (copy of a fragment of display).
is close to s ≅ [Fe(OH)2+1] = 10–9.9. Alkaline reaction for this system, i.e., [OH−1] > [H+1], results immediately from Eq. (30), and pH0 = 7.0003 (>7).
At pH = 7, Fe(OH)2+1 (not Fe+3) is the predominating species in the system, [Fe(OH)2+1]/[Fe+3] = 1021.7–14 = 5·107, i.e., the equality/assumption s* = [Fe+3] is extremely invalid. Moreover, the value [OH−1] = 3·s* = 2.94·10–10 = 10–9.532, i.e., pH = 4.468; this pH-value is contradictory with the inequality [OH−1] > [H+1] resulting from Eq. (31). Similarly, extremely invalid result was obtained in Ref. [36], where the strong hydroxo-complexes were totally omitted, and weak chloride complexes of Fe+3 ions were included into considerations.
Taking only the main dissociating species formed in the solution saturated with respect to Fe(OH)3, we check whether the reaction Fe(OH)3 = Fe(OH)2+1 + OH−1 with Ksp1 = [Fe(OH)2+1][OH−1] = 1021.7·10–38.6 = 10–16.9 can be used for calculation of solubility
Concluding, the application of the option 1, based on the stoichiometry of the reaction (29), leads not only to completely inadmissible results for s+, but also to a conflict with one of the fundamental rules of conservation obligatory in electrolytic systems, namely the law of charge conservation.
Similarly, critical/disqualifying remarks can be related to the series of formulas considered in the chapter [37], e.g., Ksp = 27(s*)4 for precipitates of A3B and AB3 type, and Ksp = 108(s*)5 for A2B3 and A3B2. For Ca5(PO4)3OH, the formula Ksp = 84375(s*)9 (!) was applied [38].
As a third example let us take a system, where an excess of Zn(OH)2 precipitate is introduced into pure water. It is usually stated that Zn(OH)2 dissociates according to the reaction
applied to formulate the expression for the solubility product
The soluble hydroxo-complexes Zn(OH)i+2−i (i=1,…,4), with the stability constants, KiOH, expressed by the values logKiOH = 4.4, 11.3, 13.14, 14.66, are also formed in the system in question. The charge balance (ChB) has the form
i.e., 2·10−15/[OH−1]2 + 104.4·10−15/[OH−1] – 1013.14·10−15∙[OH−1] – 2·1014.66·10−15∙[OH−1]2 = 0
The function (39) zeroes at pH0 = 9.121 (see Table 3). The basic reaction of this system is not immediately stated from Eq. (38) (there are positive and negative terms in expression for [OH−1] − [H+1]). The solubility s value
pH | [OH−1] | [Zn+2] | [ZnOH+1] | [Zn(OH)2] | [Zn(OH)3−1] | [Zn(OH)4−2] | y(pH) | s [mol/L] |
---|---|---|---|---|---|---|---|---|
9.118 | 1.3122E-05 | 5.8076E-06 | 1.9143E-06 | 0.0002 | 1.8113E-07 | 7.8705E-11 | 2.2702E-07 | 0.00020743 |
9.119 | 1.3152E-05 | 5.7810E-06 | 1.9099E-06 | 0.0002 | 1.8155E-07 | 7.9068E-11 | 1.3858E-07 | 0.00020740 |
9.120 | 1.3183E-05 | 5.7544E-06 | 1.9055E-06 | 0.0002 | 1.8197E-07 | 7.9433E-11 | 5.0322E-08 | 0.00020737 |
9.121 | 1.3213E-05 | 5.7280E-06 | 1.9011E-06 | 0.0002 | 1.8239E-07 | 7.9800E-11 | −3.7750E-08 | 0.00020734 |
9.122 | 1.3243E-05 | 5.7016E-06 | 1.8967E-06 | 0.0002 | 1.8281E-07 | 8.0168E-11 | −1.2564E-07 | 0.00020731 |
9.123 | 1.3274E-05 | 5.6755E-06 | 1.8923E-06 | 0.0002 | 1.8323E-07 | 8.0538E-11 | −2.1335E-07 | 0.00020728 |
Zeroing the function (39) for the system with Zn(OH)2 precipitate introduced into water; pKW = 14.
calculated at this point is different from s* = (Kso3/4)1/3 = 6.3⋅10−6, and [OH−1]/[Zn+2] ≠ 2; such incompatibilities contradict application of this formula.
Let us refer now to dissolution of precipitates MeL2 formed by cations Me+2 and anions L−1 of a strong acid HL, as presented in Table 4. When an excess of MeL2 is introduced into pure water, the concentration balances and charge balance in two-phase system thus formed are as follows:
Me+2 | MeOH+1 | Me(OH)2 | Me(OH)3−1 | L−1 | MeL+1 | MeL2 | MeL3−1 | MeL4−2 | MeL2 |
---|---|---|---|---|---|---|---|---|---|
logK1OH | logK2OH | logK3OH | logK1 | logK2 | logK3 | logK4 | pKsp | ||
Hg+2 | 10.3 | 21.7 | 21.2 | I−1 | 12.87 | 23.82 | 27.60 | 29.83 | 28.54 |
Pb+2 | 6.9 | 10.8 | 13.3 | I−1 | 1.26 | 2.80 | 3.42 | 3.92 | 8.98 |
Cl−1 | 1.62 | 2.44 | 2.04 | 1.0 | 4.79 |
logKiOH and logKi values for the stability constants Ki and Kj of soluble complexes Me(OH)i+2-i and MeLj+2-j and pKsp values for the precipitates MeL2; [MeLi+2-i] = Ki[Me+2][L−1]i, Ksp = [Me+2][L−1]2.
where [MeL2] denotes the concentration of the precipitate MeL2. At CL = 2CMe, we have
i.e., reaction of the solution is acidic, [H+1] > [OH−1]. Applying the relations for the equilibrium constants:
[Me+2][L−1]2 = Ksp, [Me(OH)i+2−i] = KiOH[Me+2][OH−1]i (i = 1,…, I), [MeLj+2−j] = Kj[Me+2][L−1]j (j = 1,…, J)
from Eqs. (43) and (44) we have
where
In particular, for I = 3, J = 4 (Table 4), we have
Applying the zeroing procedure to Eq. (46) gives the pH = pH0 of the solution at equilibrium. At this pH0 value, we calculate the concentrations of all species and solubility of this precipitate recalculated on sMe and sL. When zeroing Eq. (46), we calculate pH = pH0 of the solution in equilibrium with the related precipitate. The solubilities are as follows:
The calculations of sMe and sL for the precipitates specified in Table 4 can be realized with use of Excel spreadsheet, according to zeroing procedure, as suggested above (Table 1).
pH | [Pb+2] | [PbOH+1] | [Pb(OH)2] | [Pb(OH)3-1] | [PbCl+1] | [PbCl2] | [PbCl3−1] | [PbCl4−2] | [Cl−1] | y |
---|---|---|---|---|---|---|---|---|---|---|
4.5343 | 0.010749606 | 2.92208E-05 | 7.94315E-11 | 8.59592E-18 | 0.017405892 | 0.004466836 | 6.90723E-05 | 2.44685E-07 | 0.038842191 | 0.000138249 |
4.5344 | 0.010744657 | 2.92141E-05 | 7.94315E-11 | 8.5979E-18 | 0.017401884 | 0.004466836 | 6.90882E-05 | 2.44798E-07 | 0.038851136 | 7.7139E-05 |
4.5345 | 0.01073971 | 2.92074E-05 | 7.94315E-11 | 8.59988E-18 | 0.017397878 | 0.004466836 | 6.91041E-05 | 2.44911E-07 | 0.038860083 | 1.60945E-05 |
4.5346 | 0.010734765 | 2.92007E-05 | 7.94315E-11 | 8.60186E-18 | 0.017393872 | 0.004466836 | 6.912E-05 | 2.45023E-07 | 0.038869032 | -4.48848E-05 |
4.5347 | 0.010729823 | 2.91939E-05 | 7.94315E-11 | 8.60384E-18 | 0.017389867 | 0.004466836 | 6.91359E-05 | 2.45136E-07 | 0.038877983 | -0.000105799 |
Fragment of display for PbCl2.
For PbI2: pH0 = 5.1502, sPb = 6.5276∙10−4, sI = 1.3051∙10−3, see Table 6. The difference between sI and 2sPb = 1.3055∙10−3 results from rounding the pH0-value.
pH | [Pb+2] | [PbOH+1] | [Pb(OH)2] | [Pb(OH)3−1] | [PbI+1] | [PbI2] | [PbI3−1] | [PbI4−2] | [I−1] | y |
---|---|---|---|---|---|---|---|---|---|---|
5.15 | 0.000630817 | 7.07789E-06 | 7.94152E-11 | 3.54735E-17 | 1.47894E-05 | 6.60693E-07 | 3.54853E-09 | 1.44576E-11 | 0.001288393 | 0.000138249 |
5.1501 | 0.000630527 | 7.07626E-06 | 7.94152E-11 | 3.54816E-17 | 1.4786E-05 | 6.60693E-07 | 3.54935E-09 | 1.44643E-11 | 0.001288689 | 7.7139E-05 |
5.1502 | 0.000630236 | 7.07463E-06 | 7.94152E-11 | 3.54898E-17 | 1.47826E-05 | 6.60693E-07 | 3.55016E-09 | 1.44709E-11 | 0.001288986 | 1.60945E-05 |
5.1503 | 0.000629946 | 7.073E-06 | 7.94152E-11 | 3.5498E-17 | 1.47792E-05 | 6.60693E-07 | 3.55098E-09 | 1.44776E-11 | 0.001289283 | -4.48848E-05 |
5.1504 | 0.000629656 | 7.07137E-06 | 7.94152E-11 | 3.55061E-17 | 1.47758E-05 | 6.60693E-07 | 3.5518E-09 | 1.44843E-11 | 0.00128958 | -0.000105799 |
Fragment of display for PbI2.
For HgI2: pH0 = 6.7769, sHg = 1.91217∙10−5, sI = 3.82435∙10−5, see Table 7. The difference between sI and 2sHg = 3.82434∙10−5 results from rounding the pH-value. The concentration [HgI2] = K2Ksp = 1.90546∙10−5 is close to the sHg value. For comparison, 4(s*)3 = Ksp ⟹ s* = 1.93∙10−10, i.e., s*/s ≈ 10−5.
pH | [Hg+2] | [HgOH+1] | [Hg(OH)2] | [Hg(OH)3−1] | [HgI+1] | [HgI2] | [HgI3−1] | [HgI4−2] | [I−1] | y |
---|---|---|---|---|---|---|---|---|---|---|
6.7767 | 2.99681E-15 | 3.57569E-12 | 5.37106E-08 | 1.01569E-15 | 2.17936E-09 | 1.90546E-05 | 1.12634E-08 | 1.87646E-13 | 9.81003E-08 | 1.35932E-10 |
6.7768 | 2.99398E-15 | 3.57313E-12 | 5.36844E-08 | 1.01543E-15 | 2.17833E-09 | 1.90546E-05 | 1.12688E-08 | 1.87824E-13 | 9.81467E-08 | 7.72021E-11 |
6.7769 | 2.99114E-15 | 3.57056E-12 | 5.36583E-08 | 1.01517E-15 | 2.1773E-09 | 1.90546E-05 | 1.12741E-08 | 1.88002E-13 | 9.81932E-08 | 1.8567E-11 |
6.777 | 2.98831E-15 | 3.568E-12 | 5.36322E-08 | 1.0149E-15 | 2.17627E-09 | 1.90546E-05 | 1.12794E-08 | 1.88181E-13 | 9.82398E-08 | -3.99731E-11 |
6.7771 | 2.98548E-15 | 3.56544E-12 | 5.3606E-08 | 1.01464E-15 | 2.17524E-09 | 1.90546E-05 | 1.12848E-08 | 1.88359E-13 | 9.82863E-08 | -9.84182E-11 |
Fragment of display for HgI2.
The portions 0.1 g of calcite CaCO3 (M = 100.0869 g/mol, d = 2.711 g/cm3) are inserted into 100 mL of: pure water (task A) or aqueous solutions of CO2 specified in the tasks: B1, B2, B3, and equilibrated. Denoting the starting (t = 0) concentrations [mol/L]: Co for CaCO3 and
(A) we calculate pH = pH01 and solubility s = s(pH01) of CaCO3 at equilibrium in the system;
(B1) we calculate pH = pH02 and solubility s = s(pH02) of CaCO3 in the system, where
(B2) we calculate minimal
(B3) we plot the logsCa versus V, pH versus V and logsCa versus pH relationships for the system obtained after addition of V mL of a strong base MOH (Cb = 0.1) into V0 = 100 mL of the system with CaCO3 presented in (B1). The quasistatic course of the titration is assumed.
No. | Reaction | Expression for the equilibrium constant | Equilibrium data |
---|---|---|---|
1 | CaCO3 = Ca+2 + CO3−2 | [Ca+2][CO3−2] = Ksp | pKsp = 8.48 |
2 | Ca+2 + OH−1 = CaOH+1 | [CaOH+1] = K10[Ca+2][OH−1] | logK10 = 1.3 |
3 | H2CO3 = H+1 + HCO3−1 | [H+1][HCO3−1] = K1[H2CO3] | pK1 = 6.38 |
4 | HCO3−1 = H+1 + CO3−2 | [H+1][CO3−2] = K2[HCO3-1] | pK2 = 10.33 |
5 | Ca+2 + HCO3−1 = CaHCO3+1 | [CaHCO3+1] = K11[Ca+2][HCO3−1] | logK11 = 1.11 |
6 | Ca+2 + CO3−2 = CaCO3 | [CaCO3] = K12[Ca+2][CO3−2] | logK12 = 3.22 |
7 | Ca(OH)2 = Ca+2 + 2OH−1 | [Ca+2][OH−1]2 = Ksp1 | pKsp1 = 5.03 |
8 | H2O = H+1 + OH−1 | [H+1][OH−1] = KW | pKW = 14.0 |
Equilibrium data.
The volume 0.1/2.711 = 0.037 cm3 of introduced CaCO3 is negligible when compared with V0 at the start (t = 0) of the dissolution. Starting concentration of CaCO3 in the systems: A, B1, B2, B3 is Co = (0.1/100)/0.1 = 10−2 mol/L. At t > 0, concentration of CaCO3 is co mol/L. The balances are as follows:
where [M+1] = CbV/(V0+V).
For (A)
From Eqs. (49) and (50), we have
Considering the solution saturated with respect to CaCO3 and denoting: f1 = 1016.71−2pH + 1010.33−pH + 1, f2 = 1 + 10pH−12.7, from Eq. (53) and Table 1, we have the relations:
Inserting them into the charge balance (52), rewritten into the form
and applying the zeroing procedure to the function (54), we find pH01 = 9.904, at z = z(pH01) = 0. The solubility s = s(pH) of CaCO3, resulting from Eq. (49), is
We have s = s(pH = pH01) = 1.159⋅10−4 mol/L.
For (B1)
Subtraction of Eq. (49) from Eq. (51) gives
In this case,
where
and the charge balance is transformed into the zeroing function
where [CO3−2] = 10-8.48/[Ca+2], and [Ca+2] is given by Eq. (56). Eq. (58) zeroes at pH = pH02 = 6.031. Then from Eq. (57) we calculate s = s(pH02) = 6.393∙10−3 mol/L, at pH = pH02 = 6.031.
For (B2)
At pH = pH03, where co = 0, i.e., s = Co, the solution (a monophase system) is saturated toward CaCO3, i.e., the relation [Ca+2][CO3−2] = Ksp is still valid. Applying Eqs. (56) and (57), we find pH values zeroing Eq. (58) at different, preassumed
For (B3)
We apply again the formulas used in (B1) and (B2), and the charge balance (Eq. (52a)), which is transformed there into the function
applied for zeroing purposes, at different V values. The data thus obtained are presented graphically in Figures 2a–c. The data presented in the dynamic solubility diagram (Figure 2b), illustrating the solubility changes affected by pH changes (Figure 2a) resulting from addition of a base, MOH; Figure 2c shows a synthesis of these changes. Solubility product of Ca(OH)2 is not crossed in this system.
0.090 | 0.091 | 0.092 | 0.093 | 0.094 | 0.095 | 0.096 | 0.097 | 0.098 | 0.099 | 0.100 | 0.101 | 0.102 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
pH | 5.716 | 5.712 | 5.709 | 5.706 | 5.702 | 5.699 | 5.696 | 5.693 | 5.690 | 5.687 | 5.683 | 5.680 | 5.577 |
s | 9.58E-3 | 9.64E-3 | 9.67E-3 | 9.70E-3 | 9.77E-3 | 9.80E-3 | 9.84E-3 | 9.87E-3 | 9.91E-3 | 9.94E-3 | 10.01E-3 | 10.06E-3 | 10.10E-3 |
The set of points used for searching the
Graphical presentation of the data considered in (b3): (a) pH versus V, (b) log sCa versus V, (c) log sCa versus pH relationships.
Some solids when introduced into aqueous media (e.g., pure water) may appear to be nonequilibrium phases in these media.
The equilibrium data related to the system, where Ag2Cr2O7 is introduced into pure water, were taken from Refs. [33, 40, 41], and presented in Table 10. A large discrepancy between pKsp2 values (6.7 and 10) in the cited literature is taken here into account. We prove that Ag2Cr2O7 changes into Ag2CrO4.
Reaction | Equilibrium data |
---|---|
H2O = H+1 + OH-1 | pKw = 14.0 |
pK1 = 0.8 | |
pK2 = 6.5 | |
logK3 = 0.07 | |
logK4 = 1.52 | |
Ag+1 + OH−1 = AgOH | logK1OH = 2.3 |
logK2OH = 3.6 | |
logK3OH = 4.8 | |
pKsp1 = 11.9 | |
pKsp2 = 6.7 | |
pKsp3 = 7.84 |
Physicochemical equilibrium data relevant to the Ag2Cr2O7 + H2O system (pK = −logK), at “room” temperatures.
On the dissociation step, each dissolving molecule of Ag2Cr2O7 gives two ions Ag+1 and 1 ion Cr2O7−2, where two atoms of Cr are involved; in the contact with water, these ions are hydrolyzed, to varying degrees. In the initial step of the dissolution, before the saturation of the solution with respect to an equilibrium solid phase (not specified at this moment), we can write the concentration balances
where 2C0 is the total concentration of the solid phase in the system, at the moment (t = 0) of introducing this phase into water, [Ag2Cr2O7] is the concentration of this phase at a given moment of the intermediary step. As previously, we assume that addition of the solid phase (here: Ag2Cr2O7) does not change the volume of the system in a significant degree, and that Ag2Cr2O7 is added in a due excess, securing the formation of a solid (that is not specified at this moment), as an equilibrium solid phase. The balances in Eqs. (60) and (61) are completed by the charge balance
used, as previously, to formulation of the zeroing function, y = y(pH), and the set of relations for equilibrium data specified in Table 10. From these relations, we get
Denoting by 2c0 (< 2C0) the total concentration of dissolved Ag and Cr species formed, in a transition stage, from Ag2Cr2O7, we can write
From Table 10 and formulas (63)–(65) we get the relations:
where g0 = 1 + 10pH−11.7 + 102pH−24.4 + 103pH−37.2; g1 = 107.3−2pH + 106.5−pH + 1; g2 = 1014.59−3pH + 1014.52−2pH. Applying them in Eq. (62), we get the zeroing function
where g3 = 1 – 102pH−24.4 – 2∙103pH−37.2; g4 = 106.5−pH + 2; g5 = 1014.59−3pH + 2∙1014.52−2pH, and [Ag+1] and [CrO4−2] are defied above, as functions of pH.
The calculation procedure, realizable with use of Excel spreadsheet, is as follows. We assume a sequence of growing numerical values for 2c0. At particular 2c0 values, we calculate pH = pH(2c0) value zeroing the function (67), and then calculate the values of the products: q1 = [Ag+1]2[CrO4−2]/Ksp1 and q2 = [Ag+1]2[Cr2O7−2]/Ksp2, where: [Ag+1], [CrO4−2], and [Cr2O7−2] are presented above (Eqs. (66a), (66b) and (63a), resp.), pKsp1 = 11.9, pKsp2 = 6.7. As results from Figure 3, where logq1 and logq2 are plotted as functions of 2c0; logq1 = 0 ⇔ q1 = 1 ⇔ [Ag+1]2[CrO4−2] = Ksp1 at lower 2c0 value, whereas logq2 < 0 ⇔ q2 < 1 ⇔ [Ag+1]2[Cr2O7−2] < Ksp2, both for pK2 = 6.7 and 10, cited in the literature. The x1=1 value is attained at 2c0 = 3.5∙10−4 ⟹ c0 = 1.75∙10−4; then Ag2CrO4 precipitates as the new solid phase, i.e., total depletion of Ag2Cr2O7 occurs. It means that Ag2Cr2O7 is not the equilibrium solid phase in this system. This fact was confirmed experimentally, as stated in [42], i.e., Ag2Cr2O7 is transformed into Ag2CrO4 upon boiling with H2O; at higher temperatures, this transformation proceeds more effectively. Concluding, the formula s* = (Ksp2/4)1/3 applied for Ksp2 = [Ag+1]2[Cr2O7−2] is not “the best answer,” as stated in Ref. [43].
The convergence of logq1 and logq2 to 0 value; Ksp1 is attained at lower 2c0 value.
The system involved with Ag2CrO4 was also considered in context with the Mohr’s method of Cl−1 determination [44–46]. As were stated there, the systematic error in Cl−1 determining according to this method, expressed by the difference between the equivalence (eq) volume (Veq = C0V0/C) and the volume Vend corresponding to the end point where the Ksp1 for Ag2CrO4 is crossed, equals to
where Ksp = [Ag+1][Cl−1] (pKsp = 9.75), V0 is the volume of titrant with NaCl (C0) + K2CrO4 (C01) titrated with AgNO3 (C) solution; Vend = Veq at C01 = (1 + Vend/V0)∙Ksp1/Ksp.
All calculations presented above were realized using Excel spreadsheets. For more complex nonequilibrium two-phase systems, the use of iterative computer programs, e.g., ones offered by MATLAB [8, 47], is required. This way, the quasistatic course of the relevant processes under isothermal conditions can be tested [48].
The fact that NH3 evolves from the system obtained after leaving pure struvite pr1 in contact with pure water, e.g., on the stage of washing this precipitate, has already been known at the end of nineteenth century [49]. It was noted that the system obtained after mixing magnesium, ammonium, and phosphate salts at the molar ratio 1:1:1 gives a system containing an excess of ammonium species remaining in the solution and the precipitate that “was not struvite, but was probably composed of magnesium phosphates” [50]. This effect can be explained by the reaction [20]
Such inferences were formulated on the basis of X-ray diffraction analysis, the crystallographic structure of the solid phase thus obtained. It was also stated that the precipitation of struvite requires a significant excess of ammonium species, e.g., Mg:N:P = 1:1.6:1. Struvite (pr1) is the equilibrium solid phase only at a due excess of one or two of the precipitating reagents. This remark is important in context with gravimetric analysis of magnesium as pyrophosphate. Nonetheless, also in recent times, the solubility of struvite is calculated from the approximate formula s* = (Ksp1)1/3 based on an assumption that it is the equilibrium solid phase in such a system.
Struvite is not the equilibrium solid phase also when introduced into aqueous solution of CO2 (
The case of struvite requires more detailed comments. The reaction (68) was proved theoretically [20], on the basis of simulated calculations performed by iterative computer programs, with use of all attainable physicochemical knowledge about the system in question. For this purpose, the fractions
were calculated for: pr1 = MgNH4PO4 (pKsp1 = 12.6), pr2 = Mg3(PO4)2 (pKsp2 = 24.38), pr3 = MgHPO4 (pKsp3 = 5.5), pr4 = Mg(OH)2 (pKsp4 = 10.74) and are presented in Figure 4, at an initial concentration of pr1, equal C0 = [pr1]t=0 = 10−3 mol/L (pC0 = (ppr1)t=0 = 3); ppr1 = −log[pr1]. As we see, the precipitation of pr2 (Eq. (68)) starts at ppr1 = 3.088; other solubility products are not crossed. The changes in concentrations of some species, resulting from dissolution of pr1, are indicated in Figure 5, where s is defined by equation [20]
Plots of logqi versus ppr1 = −log[pr1] relationships, at (ppr1)t=0 = 3; i = 1,2,3,4 refer to pr1, pr2, pr3 and pr4, respectively.
The speciation curves for indicated species resulting from dissolution of pr1 at (ppr1)t=0 = 3.
involving all soluble magnesium species are identical in its form, irrespective of the equilibrium solid phase(s) present in this system. Moreover, it is stated that pH in the solution equals ca. 9–9.5 (Figure 6); this pH can be affected by the presence of CO2 from air. Under such conditions, NH4+1 and NH3 occur there at comparable concentrations [NH4+1] ≈ [NH3], but [HPO4−2]/[PO4−3] = 1012.36−pH ≈ 103. This way, the scheme (10) would be more advantageous, provided that struvite is the equilibrium solid phase; but it is not the case, see Eq. (68). The reaction (68) occurs also in the presence of CO2 in water where struvite was introduced.
The pH versus log[pr2] relationship; pr2 = Mg3(PO4)2, at [ppr1]t=0 = 3. The numbers at the corresponding lines indicate pCO2=−logCCO2 values; pCO2=∞ ⇔ CCO2= 0.
After introducing struvite pr1 (at pC0 = [ppr1]t=0 = 2) into alkaline (Cb = 10−2 mol/L KOH, pCb = 2) solution of CO2 (pCO2 = 4), the dissolution is more complicated and proceeds in three steps, see Figure 7.
The speciation curves for indicated species Xizi, resulting from dissolution of pr1 = MgNH4PO4, at (pC0, pCO2, pCb) = (2, 4, 2); s′ is defined by Eq. (71).
In step 1, pr4 precipitates first, pr1 + 2OH−1 = pr4 + NH3 + HPO4−2, nearly from the very start of pr1 dissolution, up to ppr1 = 2.151, where Ksp2 is attained. Within step 2, the solution is saturated toward pr2 and pr4. In this step, the reaction expressed by the notation 2pr1 + pr4 = pr2 + 2NH3 + 2H2O occurs up to total depletion of pr4 (at ppr1 = 2.896). In this step, the reaction 3pr1 + 2OH−1 = pr2 + 3NH3 + HPO4−1 + 2H2O occurs up to total depletion of pr1, i.e., the solubility product Ksp1 for pr1 is not crossed. The curve s′ (Figure 7) is related to the function
where s is expressed by Eq. (70).
The precipitate of nickel dimethylglyoximate, NiL2, has soluble counterpart with the same formula, i.e., NiL2, in aqueous media. If NiL2 is in equilibrium with the solution, concentration of the soluble complex NiL2 assumes constant value: [NiL2] = K2∙[Ni2+][L−]2 = K2∙Ksp, where K2 = 1017.24, Ksp = [Ni2+][L−]2 = 10−23.66 [14, 17, 18], and then [NiL2] = 10−6.42 (i.e., log[NiL2] = −6.42). The concentration [NiL2] is the constant, limiting component in expression for solubility s = sNi of nickel dimethylglyoximate, NiL2. Moreover, it is a predominant component in expression for s in alkaline media, see Figure 8. This pH range involves pH of ammonia buffer solutions, where NiL2 is precipitated from NiSO4 solution during the gravimetric analysis of nickel; the expression for solubility
Solubility curves for nickel dimethylglyoximate NiL2 in (a) ammonia, (b) acetate+ammonia, and (c) citrate+acetate+ ammonia media at total concentrations [mol/L]: CNi = 0.001, CL = 0.003, CN = 0.5, CAc = 0.3, CCit = 0.1 [14].
The effect of other, e.g., citrate (Cit) and acetate (Ac) species as complexing agents can also be considered for calculation purposes, see the lines b and c in Figure 8. The presence of citrate does not affect significantly the solubility of NiL2 in ammonia buffer media, i.e., at pH ≈ 9, where sNi ≅ [NiL2].
Calculations of s = sNi were made at CNi = 0.001 mol/L and CL = 0.003 mol/L HL, i.e., at the excessive HL concentration equal CL – 2CNi = 0.001 mol/L. Solubility of HL in water, equal 0.063 g HL/100 mL H2O (25oC) [51], corresponds to concentration 0.63/116.12 = 0.0054 mol/L of the saturated HL solution, 0.003 < 0.0054. Applying higher CL values needs the HL solution in ethanol, where HL is fairly soluble. However, the aqueous-ethanolic medium is thus formed, where equilibrium constants are unknown. To avoid it, lower CNi and CL values were applied in calculations. The equilibrium data were taken from Ref. [31].
The soluble complex having the formula identical to the formula of the precipitate occurs also in other, two-phase systems. In some pH range, concentration of this soluble form is the dominant component of the expression for the solubility s. As stated above, such a case occurs for NiL2. Then one can assume the approximation
Similar relationship exists also for other precipitates. By differentiation of Eq. (73) with respect to temperature T at p = const, and application of van’t Hoff’s isobar equation for K2 and Ksp, we obtain
where
Because, as a rule,
then
If
The redox system presented in this section is resolvable according to generalized approach to redox systems (GATES), formulated by Michałowski (1992) [8]. According to GATES principles, the algebraic balancing of any electrolytic system is based on the rules of conservation of particular elements/cores Yg (g = 1,…, G), and on charge balance (ChB), expressing the rule of electroneutrality of this system; the terms element and core are then distinguished. The core is a cluster of elements with defined composition (expressed by its chemical formula) and external charge that remains unchanged during the chemical process considered, e.g., titration. For ordering purposes, we assume: Y1 = H, Y2 = O,…. For modeling purposes, the closed systems, composed of condensed phases separated from its environment by diathermal (freely permeable by heat) walls, are considered; it enables the heat exchange between the system and its environment. Any chemical process, such as titration, is carried out under isothermal conditions, in a quasistatic manner; constant temperature is one of the conditions securing constancy of equilibrium constants values. An exchange of the matter (H2O, CO2, O2,…) between the system and its environment is thus forbidden, for modeling purposes. The elemental/core balance F(Yg) for the g-th element/core (Yg) (g = 1,…, G) is expressed by an equation interrelating the numbers of Yg-atoms or cores in components of the system with the numbers of Yg-atoms/cores in the species of the system thus formed; we have F(H) for Y1 = H, F(O) for Y2 = O, etc.
The key role in redox systems is due to generalized electron balance (GEB) concept, discovered by Michałowski as the Approach I (1992) and Approach II (2006) to GEB; both approaches are equivalent:
GEB is fully compatible with charge balance (ChB) and concentration balances F(Yg), formulated for different elements and cores. The primary form of GEB, pr-GEB, obtained according to Approach II to GEB is the linear combination
Both approaches (I and II) to GEB were widely discussed in the literature [7–12, 14, 15, 17, 18, 34, 52–74], and in three other chapters in textbooks [75–79] issued in 2017 within InTech. The GEB is perceived as a law of nature [9, 10, 17, 67, 71, 73, 74], as the hidden connection of physicochemical laws, as a breakthrough in the theory of electrolytic redox systems. The GATES refers to mono- and polyphase, redox, and nonredox, equilibrium and metastable [20, 21–23, 78, 79] static and dynamic systems, in aqueous, nonaqueous, and mixed-solvent media [69, 72], and in liquid-liquid extraction systems [53]. Summarizing, Approach II to GEB needs none prior information on oxidation numbers of all elements in components forming a redox system and in the species in the system thus formed. The Approach I to GEB, considered as the “short” version of GEB, is useful if all the oxidation numbers are known beforehand; such a case is obligatory in the system considered below. The terms “oxidant” and “reductant” are not used within both approaches. In redox systems, 2∙F(O) – F(H) is linearly independent on CHB and F(Yg) (g ≥ 3,…, G); in nonredox systems, 2∙F(O) – F(H) is dependent on those balances. This property distinguishes redox and nonredox systems of any degree of complexity. Within GATES, and GATES/GEB in particular, the terms: “stoichiometry,” “oxidation number,” “oxidant,” “reductant,” “equivalent mass” are considered as redundant, old-fashioned terms. The term “mass action law” (MAL) was also replaced by the equilibrium law (EL), fully compatible with the GATES principles. Within GATES, the law of charge conservation and law of conservation of all elements of the system tested have adequate importance/significance.
A detailed consideration of complex electrolytic systems requires a collection and an arrangement of qualitative (particular species) and quantitative data; the latter ones are expressed by interrelations between concentrations of the species. The interrelations consist of material balances and a complete set of expressions for equilibrium constants. Our further considerations will be referred to a titration, as a most common example of dynamic systems. The redox and nonredox systems, of any degree of complexity, can be resolved in analogous manner, without any simplifications done, with the possibility to apply all (prior, preselected) physicochemical knowledge involved in equilibrium constants related to a system in question. This way, one can simulate (imitate) the analytical prescription to any process that may be realized under isothermal conditions, in mono- and two-phase systems, with liquid-liquid extraction systems included.
The system considered in this section is related to iodometric, indirect analysis of an acidified (H2SO4) solution of CuSO4 [14, 64]. It is a very interesting system, both from analytical and physicochemical viewpoints. Because the standard potential E0 = 0.621 V for (I2, I−1) exceeds E0 = 0.153 V for (Cu+2, Cu+1), one could expect (at a first sight) the oxidation of Cu+1 by I2. However, such a reaction does not occur, due to the formation of sparingly soluble CuI precipitate (pKsp = 11.96).
This method consists of four steps. In the preparatory step (step 1), an excess of H2SO4 is neutralized with NH3 (step 1) until a blue color appears, which is derived from Cu(NH3)i+2 complexes. Then the excess of CH3COOH is added (step 2), to attain a pH ca. 3.6. After subsequent introduction of an excess of KI solution (step 3), the mixture with CuI precipitate and dissolved iodine formed in the reactions: 2Cu+2 + 4I−1 = 2CuI + I2, 2Cu+2 + 5I−1 = 2CuI + I3−1 is titrated with Na2S2O3 solution (step 4), until the reduction of iodine: I2 + 2S2O3−2 = 2I−1 + S4O6−2, I3−1 + 2S2O3−2 = 3I−1 + S4O6−2 is completed; the reactions proceed quantitatively in mildly acidic solutions (acetate buffer), where the thiosulfate species are in a metastable state. In strongly acidic media, thiosulfuric acid disproportionates according to the scheme H2S2O3 = H2SO3 + S [80].
We assume that V mL of C mol/L Na2S2O3 solution is added into the mixture obtained after successive addition of: VN mL of NH3 (C1) (step 1), VAc mL of CH3COOH (C2) (step 2), VKI mL of KI (C3) (step 3), and V mL of Na2S2O3 (C) (step 4) into V0 mL of titrand D composed of CuSO4 (C0) + H2SO4 (C01). To follow the changes occurring in particular steps of this analysis, we assume that the corresponding reagents in particular steps are added according to the titrimetric mode, and the assumption of the volumes additivity is valid.
In this system, three electron-active elements are involved: Cu (atomic number ZCu = 29), I (ZI = 53), S (ZS = 16). Note that sulfur in the core SO4−2 is not involved here in electron-transfer equilibria between S2O3−2 and S4O6−2; then the concentration balance for sulfate species can be considered separately.
The balances written according to Approach I to GEB, in terms of molar concentrations, are as follows:
Generalized electron balance (GEB)
CHB
F(Cu)
F(SO4)
F(NH3)
F(CH3COO)
F(K)
F(I)
F(S)
F(Na)
The GEB is presented here in terms of the Approach I to GEB, based on the “card game” principle, with Cu (Eq. (80)), I (Eq. (85)) as S (Eq. (86)) as “players,” and H, O, S (Eq. (81)), C (from Eq. (83)), N (from Eq. (82)), K, Na as “fans.” There are together 47 species involved in 2 + 6 = 8, Eqs. (78)–(83), (85), (86) and two equalities; [K+1] (Eq. (84)) and [Na+1] (Eq. (87)) are not involved in expressions for equilibrium constants, and then are perceived as numbers (not variables), at a particular V-value. Concentrations of the species in the equations are interrelated in 35 independent equilibrium constants:
Applying A = 16.92 [16], we have
In the calculations made in this system according to the computer programs attached to Ref. [64], it was assumed that V0 = 100, C0 = 0.01, C01 = 0.01, C1 = 0.25, C2 = 0.75, C3 = 2.0, C4 = C = 0.1; VN = 20, VAc = 40, VK = 20. At each stage, the variable V is considered as a volume of the solution added, consecutively: NH3, CH3COOH, KI, and Na2S2O3, although the true/factual titrant in this method is the Na2S2O3 solution, added in stage 4.
The solubility s [mol/L] of CuI in this system (Figures 8a and b) is put in context with the speciation diagrams presented in Figure 9. This precipitate appears in the initial part of titration with KI (C3) solution (Figure 8a) and further it accompanies the titration, also in stage 4 (Figure 8b). Within stage 3, at V ≥ C0V0/C3, we have
The speciation plots for indicated Cu-species within the successive stages. The V-values on the abscissas correspond to successive addition of V mL of: 0.25 mol/L NH3 (stage 1); 0.75 mol/L CH3COOH (stage 2); 2.0 mol/L KI (stage 3); and 0.1 mol/L Na2S2O3 (stage 4). For more details see text.
and in stage 4
The small concentration of Cu+1 (Figure 9, stage 3) occurs at a relatively high total concentration of Cu+2 species, determining the potential ca. 0.53–0.58 V, [Cu+2]/[Cu+1] = 10A(E – 0.153), see Figure 10a. Therefore, the concentration of Cu+2 species determine a relatively high solubility s in the initial part of stage 3. The decrease in the s value in further parts of stage 3 is continued in stage 4, at V < Veq = C0V0/C = 0.01∙100/0.1 = 10 mL. Next, a growth in the solubility s4 at V > Veq is involved with formation of thiosulfate complexes, mainly CuS2O3−1 (Figure 9, stage 4). The species I3−1 and I2 are consumed during the titration in stage 4 (Figure 9d). A sharp drop of E value at Veq = 10 mL (Figure 10b) corresponds to the fraction titrated Φeq = 1.
Plots of E versus V for (a) stage 3 and (b) stage 4.
The course of the E versus V relationship within the stage 3 is worth mentioning (Figure 10a). The corresponding curve initially decreases and reaches a “sharp” minimum at the point corresponding to crossing the solubility product for CuI. Precipitation of CuI starts after addition of 0.795 mL of 2.0 mol/L KI (Figure 11a). Subsequently, the curve in Figure 10a increases, reaches a maximum and then decreases. At a due excess of the KI (C3) added on the stage 3 (VK = 20 mL), solid iodine (I2(s), of solubility 0.00133 mol/L at 25oC) is not precipitated.
Solubility s of CuI within stage 3 (a) and stage 4 (b).
The solubility and dissolution of sparingly soluble salts in aqueous media are among the main educational topics realized within general chemistry and analytical chemistry courses. The principles of solubility calculations were formulated at a time when knowledge of the two-phase electrolytic systems was still rudimentary. However, the earlier arrangements persisted in subsequent generations [81], and little has changed in the meantime [82]. About 20 years ago, Hawkes put in the title of his article [83] a dramatic question, corresponding to his statement presented therein that “the simple algorithms in introductory texts usually produce dramatic and often catastrophic errors”; it is hard not to agree with this opinion.
In the meantime, Meites et al. [84] stated that “It would be better to confine illustrations of the solubility product principle to 1:1 salts, like silver bromide (…), in which the (…) calculations will yield results close enough to the truth.” The unwarranted simplifications cause confusion in teaching of chemistry. Students will trust us enough to believe that a calculation we have taught must be generally useful.
The theory of electrolytic systems, perceived as the main problem in the physicochemical studies for many decades, is now put on the side. It can be argued that the gaining of quantitative chemical knowledge in the education process is essentially based on the stoichiometry and proportions.
Overview of the literature indicates that the problems of dissolution and solubility calculation are not usually resolved in a proper manner; positive (and sole) exceptions are the studies and practice made by the authors of this chapter. Other authors, e.g., [13, 85], rely on the simplified schemes (ready-to-use formulas), which usually lead to erroneous results, expressed by dissolution denoted as s* [mol/L]; the values for s* are based on stoichiometric reaction notations and expressions for the solubility product values, specified by Eqs. (1) and (2). The calculation of s* contradicts the common sense principle; this was clearly stated in the example with Fe(OH)3 precipitate. Equation (27) was applied to struvite [50] and dolomite [86], although these precipitates are nonequilibrium solid phases when introduced into pure water, as were proved in Refs. [20–23]. The fact of the struvite instability was known at the end of nineteenth century [49]; nevertheless, the formula s* = (Ksp)1/3 for struvite may be still encountered in almost all textbooks and learning materials; this problem was raised in Ref. [15]. In this chapter, we identified typical errors involved with s* calculations, and indicated the proper manner of resolution of the problem in question.
The calculations of solubility s*, based on stoichiometric notation and Eq. (3), contradict the calculations of s, based on the matter and charge preservation. In calculations of s, all the species formed by defined element are involved, not only the species from the related reaction notation. A simple zeroing method, based on charge balance equation, can be applied for the calculation of pH = pH0 value, and then for calculation of concentrations for all species involved in expression for solubility value.
The solubility of a precipitate and the pH-interval where it exists as an equilibrium-solid phase in two-phase system can be accurately determined from calculations based on charge and concentration balances, and complete set of equilibrium constant values referred to the system in question.
In the calculations performed here we assumed a priori that the Ksp values in the relevant tables were obtained in a manner worthy of the recognition, i.e., these values are true. However, one should be aware that the equilibrium constants collected in the relevant tables come from the period of time covering many decades; it results from an overview of dates of references contained in some textbooks [31, 85] relating to the equilibrium constants. In the early literature were generally presented the results obtained in the simplest manner, based on Ksp calculation from the experimentally determined s* value, where all soluble species formed in solution by these ions were included on account of simple cations and anions forming the expression for Ksp. In many instances, the Ksp* values should be then perceived as conditional equilibrium constants [87]. Moreover, the differences between the equilibrium constants obtained under different physicochemical conditions in the solution tested were credited on account of activity coefficients, as an antidote to any discrepancies between theory and experiment.
First dissociation constants for acids were published in 1889. Most of the stability constants of metal complexes were determined after the announcement 1941 of Bjerrum’s works, see Ref. [88], about ammine-complexes of metals, and research studies on metal complexes were carried out intermittently in the twentieth century [89]. The studies of complexes formed by simple ions started only from the 1940s; these studies were related both to mono- and two-phase systems. It should also be noted that the first mathematical models used for determination of equilibrium constants were adapted to the current computing capabilities. Critical comments in this regard can be found, among others, in the Beck [90] monograph; the variation between the values obtained by different authors for some equilibrium constants was startling, and reaching 20 orders of magnitude. It should be noted, however, that the determination of a set of stability constants of complexes as parameters of a set of suitable algebraic equations requires complex mathematical models, solvable only with use of an iterative computer program [91–93].
The difficulties associated with the resolution of electrolytic systems and two-phase systems, in particular, can be perceived today in the context of calculations using (1o) spreadsheets (2o) iterative calculation methods. In (1o), a calculation is made by the zeroing method applied to the function with one variable; both options are presented in this chapter.
The expression for solubility products, as well as the expression of other equilibrium constants, is formulated on the basis of mass action law (MAL). It should be noted, however, that the underlying mathematical formalism contained in MAL does not inspire trust, to put it mildly. For this purpose, the equilibrium law (EL) based on the Gibbs function [94] and the Lagrange multipliers method [95–97] with laws of charge and elements conservation was suggested lately by Michałowski.
From semantic viewpoint, the term “solubility product” is not adequate, e.g., in relation to Eq. (8). Moreover, Ksp is not necessarily the product of ion concentrations, as indicated in formulas (4), (5), and (11). In some (numerous) instances of sparingly soluble species, e.g., sulfur, solid iodine, 8-hydroxyquinoline, dimethylglyoxime, the term solubility product is not applied. In some instances, e.g., for MnO2, this term is doubtful.
One of the main purposes of the present chapter is to familiarize GEB within GATES as GATES/GEB to a wider community of analysts engaged in electrolytic systems, also in aspect of solubility problems.
In this context, owing to large advantages and versatile capabilities offered by GATES/GEB, it deserves a due attention and promotion. The GATES is perceived as a step toward reductionism [19, 71] of chemistry in the area of electrolytic systems and the GEB is considered as a general law of nature; it provides the real proof of the world harmony, harmony of nature.
The innate and adaptive immune responses are key factors in the control of infections or chronic diseases. The balance between these two systems is mainly orchestrated by cytokines [1]. Cytokines are low-molecular-weight proteins that contribute to the chemical language that regulates the development and repair of tissues, hematopoiesis, inflammation, etc., through the transduction of signals mediated by binding to cellular receptors. Cytokines can act on their target cells in an autocrine, paracrine, and/or endocrine fashion to induce systemic and/or localized immune responses. In addition, cytokines have pleiotropic activity, that is, they act on different target cells, as well as affect the function of other cytokines in an additive, synergistic, or antagonistic manner [2, 3]. Cytokines can be secreted by immune cells, but they can also be produced by a wide variety of cells in response to infection or can be produced or released from cells in response to cellular damage when cellular integrity is compromised. Acting through a series of conserved signaling pathways that program transcriptional pathways by controlling many biological processes, such as cell growth, cell differentiation, apoptosis, development, and survival, can also reprogram cells in the local tissue environment to improve certain types of immune responses. Therefore, cytokines are critical mediators of communication for the immune system and are essential for host defense against pathogens [4].
The cytokine pattern that is released from the cell depends primarily on the nature of the antigenic stimulus and the type of cell being stimulated. Cytokines compromise leukocytes to respond to a microbial stimulus. Cytokines can be classified into six groups: (1) L1 superfamily, (2) TNF superfamily, (3) IL-17 family, (4) IL-6 superfamily, (5) type I superfamily, and (6) type II superfamily [5].
More than any other cytokine family, the interleukin (IL)-1 family of ligands and receptors is primarily associated with acute and chronic inflammation. The cytosolic segment of each IL-1 receptor family member contains the Toll/interleukin-1 receptor (TIR) domain. This domain is also present in each Toll-like receptor (TLR), which responds to microbial products and viruses [6]. Since TIR domains are functional for both receptor families, responses to the IL-1 family are fundamental to the innate immunity [7].
There are 11 members of IL-1 family of cytokines (IL-1α, IL-1β, IL-1Ra, IL-18, IL-33, IL-36α, IL-36β, IL-36γ, IL-36Ra IL-37, and IL-38) and 10 members of the IL-1 family of receptors (IL-1R1 to ILR10) [8, 9]. More than any other cytokine family, the IL-1 family members are closely linked to damaging inflammation; however, the same members also work to increase nonspecific resistance to infection and the development of an immune response to a foreign antigen [10].
The numerous biological properties of the IL-1 family are nonspecific. The importance of IL-1 family members to the innate response became evident upon the discovery that the cytoplasmic domain of the IL-1 receptor type 1 (IL-1R1) is also found in the Toll protein of the fruit fly. The functional domain of the cytoplasmic component of IL-1R1 is termed the TIR domain. Thus, fundamental inflammatory responses such as the induction of cyclooxygenase type 2 (COX-2), production of multiple cytokines and chemokines, increased the expression of adhesion molecules, or synthesis of nitric oxide (NO) are indistinguishable responses of both IL-1 and TLR ligands [11]. Both TLR and IL-1 families nonspecifically augment antigen recognition and activate lymphocyte function. The lymphocyte-activating function of IL-1 was first described in 1979 and is now considered a fundamental property of the acquired immune response. IL-1β is the most studied member of the IL-1 family due to its role in mediating auto-inflammatory diseases. Unquestionably, IL-1β evolved to assist host defense against infection, and this landmark study established how a low dose of recombinant IL-1β protects mice against lethal bacterial infection in the absence of neutrophils. Although we now accept the concept that cytokines like IL-1β served millions of years of evolution to protect the host, in the antibiotic and antiviral therapies era of today, we view cytokines as the cause of disease due to acute or chronic inflammation [12]. IL-1β has emerged as a therapeutic target for an expanding number of systemic and local inflammatory conditions called auto-inflammatory diseases. The neutralization of IL-1β results in a rapid and sustained reduction in disease severity. Treatment for autoimmune diseases often includes immunosuppressive drugs, whereas neutralization of IL-1β is mostly anti-inflammatory. The auto-inflammatory diseases are caused due to gain-of-function mutations for caspase-1 activity, and common ailments, such as gout, type 2 diabetes, heart failure, recurrent pericarditis, rheumatoid arthritis, and smoldering myeloma, respond to the IL-1β neutralization [7]. IL-1 family also includes member that suppress inflammation, specifically within the IL-1 family, such as the IL-1 receptor antagonist (IL-1Ra), IL-36 receptor antagonist (IL-36Ra), and IL-37. In addition, the IL-1 family member IL-38, the last member of the IL-1 family of cytokines to be studied, nonspecifically suppresses inflammation and limits the innate immunity [12].
There are 10 members of the IL-1 family receptors. IL-1R1 binds IL-1α, IL-1β, and IL-1Ra and IL-R1 binds either IL-1β or IL-1α. IL-1R2 is a decoy receptor for IL-1β. IL-1R2 lacks a cytoplasmic domain and exists not only as an integral membrane protein but also in a soluble form. The term soluble is meant to denote the extracellular domain only. The soluble domain of IL-1R2 binds IL-1β in the extracellular space and neutralizes IL-1β. The neutralization of IL-1β by soluble IL-1R2 is greatly enhanced by forming a complex with IL-1R3. IL-1R3 is the co-receptor for IL-1α, IL-1β, IL-33, IL-36a, IL-36β, and IL-36γ. IL-1R3 exists as an integral membrane receptor or in a soluble receptor form. The inflammation and infection drive liver to increase the synthesis and levels of soluble IL-1R3 in the circulation [13].
Tumor necrosis factor superfamily (TNFSF) is a group of cytokines composed of 19 ligands and 29 receptors [14]. This family plays a pivotal role in immunity, inflammation and controlling cell cycle, proliferation, differentiation, and apoptosis [15]. TNFSF receptors can be divided into two different groups depending on the presence or absence of the intracellular death domain (DD) [16]. Signaling via the death domain demands the involvement of adapter proteins Fas-associated death domain (FADD) and TNF receptor-associated proteins (TRADD), leading to the activation of caspases that result in apoptotic death of a cell. The second group of TNFSF receptor signals acts only via adapter proteins termed tumor necrosis factor receptor-associated proteins (TRAFs). The DD containing receptors may use the pathway [17]. The functional activity of TNFSF receptors depends on the cellular context and the balance between pro- and antiapoptotic factors inside the cell and in the environment. Mostly, the TNFSF members are revealed on the cells of immune system and play a notable function in maintaining the equilibrium of T-cell–mediated immune responses by arranging direct signals required for the full activation of effector pool and survival of memory T cells. The TNFSF members are necessary in the development of pathogenesis of many T-cell–mediated autoimmune diseases, such as asthma, diabetes, and arthritis [16].
Tumor necrosis factor (TNF)-α is classified as homotrimeric transmembrane protein with a prominent role in systemic inflammation. Macrophages/monocytes are capable to produce TNF-α in the acute phase of inflammation, and this cytokine drives a wide range of signaling events within cells, leading to necrosis or apoptosis [17]. The TNF superfamily incorporates receptor activator of nuclear factor κB (RANK), cluster of differentiation (CD)-40, CD27, and FAS receptor. This protein was discovered in the circulation of animals subsequent to the stimulation of their reticuloendothelial system and lipopolysaccharide (LPS) challenge. This protein has been found to provoke a rapid necrotic regression of certain forms of tumors [16].
Several biological functions are ascribed to the TNF-α, and for this reason, the mechanism of action is somewhat complex. Because this protein confers resistance to certain types of infections and in parallel causes pathological complications, it carries out contradictory roles. This may be connected to the varied signaling pathways that are activated. TNF-α modulates several therapeutic roles within the body, such as immunostimulation, resistance to infection agents, resistance to tumors, sleep regulation, and embryonic development [17]. On the other hand, parasitic, bacterial, and viral infections become more pathogenic or fatal due to TNF circulation. The major role of TNF is explicated as mediator in resistance against infections. Moreover, it was postulated that TNF plays a pathological role in several autoimmune diseases such as graft versus host rejection or rheumatoid arthritis. In addition, TNF exhibits antimalignant cell cytotoxicity in association with interferon. High concentrations of TNF-α are toxic to the host. The enhancement in the therapeutic index by decreasing toxicity or by increasing effectiveness is indeed needed. This may be possible through the mutations that reduce systemic cytotoxicity and increase TNF’s effectiveness in selectively eliminating tumor cells. TNF-α is also implicated in physiological sleep regulation. TNF-related proteins such as receptor activator for nuclear factor κB ligand (RANKL) are required for osteoclast differentiation necessary for bone resorption [16].
IL-17 is a pro-inflammatory cytokine. There are six family known members of IL-17. Also, we have just a little information of its biological functions, being the IL-17A and the IL-17F described recently [18]. IL-17–related cytokines play key roles in defense against extracellular pathogen, and their participation in the development of autoimmune diseases has drawn significant attention. Moreover, some of these molecules are involved in the amplification and perpetuation of pathological processes in many inflammatory diseases. However, the same cytokines can exert anti-inflammatory effects in specific settings, as well as play a key role in the control of immune homeostasis [19, 20].
IL-6 family is a group of cytokines and colony-stimulating factors (CSFs) that include IL-6, IL-27, IL-31, IL-35, ciliary neurotrophic factor (CNTF), leukemia inhibitory factor (LIF), oncostatin M (OSM), cardiotrophin (CT)-1, and cardiotrophin-like cytokine (CLC), among others [16, 17]. This cytokine family binds to its receptor, allowing a binding with the gp130 subunit [21, 22]. This binding allows dimerization of the subunit homogeneously or heterogeneously (either with the same subunit or cytokine receptor), creating a receptor complex. This complex allows associated proteins phosphorylation, such as Janus kinases (JAK) type 1, 2, and tyrosine kinase (TYK) 2, among others, which triggers a signaling pathway through phosphorylation toward types of signal transducer and activator of transcription (STAT) 1–6, forming another dimerization, homogeneous or heterogeneous with other STATs, that gets into the nucleus, recognizing promoter regions and initiating the regulation of the expression of specific genes [22, 23].
In IL-6 family, there are soluble receptors that have different signaling pathways, which are mostly of inhibitory function. Although they bind to the same cytokine and to the same subunit, they transmit different signaling called trans-signaling. It is observed that these soluble receptors prolong its effect and have action on cells where cytokine emerges effect; namely, all cells reactive to IL-6 will have the soluble receptor of IL-6 (IL-6Rs) function [21, 24]. Main functions of this IL-6 family cytokines are inflammation proteins production in acute phase, B cell differentiation into antibody-forming plasma cell, T cell modulator, development of Th17, and hematopoiesis, among other functions [24, 25, 26].
Type I cytokine family, also known as hematopoietins, is made up of several types of cytokines, including IL-2, IL-3, IL-4, IL-6, IL-7, IL-9, IL-12, IL-15, IL-21, and granulocyte-macrophage colony-stimulating factor (GM-CSF), among others. This group of cytokines has α, β, and γ chain in common. IL-2, -4, -7, -9, -13, -15, and -21 have in common the γ chain (also known as IL2Rγ or CD132) for activation of JAK1/JAK3 and downstream STAT 1–5. While IL-3, -5, and GM-CSF share the common β chain (CSF2RB/CD131) for activation of the JAK/STAT pathway through interactions with JAK2 [3, 27], α chains do not activate signaling pathways but increase the binding affinity between the cytokine and β and γ subunit [3, 28], helping receptor specificity for gene expression [27]. While the receptor is more complex, there is more affinity of the cytokines of the receptor, which increases the signaling [27, 29]. The specificity of the receptor is conferred by α and β subunit, that in combination with γ subunit provides different stimulations. This means that the same cytokines can have different effects on the cell, depending on the receptor complexity; for example, IL-2 binds to its γ chain receptor (CD132) and β chain (IL-2Rβ), forming an intermediate affinity dimer, or also the binding of α chain (IL-2Rα), generating a high affinity. Phosphorylating tyrosine residues in JAKs, which lead to signaling to STAT5, prolonging and increasing its effect unlike the intermediate affinity [30]. Among the main functions of this cytokine family are the growth and differentiation of precursor leukocytes, as well as being modulators and initiators of the inflammatory response [3, 27].
The type II superfamily is composed of the subfamilies of interferons (IFNs) and IL-10. IFN family has the characteristic of inducing antiviral response in both hematopoietic and structural cells, serving as an essential mediator of cross talk between the immune system and host physiology during viral infections [3, 29]. This family is divided into three types INFs families: types I, II, and III.
Type I IFNs family is mainly composed of IFN-α and -β. IFN-α is expressed in leukocytes and IFN-β in fibroblasts, dendritic, and plasmacytoid cells. These IFNs have signaling pathways through JAK1 and TYK2 to phosphorylate STAT1 and STAT2 [29, 31]. These IFNs have a powerful proinflammatory effect and an antiviral response in immune and nonhematopoietic cells, as well as they can synergize with type II interferon (i.e., IFNγ) to potentiate Th1 lineage commitment by T-helper cells and cytotoxic activity by CD8+ cells [3].
Type II IFNs family is composed only by IFN-γ, which is produced by active CD4+ and CD8+ T cells, NK cells, and macrophages by stimulation of IL-12, IL-18, and TNF-α [3, 29, 32]. IFN-γ has signaling pathways with STAT1 through JAK1 and JAK2 [29]. IFN-γ is mediator of interaction of innate and adaptive immune cells. IFN-γ promotes B-cell differentiation toward plasma cells immunoglobulin (Ig)-G-production. Also, IFN-γ induces phagocytosis through the antimicrobial potential activation on macrophages. IFN-γ increases the expression of major histocompatibility complex (MHC) I and II, molecules in antigen-presenting cells, promotes complement activation, and increases cytotoxic activity of T cells and differentiation Th1 cell differentiation for the clearance of infectious pathogens [3, 32].
Type III INFs family is composed by IFNλ-1 (IL-29), IFNλ-2 (IL-28A), and IFNλ-3 (IL-28B) [3, 29, 32]. IFNλ-1 and -2 regulate IFN expression [3], being structurally and functionally like them by sharing beta chain but with less intensity [32]. IFNλ-3 induces antiviral response in cells through STAT1 and STAT2 [3, 33].
IL-10 is a potent pro-inflammatory cytokine, which is produced by different cells such as monocytes, macrophages, Th2, and Treg cells. The IL-10 performs its functions through the activation of the STAT1, STAT3, PI3K, and p38 mitogen-activated protein kinases (MAPK) pathways. Among its most important functions are the suppression of Th1 cytokines, the classically activated/M1 macrophage inflammatory gene expression, and the presentation of antigen [3].
During a bacterial infection in the host, a nonspecific and immediate immune response is initiated to eliminate the pathogen, and this nonspecific response involves the recruitment of neutrophils, macrophages and dendritic cells, complement activation, and cytokine production [34]. This response can inhibit or limit microbial growth but also can cause host damage, and so it is necessary to keep this response under control; to achieve this, the host performs some strategies, including the production of cytokines. These molecules play an important role in intercellular communication and coordinate the innate and adaptive response [35].
In microbial infections, the pattern-recognition receptors (PRRs) recognize several PAMPs [36] such as DNA, double-stranded RNA (dsRNA), single-stranded RNA (ssRNA), and 5′-triphosphate RNA, as well as lipoproteins, surface glycoproteins, membrane components peptidoglycans, lipoteichoic acid (LTA), lipopolysaccharide (LPS), and glycosyl-phosphatidyl-inositol. The recognition of PAMPs by PRRs leads to the activation of NF-κB and/or MAPK [37] to produce several cytokines such as IL-1α, IL-1β, TNFα, IFN-γ, IL-12, and IL-18, being TNF-α and IL-1β the main inflammatory mediators, since they play an important role in mediating the local response through cellular activation. The inflammatory response that occurs in the presence of an infection consists of several protective effector mechanisms that promote the microbicidal functions and in turn stimulate adaptive immunity, which contributes to reduce the damage of the tissues [38] (Figure 1).
Cytokines profile in bacterial infections. In response to bacterial infection, the IL-1 family cytokines, such as IL-1β, potently induces the expression of adhesion molecules in the endothelial cells and promotes the recruitment of neutrophils to the site of inflammation. TNF-α plays an important role through the recruitment of neutrophils and macrophages, besides inducing the expression of proinflammatory mediators to the site of infection. Th17 cells produce IL-17A, which induces the production of inflammatory mediators such as IL-1β, IL-6, GM-CSF, G-CSF, and TNF-α, as well as adhesion molecules. IL-18 also promotes the secretion of other proinflammatory cytokines like TNF-α, IL-1β, IL-8, and GM-CSF and consequently enhancement, migration, and activation of neutrophils during infections.
IL-1β is a cytokine that is inducible through the activation of PRRs such as TLRs, by microbial products or damaged cell factors [39], once the recognition of the ligands through the receptors activates the downstream signaling pathways activating the NF-κB, activator protein (AP)-1, MAPK, and type I IFNs pathways, resulting in an upregulation of inflammatory mediators, as well as chemotactic factors [40]. IL-1β is synthesized as a precursor peptide (pro-IL-1β) that is cut to generate its mature form (mIL-1β); this process involves caspase 1, and the proenzyme (procaspase-1) requires it to be cut by the inflammasome, which is a multimeric cytosolic protein complex, composed of NLR family-pyrin domain containing 3 (NALP3) and the adapter protein containing CARD (ASC) and caspase-1; once IL-1β is cut by this complex, it binds to the IL-1R1 receptor, thus initiating the signaling that induces the expression of adhesion molecules in the endothelial cells and promotes the recruitment of neutrophils to the site of inflammation, as well as of the monocytes. It also has a potent stimulatory effect on phagocytosis, and it produces a chemotactic effect on leukocytes and induces the production of other inflammatory mediators of the lipid type, as well as other cytokines [41]. In vivo studies show that IL-1β is an important cytokine for the host defense against some microbial pathogens. During infection with Staphylococcus aureus, it was shown that the interaction of IL-1β with its receptor IL-1R plays an important role in the recruitment of neutrophils, suggesting that IL-1β is crucial for host defense against S. aureus and this can be transpolar to infections induced by other microorganisms [42].
Another cytokine that accompanies the IL-1β response is TNF-α, and this cytokine is produced initially during endotoxemia, as well as in response to some microbial products. TNF-α shares with IL-6 an important inflammatory property, that is, the induction of acute phase reactant protein by the liver [43]. In vivo studies show that TNF-α plays an important role in mediating clearance through the recruitment of neutrophils and macrophages to the site of infection after a bacterial intraperitoneal challenge [44], followed by an increase in the expression of COX-2, as well as inducible nitric oxide synthase (iNOS), which leads to the production of prostaglandin (PG)-E2 and NO to eradicate the pathogen and recover homeostasis [45].
During bacterial infections, the IL-17 is another important cytokine produced. IL-17A plays an important role in the defense of the host against extracellular bacteria. The cells that are characterized mainly by producing IL-17 are a subpopulation of CD4+ T cells, and their differentiation and maturation are favored by a mixture of cytokines, including transforming growth factor (TGF)-β and IL-6, IL-21 and TGF-β, or IL-1, IL-6, and IL-23 [46, 47]. The protective capacity of IL-17A against infectious agents can be mediated through several mechanisms, among these is the ability of IL-17A in the barrier surfaces to induce the production of inflammatory mediators such as IL-1β, IL-6, GM-CSF, granulocyte colony stimulating factor (G-CSF), and TNF-α, as well as adhesion molecules. IL-17A also induces the production of chemotactic factors, such as chemokine-(C-C motif)-ligand (CCL)-2, CCL7, CXCL1, CXCL2, CXCL5, and CXCL8, responsible for recruiting neutrophils and monocytes, as well as the CCL20 that is involved in the recruitment of dendritic cells, with the aim of eliminating the extracellular pathogen [48]. In vivo and in vitro studies show that signaling through TLR4 is the main mechanism by which IL-17 is induced in response to Klebsiella pneumoniae infection, which induces an upregulation of granulopoietic cytokines involved in the recruitment of neutrophils [49]. In mice lacking the IL-17 receptor, the recruitment of neutrophils decreased, the bacterial load increased, and survival was compromised. Whereas overexpression of IL-17 through an adenovirus, resulted in the production of cytokines mainly, macrophage inflammatory protein (MIP)-2, G-CSF, TNF-α, and IL-1β, increasing the recruitment of neutrophils, bacterial clearance and finally survival after infection with K. pneumoniae [50]. And finally, PGE2 increases the expansion of Th17 cells in an IL-1β dependent manner, thus favoring the recruitment of these cells to the site of damage. In vitro studies show that Th17 cells in the presence of PGE2 increase the production of CCL20, thus favoring the control of infection [51].
IL-18 also promotes the secretion of other proinflammatory cytokines like TNF-α, IL-1β, IL-8, and GM-CSF and consequently enhancement, migration, and activation of neutrophils during infections. IL-18 increases the cytotoxic activity and proliferation of CD8+ T and NK cells, as well as promotes the secretion of inflammatory mediators of the type TNF-α, IL-1β, IL-8, and GM-CSF, which will activate neutrophils, thus increasing their migration [38]. During a bacterial infection, IL-18 plays an important role, since it induces IFN-γ production of NK cells [52]. The IFN-γ that is produced activates macrophages and produces cytokines that induce antimicrobial pathways against intracellular and extracellular pathogens [53]. Infection with strains of lactobacillus nonpathogenic and with streptococcus pyogenes induces the expression of IL-1β, IL-6, TNF-α, IL-12, IL-18, and IFN-γ, suggesting that this type of bacterial strains induces Th1 type cytokines [54].
As well as the response to bacteria, the response against fungi also requires coordination of the innate and adaptive immune system. The innate immune system performs its effect through the cells that have the phagocytic and antigen presenting function. These cells include neutrophils, macrophages, and dendritic cells [55]. The recognition of pathogens by the immune system involves four class of PRRs: TLRs, C-type lectin receptors (CLRs), nucleotide-binding oligomerization domain-like (NOD-like) receptors (NLRs), and retinoic acid-inducible gene I (RIG-I) like receptors (RLRs) [56]. The CLRs, especially Dectin-1 and 2, play an important role in the pathogen recognition from Candida spp.; this is because the cell wall is made up of mannoproteins with O-glycosylated oligosaccharide and N-glycosylated polysaccharide moieties, with an inner layer of chitin and β (1, 3) and β (1, 6) glucans are recognized and initiate a downstream signaling through these receptors, which leads to activation of the transcription factor NF-κB and other signaling pathways that induce the production of pro-inflammatory cytokines such as IL-6, IL-1β, and IL-23 that induce the Th17 cytokines [57] (Figure 2).
Cytokines profile in fungal infections. The PRRs recognize fungal PAMPs and initiate a downstream signaling, which leads to the activation of the NF-κB and other signaling pathways inducing the production of cytokines such as IL-6, IL-1β, IL-12, TNF-α, GM-CSF, IFN-γ, and IL-23. These cytokines induce the differentiation of Th1 and Th17 immune responses against fungi infection, stimulating the migration, adherence, and phagocytosis of neutrophils and macrophages.
The recognition of fungi by phagocytic cells occurs mainly through the detection of cell wall components such as mannan, β-glucan, phosphocholine, β-1,6 glucan, and even internal components such as DNA can be recognized [58, 59]. The recruitment and activation of phagocytic cells are mediated through the induction of proinflammatory cytokines, chemokines, and complement components. Fungi are killed by oxidative and nonoxidative mechanisms and antimicrobial peptides. These activities are influenced by the action of cytokines such as IFN-γ [59]. This cytokine produced mainly by T and NK cells stimulates the migration, adherence, and phagocytosis of neutrophils and macrophages and production of opsonizing antibodies and maintains a Th1 response as a protective response against fungi. It also induces a classical activation of macrophages that is important to stop the growth of intracellular fungal pathogens [60]. The Th1 response occurs through the release of proinflammatory cytokines IFN-γ, TNF-α, and GM-CSF, increasing the permeability in the tissue, as well as the phagocytic cells at the site of infection to efficiently clean the infection [61] (Figure 2).
Another important cytokine in immunity against fungi is IL-12, and this cytokine is considered the main cytokine that induces IFN-γ production. IL-12 is produced by monocytes, macrophages, and dendritic cells, in response to microbial products, and acts on NK and T cells to induce IFN-γ. On the other hand, the late secretion of IL-12 in the lymph nodes induces naive T cells to produce IFN-γ and therefore amounting a Th1 response is promoted [62]. The ability of IFN-γ to increase the production of IL-12 forms a positive feedback during the inflammatory process and the Th1 response, and this interferon in turn activates monocytes and macrophages to induce the production of IL-12 [63] (Figure 2). Studies in Il12p35−/− and IFN-γ−/− mice show an increase in susceptibility to infections with Candida albicans, and this suggests that IL-12 and the Th1 responses play an important role in controlling Candida infection [64]. On the other hand, neutrophils kill the extracellular and intracellular fungi through effector mechanism that includes the production of reactive oxygen and nitrogen species, as well as the release of hydrolytic enzymes and their granules containing antimicrobial peptides [65].
IL-23 is a member of the IL-12 family and plays a central role in the expansion of Th17 cells as well as their function, composed of a p19 and p40 subunit that shares it with IL-12 [66, 67]. IL-23 is produced primarily by dendritic cells, the binding of β-glucan to Dectin-1 activates the syk-CARD-9 signaling pathway leading to the production of IL-23, which promotes the Th17 response, through the differentiation of naïve CD4+ T cells into Th17 cells and the release of IL-17A, IL-17F and IL-22 in response to infections caused by mucosal fungi [68]. These cytokines in conjunction with IL-23 have various functions in the body from a proinflammatory, anti-inflammatory, or regulatory activity, which depends on the type of microorganism, the site of infection, and the immunological status of the host (Figure 2). In vivo studies have shown that mice deficient of the IL-17 receptor (IL-17RA−/−) cannot limit systemic candidiasis, as well as oropharyngeal candidiasis, being more susceptible to developing mucocutaneous candidiasis, suggesting that the Th17 lineage strongly acts through IL-17, regulating the expansion, recruitment, and migration of neutrophils, as well as CXC-chemokines and antimicrobial proteins such as β-defensin 3 [66, 69].
In viral infections, the cytokines are implicated to establish an antiviral state as the unspecific first line of defense and virus-specific response. This process initiates through recognition of viral molecules by PRRs, which can be found as transmembrane receptors or in different intracellular compartment. The receptor undergoes a structural change, activating a route of signalization in the cytoplasm that end with the activation of cytoplasmic transcription factors that translocate into the nuclei to promote the expression of different cytokines. Depending of the virus and the type of cell, the type of cytokine produced may vary [70, 71].
Viruses can infect virtually all cells of an organism. Epithelial, endothelial, fibroblasts, neurons, as well as innate and adaptive immune cells can be infected. PRRs are present in both nonhematopoietic origin cell and immune cells. Some PRRs recognize viral proteins, but other can detect viral single or double RNA or DNA. In human, there are 10 TLRs distributed in plasmatic membrane and endosome membranes. Of them, TLR-2 and TLR-4 can detect viral surface glycoprotein before the viral penetration. Others like TLR-3, TLR-8, and TLR-9 sense different types of viral nucleic acids in endosomes during virus entering. TLR-8 senses genomic ssRNA, TLR-3 senses dsRNA, and TLR-9 detects nonmethylated CpG viral DNA [72, 73]. Another type of receptors that sense viral RNA are the RNA helicases receptors like RIG-I and melanoma differentiation-associated gene 5 (MDA5) [71, 74]. These receptors have been demonstrated to detect viral dsRNA. This dsRNA can be genomic or an intermediate form during replication, which is formed, virtually, for all virus of single or double RNA during viral replication. However, there is evidence that some dsRNA replicative intermediators can translocate to endosomes where TLR can sense and trigger the signalization way [75].
There are many cytokines with distinct functions. All of them are molecules with less than 20 KDa and can be pleiotropic or redundant, and also, they can synergize or antagonize each other. However, all of them are produced to ensure the virus elimination through the regulation of the immune response against the virus [76]. The process includes detection of the pathogen, signal to neighbor cells, activation and differentiation of innate immune cells, production of adhesion molecules on endothelial cell for extravasation of immune circulating cell, chemotactic molecules to attract cell to the infection foci, increase of phagocytosis, and activation of adaptive cells to specifically eliminate infected cells and extracellular virus [77].
Cytokine network against viruses starts with some cytokines produced by virus-infected cells (Figure 3). Epithelial cell can produce IFN, IL-8, IL-6, IL-1, GM-CSF [78, 79], TNFα [80], IL-18 [81], IL-12 [82], IL-2 [83], and IL-23 [84, 85]. The role of these cytokines is varied, IFN induces an antiviral state, and IL-8 is a potent inflammatory attracting phagocyte cell to the site of infection. IL-1 can promote apoptosis, and it is proinflammatory and chemotactic to neutrophils. GM-CSF is a hematopoietic grow factor that recruits various immune cells to host defense [76, 86]. Moreover, in the infection course, varies cytokines are also produced by innate and adaptive cell that can also be infected or activated. In filovirus infection, IL-1β, IL-5, IL-8, and IL-18, as well as varies chemokines like MIP-1α and β, monocyte chemoattractant protein 1 (MCP-1), and IFN-γ–inducible protein 10 (IP10) among others are produced [77]. In influenza virus infection, TNF-α, IL-1 α and β, and IL-6 and IL-8 are produced [87], and hepatitis C virus can promote the expression of IL-6, IL-8, MIP-1α, and MIP-1β and IL-1 [88], while rotavirus can induce the production of IFN, IL-8, IL-6, IL-1 [89], TNF-α [80], IL-18 [81], IL-12 [82], IL-2 [83], and IL-23 [84, 85]. Thus, the infected cell can upregulate multiple cytokine genes involved in different process as activation of NK, macrophages, and dendritic cells. Increasing the production of cytokines that serve as bridge between innate and adaptive response. In the inflammation process, virus-infected cells produce and secrete proinflammatory cytokines like IL-1, IL-6, IL-8, TNF [70] and IFN. These cytokines can be involved in the early defense of the organism. They can activate cells present in the site of infection, and they can recruit leukocyte cells from circulating system through inflammation process (Figure 3).
Cytokines profile in viral infections. The immune response against viruses initiates through recognition of viral molecules by PRRs. These PRRs can activate a signal system culminating in the activation of transcription factors involved in the establishment of an antiviral state and an inflammation process. Cytokine network against viruses start with some cytokines produced by virus infected cells, such as IFNs, IL-8, IL-6, IL-1, GM-CSF, TNFα, IL-18, IL-12, IL-2 and IL-23, inducing a potent inflammatory response, attracting and activating phagocyte cells (e.g. neutrophils, macrophages, dendritic cells), mast cells and NK cells, to the site of infection. Furthermore, these cytokines are involved in the induction of an immune response type Th1/TCL with the purpose of eliminate infected cells and extracellular virus while cytokines such as IL-4, IL-10, IL-13, IL-37, and TGF-β modulate the immune response to a Th2 and Th17 phenotype, which produce immunomodulatory and anti-inflammatory actions.
IFN is a pleiotropic cytokine produced by virus infection. Although there are three types of IFN called type I (α/β), type II (γ) and type III (λ). Type I IFN plays an important role in control early viral infections. The role of type I IFN is to interfere with viral replication through activating the expression of antiviral molecules. Once IFN is secreted, it can act in autocrine or paracrine (like other cytokines) way, interacting with interferon receptor to induce the production of an antiviral state in the infected and noninfected neighboring cells, inhibiting different step of viral replication [76]. Also, IFN promotes the production of cytokines like IL-12, IL-6, IFN-γ, and TNF-α in innate cells including NK cells and macrophages [90]. Another function of IFN is to enhance differentiation of dendritic cells [91] and promote the antigen presentation [90] to stimulate T and B cells [92], which is redundant with the function of the IL-12 and IL-18 [93, 94]. NK cells are activated by synergism between type 1 IFNs and IL-12. However, cytokines such as IL-10, IL-6, IL-4, IL-13, and TGF-β suppress the actions of IFN, and these cytokines are known for their immunomodulatory and anti-inflammatory actions [95].
TNF-α is other pleiotropic cytokine produced by also nonhematopoietic infected cells and innate and adaptive immune cells, including macrophages, dendritic cells, natural killer, and T and B lymphocytes after being activated [96]. This cytokine can activate the production of adhesion molecules in endothelial cells and promote the extravasation of neutrophils, monocytes, and others immune cells to be attracted to infection foci. TNF also can participate in apoptosis through activating caspases. TNF-α, together with IFN-γ, acts on macrophages, inducing the production of superoxide anions and oxygen and nitrogen radicals [97]. Macrophages can also produce cytokines such as IL-1, IL-6, IL-23, IL-12, and more TNF-α [95].
IL-1 was the first interleukin to be identified and is a pleiotropic cytokine, and it acts synergically with IL-6 on the central nervous system, inducing fever by activation of the hypothalamus-pituitary-adrenal (HPA) axis [98]. This molecule also activates mast cells and induces histamine production, acting as a vasodilator, thus increases the permeability of the membrane [99]. Also, IL-1 is chemotactic factor that induces the passage of neutrophils to the site of infection. This chemotactic function is redundant with the action of IL-8, also known as chemokine CXCL8 [86] also produced by the infected cell. There are cytokines that antagonize these functions of IL-1 such as IL-10, IL-4, and IL-13 recognized for their anti-inflammatory actions [100].
Another pleiotropic cytokine is IL-18, first described as “interferon-γ-inducing factor” and member of IL-1 family. This interleukin and type I IFN are recognized by dendritic cells and trigger a signaling pathway through TRF6 and induce the expression of CD11b+ in the surface of the cell [94]. These activated cells can express cytokines like IL-12, IL-6, IFN-γ, TNFα, and IFN-α, which also participates in other hematopoietic cells [101, 102]. IL-18 also participates synergistically with interleukin 12 on the activation of NK cells [93], stimulating the expression of CD25 and CD69 molecules, promoting their proliferation and cytotoxic capacity, respectively. Once activated, NK cells can induce apoptosis in virus-infected cells and produce other cytokines such as IL-12, IL-6, IL-10, IFN-γ, and TNF-α. Within the cytokines that block these functions of IL-18 are IL-37, IL-10, and TGF-β [103].
IL-6 is a soluble mediator with a pleiotropic effect on inflammation, immune response, and hematopoiesis. IL-6 is an important mediator of fever and of the acute phase response, which is redundant with IL-1 and TFN-α and promotes the differentiation of cytotoxic T lymphocytes, which induce the death of infected cells by osmotic lysis [104]. IL-6 synergistically with IL-23 participates in the differentiation of Th17 [105], through the production of RORγt. Once activated, Th17 induces inflammatory response through the expression of cytokines as IL-17 and IL-22. IL-6 also promotes the proliferation of B cells by binding to a complex of receptors (gp80, CD126, and CD130) [106] and, like IL-21 [107], induces the differentiation of plasma cells stimulating the antibody production [108]. However, there exist antagonist cytokines like IL-10, IL-13, and TGF-β that inhibit all these functions of the IL-6 [103].
IL-12, also known as a T cell-stimulating factor, which together with IFN-γ, promotes differentiation of Th1 cells by activation of T-bet, and these cells can activate macrophages through expression of other cytokines like IFN and TNF, amplifying the produced immune response [109]. Although, there is evidence that viruses may selectively induce IFN production and Th1 differentiation even in the absence of IL-12 [110].
IL-2 participates in the differentiation and proliferation of Th2 (redundant with IL-4) and Treg cells by the expression of GATA-3 and FOXP3, respectively [111, 112]. Th2 cells can express IL-4, IL-5, IL-9, and IL-13, which also have pleiotropic effects in promoting type 2 effector mechanisms, such as B cells secretion of immunoglobulins, eosinophilia, mastocytosis, and M2 macrophage polarization [113]. Treg cells regulate the immune response, suppressing T-cell activation [114]. Treg and Th2 are known for their immunomodulatory and anti-inflammatory actions [95]. Finally, GM-CSF stimulates the generation of dendritic cells and participates in polarization of macrophages M1 [115]. Moreover, GM-CSF has also been associated with Th2 immunity and therefore M2 polarization. GM-CSF is considered a pleiotropic cytokine with inflammatory and anti-inflammatory functions [116].
In parasitic infections is difficult to generalize about the mechanisms of antiparasitic immunity because there is a great variety of different parasites that have different morphology and reside in different locations of tissues and hosts during their life cycles [117]. In this section of the chapter, we will talk about the immune response against protozoa and helminths, two of the main parasites of medical importance for human health.
Protozoan parasites are much larger and more complex pathogens than viruses or bacteria and have developed additional and sophisticated strategies to escape the immune attack of the host. Currently, 30% of humans suffer parasitic protozoan infections worldwide. Life cycles of protozoans generally involve several stages of specific antigenicity, which facilitates their survival and propagation within different cells, tissues, and hosts. Frequently, the host fails to eliminate protozoan infections, which often results in a chronic disease or inapparent infections, in which the host continues to act as a reservoir of parasites [118].
The immune defense mechanisms against protozoan parasites frequently involve several immune cells such as neutrophils, macrophages, and NK cells that mediate the innate response against extracellular protozoan parasites. NK cell and cytokine-activated macrophages are central to the innate response to intracellular parasites. Innate cytokine and dendritic cell responses also play a critical role in the induction of adaptive immunity [119].
During the initial stage of parasitic protozoan infections, intestinal epithelial cells (IECs) bind and recognize PAMPs through PRRs [120] such as TLR-2 and TLR-4 [121], which activates NF-κB and leads to the production of proinflammatory cytokines [122], including IL-1β, IL-6, IL-8, IL-12, IFN-γ, and TNF-α [123, 124], which induces the activation of a Th1 type response [125]. IFN-γ is involved in clearance of infection, through the activation of neutrophils and macrophages (Figure 4) [126, 127, 128, 129, 130, 131, 132]. It has been also shown that IFN-γ-producing CD4+ T cells are involved protection in vaccinated mice [133]. Several studies suggest a role for IFN-γ in the pathogenesis of parasitic protozoan infections. In both humans and animal models, the production of high levels of IFN-γ is associated with resistance to infection [134, 135, 136], while low levels of IFN-γ are associated with an increased susceptibility to infection. Therefore, it is considered highly probable that IFN-γ provides protection against infection by activation of neutrophils and/or macrophages [125]. The production of reactive oxygen species (ROS) and NO through the complex of NADPH oxidase and iNOS, respectively, plays a critical role in the elimination of protozoan parasites [131, 132]. In experimental studies, infection protection was mediated by IFN-γ from NK T cells (NKT), while TNF-α is produced by increased tissue damage [137, 138], together with IL-1 and IL-8 [139] (Figure 4).
Cytokines profile in parasitic protozoan infections. The immune defense mechanisms against protozoan parasites involve several immune cells such as neutrophils, macrophages, NK cells, and CD4+ T cells. These cells are capable to produce proinflammatory cytokines, such as IL-1β, IL-6, IL-8, IL-12, IFN-γ, and TNF-α, promoting type 1 immune response. Likewise, protozoan parasites activate a Th2-type immune response, producing anti-inflammatory cytokines such as IL-4, IL-10, IL-5, and IL-13, suppressing the production of Th1 cytokines.
On the other hand, the antigenic exposure of protozoan parasites activates a Th2-type immune response by the host, inducing the production of anti-inflammatory cytokines such as IL-4, IL-10 [125], IL-5 and IL-13, which try to attenuate the Th1 type response characterized also by the INF-γ production, leading to upregulation of Th2 cytokine responses (IL-4, IL-5, and IL-13) and Th17 (IL-17), suppressing the production of Th1 cytokines [140] (Figure 4). In addition, another cytokine of anti-inflammatory importance is TGF-β, which acts in a synergistic manner to counteract this Th1 type response, activating macrophages which produce NO, through iNOS, for the elimination of the parasite [138]. Therefore, Th1-type cytokine response is characterized mainly by the production of IFN-γ, whereas susceptibility to tissue damage by protozoan parasites is critically dependent on a Th2-type cytokine response mediated mainly by IL-4.
More than two billion people around the world are infected with helminth parasites. Parasitic helminth infections are a major public health problem worldwide due to their ability to cause great morbidity and socioeconomic loss [141, 142].
The immune response against helminth parasites is characterized by the induction of an early Th1-type immune response, with the subsequent predominance of a Th2 type immune response, resulting in a mixture of both Th1/Th2 immune responses [143, 144], which depend on the CD4+ T cells [145]. The CD4+ T cells have a key role in the establishment of the cytokine environment during helminth parasite infection, thus directing their differentiation either by suppressing or favoring the inflammatory response at the intestinal level, which is crucial for the elimination of the parasite [146] (Figure 5).
Cytokines profile in parasitic helminth infection. The immune response against helminth parasites is characterized by the induction of an early Th1 type immune response, which results in a significant increase of Th1 cytokines such as IL-12, INF-γ, IL-1β, and TNF-α. Then, there is a subsequent predominance of a Th2 type immune response characterized by the release of IL-4, IL-5, IL-10, and IL-13 favoring helminth parasites expulsion.
PAMPs derived from helminth parasites induce the activation and maturation of dendritic cells [147, 148], promoting the development of the Th1 immune response [149], which results in a significant increase of Th1 cytokines such as IL-12 [150, 151, 152], INF-γ [149, 150, 151, 152, 153], IL-1β [152, 154], and TNF-α [150, 151, 152, 155] (Figure 5). However, in recent years, several studies have shown that this immune response of Th1 type favors infection by helminth parasites. On the one hand, IL-12 and INF-γ are two important cytokines against infection by helminth parasites, since they participate in the polarization of the Th1 type immune response [149, 150, 151, 153]. However, exogenous IL-12 is capable of suppressing intestinal mastocytosis, delaying the parasite expulsion, and increasing the parasite burden at the muscular level [156]. INF-γ induces the expression of iNOS, activates transcription factors such as NF-κB [157], and regulates the production of pro-inflammatory cytokines such as TNF-α [158]. Studies have shown that TNF-α is a cytokine that is produced during intestinal infection by helminth parasites [150, 151, 159], which is necessary in the protection against the parasite through the Th2 immune response [160]. However, several studies have associated the production of TNF-α with the development of intestinal pathology during infection by helminth parasites [155, 161, 162]. One of the effects of TNF-α is the iNOS expression and consequently the NO production [163, 164, 165]. Helminth parasite antigens are capable to induce the expression of iNOS, with the subsequent production of NO [166], which acts mainly as an effector molecule against both extracellular and intracellular parasites [167]. Studies in iNOS knockout mice infected with helminth parasites, showed a reduction in the expression of Th2 cytokines (IL-4, IL-5), a reduced humoral response (IgG and IgE), with a decrease in mastocytosis. However, no significant difference was observed in the helminth parasite expulsion, although iNOS knockout mice showed a decrease in intestinal pathology compared to wild-type animals. These results suggest that NO is not required for the helminth parasite expulsion, but its production is responsible for the intestinal pathology [155, 168]. With respect to IL-1β, it is well known that it participates in the intestinal inflammatory response in the helminth parasites infection, observing high levels during intestinal infection. However, until now, the role of IL-1β is not well understood [159].
With respect to the Th2 type immune response, in vitro studies have shown that helminth parasite antigens are capable of dendritic cells activating, inducing the synthesis of Th2 cytokines such as IL-4, IL-5, IL-10, and IL-13 [147, 149, 153, 169]. Likewise, studies in in vivo models have shown that helminth parasites infection is a significant increase in the synthesis of IL-4, IL-5, IL-10, and IL-13 [150, 151, 159, 170] (Figure 5). IL-10 may suppress antigen presentation by dendritic cells and inhibition of IL-12 secretion. In addition, helminth parasite antigens increased both IL-4 and IL-10 production derived from Th2 cells with a decrease in INF-γ production, polarizing the immune response to a strong Th2 cellular immune response, protective and responsible for the helminth parasite expulsion [143]. IL-10 is a Th2 cytokine, which is necessary for a successful intestinal immune response. This is because the absence or decrease of IL-10 causes a significant delay in the helminth parasite expulsion and an increase in the parasite burden [171]. IL-4 and IL-13 induce muscle cells hypercontractility of the jejunum and intestinal mastocytosis, promoting the helminth parasite expulsion [161, 172]. In IL-4/IL-13 mice deficient, a reduction in the helminth parasite expulsion, mastocytosis, and development of intestinal pathology was observed [161, 162, 173, 174]. Therefore, these studies suggest that IL-4 and IL-13 can regulate the induction of the protective Th2 immune response and intestinal inflammation, both associated with the helminth parasite expulsion [162]. During the Th2 immune response, the cytokines such as IL-4, IL-5, and IL-13 stimulate IgE synthesis [175], inducing mast cell and eosinophil hyperplasia [176], triggering immediate hypersensitivity reactions, and promoting the helminth parasite expulsion from the intestine [177]. However, mast cells and eosinophils are involved in tissue damage, thus promoting the inflammatory response. It suggests that the protective role of the Th2 type immune response is not sufficient facing the challenge against helminth parasite infections, as it contributes to the development of immunopathology [178] (Figure 5).
Although cytokines are produced with the purpose of modulating the immune response against infections caused by microorganisms, such as bacteria, fungi, viruses, and parasites, there is evidence that these microorganisms can induce cytokine production with bad prognostic to host recovery. In this sense, overproduction of inflammatory cytokines may be responsible for the severe damage observed in many microorganism infections. For this reason, a better understanding over the cytokine balance related to diseases by microorganisms is required to avoid severe damage against the organism caused by overreaction of the immune system.
We thank the authors who collaborated in the writing of this chapter: Dr. José Luis Muñoz, Dr. Juan Francisco Contreras, Dr. Oscar Gutiérrez, Dra. Paola Trinidad Villalobos, Dra. Viridiana Elizabeth Hernández and Luis Guillermo; as well as the Universities involved: Cuauhtémoc University Aguascalientes, Autonomous University of Nuevo Leon, and University of Guadalajara. We also thank the financial support for chapter publication.
We have no conflict of interest related to this work.
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",metaTitle:"What Does It Cost?",metaDescription:"Open Access publishing helps remove barriers and allows everyone to access valuable information, but article and book processing charges also exclude talented authors and editors who can’t afford to pay. The goal of our Women in Science program is to charge zero APCs, so none of our authors or editors have to pay for publication.",metaKeywords:null,canonicalURL:null,contentRaw:'[{"type":"htmlEditorComponent","content":"We are currently in the process of collecting sponsorship. If you have any ideas or would like to help sponsor this ambitious program, we’d love to hear from you. Contact us at info@intechopen.com.
\\n\\nAll of our IntechOpen sponsors are in good company! The research in past IntechOpen books and chapters have been funded by:
\\n\\nWe are currently in the process of collecting sponsorship. If you have any ideas or would like to help sponsor this ambitious program, we’d love to hear from you. Contact us at info@intechopen.com.
\n\nAll of our IntechOpen sponsors are in good company! The research in past IntechOpen books and chapters have been funded by:
\n\n