Metal ion vs. log βMY values.
\r\n\tThe aim of this book is to provide the reader with a comprehensive state-of-the-art in artificial neural networks, collecting many of the core concepts and cutting-edge application behind neural networks and deep learning.
",isbn:"978-1-83962-375-2",printIsbn:"978-1-83962-374-5",pdfIsbn:"978-1-83962-376-9",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"5cc6cd7972551be6cfc4d3c87bf8fb5c",bookSignature:"Dr. Pier Luigi Mazzeo and Dr. Paolo Spagnolo",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/10390.jpg",keywords:"Recurrent, Recursive Nets, Face Recognition, Crowd Analysis, Different Applications, Object Detection, Classification, Visual Tracking, Speech Recognition, Grams, Reinforcement Learning, 3-D Map",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"September 25th 2020",dateEndSecondStepPublish:"October 23rd 2020",dateEndThirdStepPublish:"December 22nd 2020",dateEndFourthStepPublish:"March 12th 2021",dateEndFifthStepPublish:"May 11th 2021",remainingDaysToSecondStep:"3 months",secondStepPassed:!0,currentStepOfPublishingProcess:4,editedByType:null,kuFlag:!1,biosketch:"Author and co-author of more than 80 works in national and international journals, conference proceedings, and book chapters, with Ph.D. in Computer Science Engineering.",coeditorOneBiosketch:"Dr. Spagnolo received the engineering degree in computer science from the University of Lecce, Italy. Since 2002 he has been with the Italian National Research Council. His work includes more than 80 publications on AI.",coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"17191",title:"Dr.",name:"Pier Luigi",middleName:null,surname:"Mazzeo",slug:"pier-luigi-mazzeo",fullName:"Pier Luigi Mazzeo",profilePictureURL:"https://mts.intechopen.com/storage/users/17191/images/system/17191.jpeg",biography:"Pier Luigi Mazzeo received the engineering degree in computer science from the University of Lecce, Lecce, Italy, in 2001. \nSince 2015 he has been with Institute of Applied Sciences and Intelligent Systems of the Italian National Research Council, Lecce, Italy. The most relevant topics, in which he is currently involved, include algorithms for video object tracking , face detection and recognition, facial expression recognition, deep neural network (CNN) and machine learning.\nHe has taken part in several national and international projects and he acts as a reviewer for several international journals and for some book publishers. He has been regularly invited to take part in the Scientific Committees of national and international conferences. \nDr. Mazzeo is author and co-author of more then 80 works in national and international journals, conference proceedings and book chapters.",institutionString:"Institute of Applied Sciences and Intelligent Systems (CNR)",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"1",totalChapterViews:"0",totalEditedBooks:"1",institution:{name:"Institute of Applied Science and Intelligent Systems",institutionURL:null,country:{name:"Italy"}}}],coeditorOne:{id:"20192",title:"Dr.",name:"Paolo",middleName:null,surname:"Spagnolo",slug:"paolo-spagnolo",fullName:"Paolo Spagnolo",profilePictureURL:"https://mts.intechopen.com/storage/users/20192/images/system/20192.jpg",biography:"Paolo Spagnolo received the engineering degree in computer science from the University of Lecce, Lecce, Italy, in 2002.\nSince then he has been with the Italian National Research Council.\nHe has been working on several research topics regarding Artificial Intelligence and Computer Vision studying techniques and methodologies for multidimensional digital signal processing; linear and non-linear signal characterization; signal features extraction; supervised and unsupervised classification of signals; deep neural network (CNN).\nDr. Spagnolo is an author of over 80 papers on Artificial Intelligence. He also acts as a reviewer for several international journals.\nHe has also participated in a number of international projects in the area of image and video analysis and has been regularly invited to take part in the Scientific Committees of national and international conferences.",institutionString:"Institute of Applied Sciences and Intelligent Systems (CNR)",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"1",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"Institute of Applied Science and Intelligent Systems",institutionURL:null,country:{name:"Italy"}}},coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"9",title:"Computer and Information Science",slug:"computer-and-information-science"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"297737",firstName:"Mateo",lastName:"Pulko",middleName:null,title:"Mr.",imageUrl:"https://mts.intechopen.com/storage/users/297737/images/8492_n.png",email:"mateo.p@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. Whether that be identifying an exceptional author and proposing an editorship collaboration, or contacting researchers who would like the opportunity to work with IntechOpen, I establish and help manage author and editor acquisition and contact."}},relatedBooks:[{type:"book",id:"8725",title:"Visual Object Tracking with Deep Neural Networks",subtitle:null,isOpenForSubmission:!1,hash:"e0ba384ed4b4e61f042d5147c97ab168",slug:"visual-object-tracking-with-deep-neural-networks",bookSignature:"Pier Luigi Mazzeo, Srinivasan Ramakrishnan and Paolo Spagnolo",coverURL:"https://cdn.intechopen.com/books/images_new/8725.jpg",editedByType:"Edited by",editors:[{id:"17191",title:"Dr.",name:"Pier Luigi",surname:"Mazzeo",slug:"pier-luigi-mazzeo",fullName:"Pier Luigi Mazzeo"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1591",title:"Infrared Spectroscopy",subtitle:"Materials Science, Engineering and Technology",isOpenForSubmission:!1,hash:"99b4b7b71a8caeb693ed762b40b017f4",slug:"infrared-spectroscopy-materials-science-engineering-and-technology",bookSignature:"Theophile Theophanides",coverURL:"https://cdn.intechopen.com/books/images_new/1591.jpg",editedByType:"Edited by",editors:[{id:"37194",title:"Dr.",name:"Theophanides",surname:"Theophile",slug:"theophanides-theophile",fullName:"Theophanides Theophile"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3092",title:"Anopheles mosquitoes",subtitle:"New insights into malaria vectors",isOpenForSubmission:!1,hash:"c9e622485316d5e296288bf24d2b0d64",slug:"anopheles-mosquitoes-new-insights-into-malaria-vectors",bookSignature:"Sylvie Manguin",coverURL:"https://cdn.intechopen.com/books/images_new/3092.jpg",editedByType:"Edited by",editors:[{id:"50017",title:"Prof.",name:"Sylvie",surname:"Manguin",slug:"sylvie-manguin",fullName:"Sylvie Manguin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3161",title:"Frontiers in Guided Wave Optics and Optoelectronics",subtitle:null,isOpenForSubmission:!1,hash:"deb44e9c99f82bbce1083abea743146c",slug:"frontiers-in-guided-wave-optics-and-optoelectronics",bookSignature:"Bishnu Pal",coverURL:"https://cdn.intechopen.com/books/images_new/3161.jpg",editedByType:"Edited by",editors:[{id:"4782",title:"Prof.",name:"Bishnu",surname:"Pal",slug:"bishnu-pal",fullName:"Bishnu Pal"}],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:"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:"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:"371",title:"Abiotic Stress in Plants",subtitle:"Mechanisms and Adaptations",isOpenForSubmission:!1,hash:"588466f487e307619849d72389178a74",slug:"abiotic-stress-in-plants-mechanisms-and-adaptations",bookSignature:"Arun Shanker and B. 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:"878",title:"Phytochemicals",subtitle:"A Global Perspective of Their Role in Nutrition and Health",isOpenForSubmission:!1,hash:"ec77671f63975ef2d16192897deb6835",slug:"phytochemicals-a-global-perspective-of-their-role-in-nutrition-and-health",bookSignature:"Venketeshwer Rao",coverURL:"https://cdn.intechopen.com/books/images_new/878.jpg",editedByType:"Edited by",editors:[{id:"82663",title:"Dr.",name:"Venketeshwer",surname:"Rao",slug:"venketeshwer-rao",fullName:"Venketeshwer Rao"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"4816",title:"Face Recognition",subtitle:null,isOpenForSubmission:!1,hash:"146063b5359146b7718ea86bad47c8eb",slug:"face_recognition",bookSignature:"Kresimir Delac and Mislav Grgic",coverURL:"https://cdn.intechopen.com/books/images_new/4816.jpg",editedByType:"Edited by",editors:[{id:"528",title:"Dr.",name:"Kresimir",surname:"Delac",slug:"kresimir-delac",fullName:"Kresimir Delac"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"54464",title:"The Synthesis of Milk Medium-Chain Fatty Acids in Mammary Gland",doi:"10.5772/67694",slug:"the-synthesis-of-milk-medium-chain-fatty-acids-in-mammary-gland",body:'\nThe composition of milk fatty acid varies greatly among different species. Long-chain fatty acid is the most abundant fatty acid (C14-C18) in guinea pigs, medium-chain fatty acid takes a large part of medium-chain fatty acid (C8-C10), and long-chain and short-chain (C4-C6) fatty acids are the most abundant in cow’s milk [1]; however, in goat milk all carbon-chain fatty acids are observed including short-chain, medium-chain, and long-chain fatty acids [2]. The short-chain and medium-chain fatty acids are mainly de novo synthesized in mammary gland [3–5].
\nThe synthesis of fatty acid in mammary gland is mainly catalyzed by fatty acid synthase (FASN) and acetyl CoA carboxylase (ACC). In mammalian cells, the functional form of FASN is a homodimer (MW ~540,000 Da) [6]. FASN is composed of seven domains, including b-ketoacyl synthase (KS), acetyl/malonyl-CoA transferase (MAT), b-hydroxyacyl dehydratase (DH), enoyl reductase (ER), b-ketoacyl reductase (KR), acyl-carrier protein (ACP), and thioesterase I (TE I) (Figure 1). The core region between the DH and ER domains has no catalytic activity. At first, the acyl moiety of acetyl-CoA (initiation substrate) is transferred to the ACP catalyzed by MAT to generate malonyl-CoA (elongation substrate). And then, the acyl moiety is momentarily transferred to KS, and transacylation of malonyl-CoA is catalyzed by MAT to ACP. Acetoacetyl-ACP is then generated with decarboxylative condensation catalyzed by KS. This process follows catalyzation by KR and DH, which are responsible for the NADPH-dependent reduction of the b-carbon, and the dehydration of b-hydroxyacyl-ACP to a,b-enoyl, respectively. And then, by the catalyzation of ER, a four-carbon acyl chain is produced from NADPH-dependent reduction of the enoyl. The subsequent elongation cycles are performed with the malonyl-CoA as two-carbon units. Lastly, TE I is responsible for the release of fatty acid, with a length of 16 carbons, from ACP [6].
The structure of FASN gene and the fatty acid synthesis cycle. (a) The domain structure of FASN and the active site residues. (b) De novo fatty acid synthesis cycle catalyzed by domains of FASN.
FASN is the crucial enzyme for milk fat synthesis [7]. It plays an important role in the regulation of energy metabolism, cell membrane formation, signaling pathway regulation, and epigenetics [8]. By comparing the sequences of FASN in different species, including goat, sheep, cattle, human, chicken, and rats, FASN genes contain 42 exons in cattle and 43 exons in human and mice, and so on [9] (Figure 2).
Prediction of exons and functional domains of FASN cloned from the goat mammary gland. Goat FASN gene includes 42 exons represented by seven function domains, in which three catalytic domains in the N-terminal section (KS, MAT, and DH) were separated by a core region from four C-terminal domains (ER, KR, ACP, and TE I). The sheep FASN gene contains 41 exons (XM 004013447).
FASN is also important for the regulation of the genes related to fatty acid synthesis in mammary gland. The inhibition of FASN with orlistat, a natural inhibitor of FASN, suppressed the expression of ACC, lipoprotein lipase (LPL), and heart-type fatty acid-binding protein (H-FABP) [10]. The inhibition of FASN in mammary cells by C75-mediated interference, a synthetic inhibitor of FASN activity, and short hairpin RNA-mediated interference significantly suppressed the deposition of triglyceride, decreased the expression of glycerol-3-phosphate acyltransferase (GPAT), 1-acylglycerol-3-phosphate O-acyltransferase (AGPAT6), and diacylglycerol acyltransferase (DGAT2), which are important for cellular triglyceride synthesis. The inhibition of FASN also enhanced the expression of adipose triglyceride lipase (ATGL) and hormone-sensitive lipase (HSL), both of which are crucial for lipolysis. This is consistent with the markedly lower expression of genes related to lipid-droplet formation and secretion (hormone-sensitive lipase, TIP47; adipose differentiation-related protein, ADFP; xanthine oxidoreductase, XDH; butyrophilin 1A1, BTN1A1) [10].
\nDespite the effect of FASN inhibition on gene expression and lipid metabolism, the exact mechanism underlying the effect remains unclear. As a terminal enzyme for de novo fatty acid synthesis, previous studies indicated that FASN could help control lipid metabolism through indirect, hence, secondary effects. For instance, FASN could be involved in the control of fatty acid synthesis and oxidation through a direct effect on the concentration of malonyl-CoA, which was shown to help control lipid metabolism through the inhibition (allosteric) of β-oxidation by carnitine palmitoyltransferase 1 (CPT1) [11, 12]. In addition, FASN also helps generate ligands for transcription regulators, including peroxisome proliferator-activated receptors (PPARs) [13, 14], sterol-regulatory element-binding protein 1 (SREBP1), hepatocyte nuclear factor 4a (HNF4α), NF-E2-related factor-2 (NRF2), and Toll-like receptor 4 (TLR4) [14], all of which are important for lipid metabolism regulation. FASN also may affect protein activity indirectly, for example, endothelial nitric-oxide synthase, through palmitoylation [15]. Lastly, FASN may interact directly with caveolin-1 and lipid raft, which was involved in lipid secretion [16, 17]. However, the exact mechanism of how FASN affects the expression of genes related to milk fat synthesis remains unclear.
The activity of hydrolase was necessary for the control of the length of the fatty acids produced by FASN with the main product of FASN being C16 palmitate. The thioesterase domain, TE I, catalyzes the termination step by hydrolyzing the thioester bond between palmitate and the 4ʹ-phosphopantetheine moiety of the acyl-carrier protein (ACP) domain. Orlistat is a natural inhibitor of FASN, which was captured in the active sites of two thioesterase molecules as a stable acyl-enzyme intermediate and as the hydrolyzed product. The release of the thioesterase from FASN by limited proteolysis, however, results in the production of fatty acids containing 20–22 carbons [18]. Thus, the thioesterase domain is essential in regulating the length of the fatty acid chain.
\nCarey et al. [4, 19] purified the FASN protein from rabbit, mouse, and pig; the results showed that they just synthesized long-chain and short-chain fatty acids but not medium-chain fatty acids. However, with the help of TE II, FASN can produce all kinds of fatty acids, including C8, C10, C12, and so on [20, 21]. The medium-chain fatty acids synthesized de novo can be incorporated directly into triacylglycerol without the need of an activation step [22].
\nTE II is a tissue-specific enzyme independent of FASN. TE II can interact with TE I, which is a part of FASN, and terminate the elongation of fatty acids at about 10 carbons [23]. Decanoyl-CoA and decanoyl-pantetheine are the best substrates for TE II [24]. Ser101 and His237 of TE II are critical for the interaction. Asp236 of TE II enhances but is not essential for the reactivity of Ser101 and His237. For Leu262, it is involved in the interaction of TE II with TE I [23]. The interaction between TE II and FASN is stimulated by polyethylene glycol and suppressed by high concentrates of salt. Orlistat is a natural inhibitor and has a significant inhibition effect on FASN activity by curbing the binding of TE domain between FASN subunits [25]. TE II also can interact with P53 and is involved in the cancer development [25].
As a tissue-specific enzyme, TE II is only observed in non-ruminants. A similar enzyme is not present in goat mammary gland, although octanoic acid, decanoic acid, and dodecanoic acid amount to 20 mol% of the fatty acids synthesized in this tissue [26]. By contrast, goat mammary-gland fatty acid synthetase is by itself able to synthesize medium-chain fatty acids in the presence of the microsomal fraction and substrates for triacylglycerol synthesis [27]. Goat mammary-gland fatty acid synthetase exhibits both medium-chain thioesterase [21] and transacylase activity [28]. It seems that there are some differences about the activity of FASN between goat and other species. By treating the FASN protein of goat FASN with PMSF, an inhibitor of TE activity results in the termination of long-chain fatty acid synthesis, but not the medium-chain fatty acids. These results showed that there must be another hydrolase center in FASN protein. Hansen and Knudsen found that the supplementary of malonyl-CoA changed the proportion of medium-chain fatty acids [29]. Considering that the malonyl-CoA is transferred into the reaction by MAT activity, it was predicted that MAT may be involved in the synthesis of medium-chain fatty acid. Engese et al. first found that MAT can transfer not only C2 but also C4, C6, and C10 fatty acids from CoA [28, 30], although the malonyl-CoA showed the strongest affinity with MAT. Supporting the results, the interference of FASN reduced the synthesis of C10:0 and C12:0, increased the content of C14:0, but without an effect on C16:0 and C18:0, in goat mammary epithelial cells [31]. These literatures indicate that the MAT of goat FASN may be responsible for the termination of short- and medium-chain fatty acids in mammary gland.
\nRangan and Smith cloned the MAT protein from rat, and showed that MAT expressed in Escherichia coli, and refolded in vitro as a catalytically active malonyl-/acetyltransferase [32], similar as our previous study in goat expressed for goat mammary epithelial cells that the MAT domain is capable of folding correctly as an independent protein (unpublished). Replacement of the highly conserved residue His-683 with Ala reduced the activity by 99.95%, and the residual activity was relatively unaffected by diethyl pyrocarbonate. The rate of acylation of the active site serine residue was also reduced by several orders of magnitude in the His-683 to Ala mutant, indicating that His-683 plays an essential role in catalysis, likely by accepting a proton from the active site serine, thus increasing its nucleophilicity. In addition, Ser581 is also important for the activity of MAT. The Ser-581 to Ala mutant was completely inactive with either substrate. The Ser-581 to Cys mutant, however, retained approximately 1% of the activity of the “wild-type” enzyme compared with about 0.05% retained by His-683 to Ala mutation.
\nActually, many other stimulants altered the relative content of medium-chain fatty acids. By treating the goat FASN with 5.2 mg/mL, albumin increases the content of C10 fatty acids relative to C12, while 10.4 mg/mL results in four times of C10 than C12 [33]. The supplementary of Malonyl-CoA enhances the synthesis of C12, similar as the effect of globin treatment. These treatments can only change the relative content among different kinds of medium-chain fatty acids, but not alter the total proportion of medium-chain fatty acids relative to long-chain fatty acids [33, 34].
\nThe role of MAT is predicted to be critical for the goat medium-chain fatty acid synthesis; however, there is no direct evidence for the effect of MAT on fatty acid compositions. Although several genes have been proved to be involved in the regulation of fatty acid metabolism in mammary gland, how the activity of MAT, not for the whole FASN, on medium-chain fatty acid synthesis is controlled remains unclear. Recently, our study showed that malonyl-CoA is not only the elongation subtract for de novo fatty acid synthesis but also a regulatory for fatty acid deposition as triglyceride and fatty acid oxidation by inhibiting the activity of carnitine palmitoyl transferase 1 (CPT1), which is important for the transportation of long-chain fatty acids from cytoplasm to mitochondria [35]. Thus, it is the controller that directly interacts with MAT domain indicating that malonyl-CoA may be the balancer of lipid metabolism. The concentration of malonyl-CoA is mainly regulated by the activity of ACC and FASN, both of which are the terminates of lipid metabolism regulation. The hypothesis is that malonyl-CoA may be the indicator of fatty acid metabolism in mammary gland and may be the main mediator for the length of fatty acid responses to the environment around the mammary gland. This may be a good point for revealing the mechanism of fatty acid chain length determination in the future study.
Stability constant of the formation of metal complexes is used to measure interaction strength of reagents. From this process, metal ion and ligand interaction formed the two types of metal complexes; one is supramolecular complexes known as host-guest complexes [1] and the other is anion-containing complexes. In the solution it provides and calculates the required information about the concentration of metal complexes.
Solubility, light, absorption conductance, partitioning behavior, conductance, and chemical reactivity are the complex characteristics which are different from their components. It is determined by various numerical and graphical methods which calculate the equilibrium constants. This is based on or related to a quantity, and this is called the complex formation function.
During the displacement process at the time of metal complex formation, some ions disappear and form a bonding between metal ions and ligands. It may be considered due to displacement of a proton from a ligand species or ions or molecules causing a drop in the pH values of the solution [2]. Irving and Rossotti developed a technique for the calculation of stability constant, and it is called potentiometric technique.
To determine the stability constant, Bjerrum has used a very simple method, and that is metal salt solubility method. For the studies of a larger different variety of polycarboxylic acid-, oxime-, phenol-containing metal complexes, Martel and Calvin used the potentiometric technique for calculating the stability constant. Those ligands [3, 4] which are uncharged are also examined, and their stability constant calculations are determined by the limitations inherent in the ligand solubility method. The limitations of the metal salt solubility method and the result of solubility methods are compared with this. M-L, MLM, and (M3) L are some types of examples of metal-ligand bonding. One thing is common, and that is these entire types metal complexes all have one ligand.
The solubility method can only usefully be applied to studies of such complexes, and it is best applied for ML; in such types of system, only ML is formed. Jacqueline Gonzalez and his co-worker propose to explore the coordination chemistry of calcium complexes. Jacqueline and et al. followed this technique for evaluate the as partial model of the manganese-calcium cluster and spectrophotometric studies of metal complexes, i.e., they were carried calcium(II)-1,4-butanediamine in acetonitrile and calcium(II)-1,2-ethylendiamine, calcium(II)-1,3-propanediamine by them.
Spectrophotometric programming of HypSpec and received data allows the determination of the formation of solubility constants. The logarithmic values, log β110 = 5.25 for calcium(II)-1,3-propanediamine, log β110 = 4.072 for calcium(II)-1,4-butanediamine, and log β110 = 4.69 for calcium(II)-1,2-ethylendiamine, are obtained for the formation constants [5]. The structure of Cimetidine and histamine H2-receptor is a chelating agent. Syed Ahmad Tirmizi has examined Ni(II) cimetidine complex spectrophotometrically and found an absorption peak maximum of 622 nm with respect to different temperatures.
Syed Ahmad Tirmizi have been used to taken 1:2 ratio of metal and cimetidine compound for the formation of metal complex and this satisfied by molar ratio data. The data, 1.40–2.4 × 108, was calculated using the continuous variation method and stability constant at room temperature, and by using the mole ratio method, this value at 40°C was 1.24–2.4 × 108. In the formation of lead(II) metal complexes with 1-(aminomethyl) cyclohexene, Thanavelan et al. found the formation of their binary and ternary complexes. Glycine,
Using the stability constant method, these ternary complexes were found out, and using the parameters such as Δ log K and log X, these ternary complex data were compared with binary complex. The potentiometric technique at room temperature (25°C) was used in the investigation of some binary complex formations by Abdelatty Mohamed Radalla. These binary complexes are formed with 3D transition metal ions like Cu2+, Ni2+, Co2+, and Zn2+ and gallic acid’s importance as a ligand and 0.10 mol dm−3 of NaNO3. Such types of aliphatic dicarboxylic acids are very important biologically. Many acid-base characters and the nature of using metal complexes have been investigated and discussed time to time by researchers [7].
The above acids (gallic and aliphatic dicarboxylic acid) were taken to determine the acidity constants. For the purpose of determining the stability constant, binary and ternary complexes were carried in the aqueous medium using the experimental conditions as stated above. The potentiometric pH-metric titration curves are inferred for the binary complexes and ternary complexes at different ratios, and formation of ternary metal complex formation was in a stepwise manner that provided an easy way to calculate stability constants for the formation of metal complexes.
The values of Δ log K, percentage of relative stabilization (% R. S.), and log X were evaluated and discussed. Now it provides the outline about the various complex species for the formation of different solvents, and using the concentration distribution, these complexes were evaluated and discussed. The conductivity measurements have ascertained for the mode of ternary chelating complexes.
A study by Kathrina and Pekar suggests that pH plays an important role in the formation of metal complexes. When epigallocatechin gallate and gallic acid combine with copper(II) to form metal complexes, the pH changes its speculation. We have been able to determine its pH in frozen and fluid state with the help of multifrequency EPR spectroscopy [8]. With the help of this spectroscopy, it is able to detect that each polyphenol exhibits the formation of three different mononuclear species. If the pH ranges 4–8 for di- or polymeric complex of Cu(II), then it conjectures such metal complexes. It is only at alkaline pH values.
The line width in fluid solutions by molecular motion exhibits an incomplete average of the parameters of anisotropy spin Hamilton. If the complexes are different, then their rotational correlation times for this also vary. The analysis of the LyCEP anisotropy of the fluid solution spectra is performed using the parameters determined by the simulation of the rigid boundary spectra. Its result suggests that pH increases its value by affecting its molecular mass. It is a polyphenol ligand complex with copper, showing the coordination of an increasing number of its molecules or increasing participation of polyphenol dimers used as ligands in the copper coordination region.
The study by Vishenkova and his co-worker [8] provides the investigation of electrochemical properties of triphenylmethane dyes using a voltammetric method with constant-current potential sweep. Malachite green (MG) and basic fuchsin (BF) have been chosen as representatives of the triphenylmethane dyes [9]. The electrochemical behavior of MG and BF on the surface of a mercury film electrode depending on pH, the nature of background electrolyte, and scan rate of potential sweep has been investigated.
Using a voltammetric method with a constant-current potential sweep examines the electrical properties of triphenylmethane dye. In order to find out the solution of MG and BF, certain registration conditions have been prescribed for it, which have proved to be quite useful. The reduction peak for the currents of MG and BF has demonstrated that it increases linearly with respect to their concentration as 9.0 × 10−5–7.0 × 10−3 mol/dm3 for MG and 6.0 × 10−5–8.0 × 10−3 mol/dm3 for BF and correlation coefficients of these values are 0.9987 for MG and 0.9961 for BF [10].
5.0 × 10−5 and 2.0 × 10−5 mol/dm3 are the values used as the detection limit of MG and BF, respectively. Stability constants are a very useful technique whose size is huge. Due to its usefulness, it has acquired an umbrella right in the fields of chemistry, biology, and medicine. No science subject is untouched by this. Stability constants of metal complexes are widely used in the various areas like pharmaceuticals as well as biological processes, separation techniques, analytical processes, etc. In the presented chapter, we have tried to explain this in detail by focusing our attention on the applications and solutions of stability of metal complexes in solution.
Stability or formation or binding constant is the type of equilibrium constant used for the formation of metal complexes in the solution. Acutely, stability constant is applicable to measure the strength of interactions between the ligands and metal ions that are involved in complex formation in the solution [11]. A generally these 1-4 equations are expressed as the following ways:
Thus
K1, K2, K3, … Kn are the equilibrium constants and these are also called stepwise stability constants. The formation of the metal-ligand-n complex may also be expressed as equilibrium constants by the following steps:
The parameters K and β are related together, and these are expressed in the following example:
Now the numerator and denominator are multiplied together with the use of [metal-ligand] [metal-ligand2], and after the rearranging we get the following equation:
Now we expressed it as the following:
From the above relation, it is clear that the overall stability constant βn is equal to the product of the successive (i.e., stepwise) stability constants, K1, K2, K3,…Kn. This in other words means that the value of stability constants for a given complex is actually made up of a number of stepwise stability constants. The term stability is used without qualification to mean that the complex exists under a suitable condition and that it is possible to store the complex for an appreciable amount of time. The term stability is commonly used because coordination compounds are stable in one reagent but dissociate or dissolve in the presence of another regent. It is also possible that the term stability can be referred as an action of heat or light or compound. The stability of complex [13] is expressed qualitatively in terms of thermodynamic stability and kinetic stability.
In a chemical reaction, chemical equilibrium is a state in which the concentration of reactants and products does not change over time. Often this condition occurs when the speed of forward reaction becomes the same as the speed of reverse reaction. It is worth noting that the velocities of the forward and backward reaction are not zero at this stage but are equal.
If hydrogen and iodine are kept together in molecular proportions in a closed process vessel at high temperature (500°C), the following action begins:
In this activity, hydrogen iodide is formed by combining hydrogen and iodine, and the amount of hydrogen iodide increases with time. In contrast to this action, if the pure hydrogen iodide gas is heated to 500°C in the reaction, the compound is dissolved by reverse action, which causes hydrogen iodide to dissolve into hydrogen and iodine, and the ratio of these products increases over time. This is expressed in the following reaction:
For the formation of metal chelates, the thermodynamic technique provides a very significant information. Thermodynamics is a very useful technique in distinguishing between enthalpic effects and entropic effects. The bond strengths are totally effected by enthalpic effect, and this does not make any difference in the whole solution in order/disorder. Based on thermodynamics the chelate effect below can be best explained. The change of standard Gibbs free energy for equilibrium constant is response:
Where:
R = gas constant
T = absolute temperature
At 25°C,
ΔG = (− 5.708 kJ mol−1) · log β.
The enthalpy term creates free energy, i.e.,
For metal complexes, thermodynamic stability and kinetic stability are two interpretations of the stability constant in the solution. If reaction moves from reactants to products, it refers to a change in its energy as shown in the above equation. But for the reactivity, kinetic stability is responsible for this system, and this refers to ligand species [14].
Stable and unstable are thermodynamic terms, while labile and inert are kinetic terms. As a rule of thumb, those complexes which react completely within about 1 minute at 25°C are considered labile, and those complexes which take longer time than this to react are considered inert. [Ni(CN)4]2− is thermodynamically stable but kinetically inert because it rapidly exchanges ligands.
The metal complexes [Co(NH3)6]3+ and such types of other complexes are kinetically inert, but these are thermodynamically unstable. We may expect the complex to decompose in the presence of acid immediately because the complex is thermodynamically unstable. The rate is of the order of 1025 for the decomposition in acidic solution. Hence, it is thermodynamically unstable. However, nothing happens to the complex when it is kept in acidic solution for several days. While considering the stability of a complex, always the condition must be specified. Under what condition, the complex which is stable or unstable must be specified such as acidic and also basic condition, temperature, reactant, etc.
A complex may be stable with respect to a particular condition but with respect to another. In brief, a stable complex need not be inert and similarly, and an unstable complex need not be labile. It is the measure of extent of formation or transformation of complex under a given set of conditions at equilibrium [15].
Thermodynamic stability has an important role in determining the bond strength between metal ligands. Some complexes are stable, but as soon as they are introduced into aqueous solution, it is seen that these complexes have an effect on stability and fall apart. For an example, we take the [Co (SCN)4]2+ complex. The ion bond of this complex is very weak and breaks down quickly to form other compounds. But when [Fe(CN)6]3− is dissolved in water, it does not test Fe3+ by any sensitive reagent, which shows that this complex is more stable in aqueous solution. So it is indicated that thermodynamic stability deals with metal-ligand bond energy, stability constant, and other thermodynamic parameters.
This example also suggests that thermodynamic stability refers to the stability and instability of complexes. The measurement of the extent to which one type of species is converted to another species can be determined by thermodynamic stability until equilibrium is achieved. For example, tetracyanonickelate is a thermodynamically stable and kinetic labile complex. But the example of hexa-amine cobalt(III) cation is just the opposite:
Thermodynamics is used to express the difference between stability and inertia. For the stable complex, large positive free energies have been obtained from ΔG0 reaction. The ΔH0, standard enthalpy change for this reaction, is related to the equilibrium constant, βn, by the well thermodynamic equation:
For similar complexes of various ions of the same charge of a particular transition series and particular ligand, ΔS0 values would not differ substantially, and hence a change in ΔH0 value would be related to change in βn values. So the order of values of ΔH0 is also the order of the βn value.
Kinetic stability is referred to the rate of reaction between the metal ions and ligand proceeds at equilibrium or used for the formation of metal complexes. To take a decision for kinetic stability of any complexes, time is a factor which plays an important role for this. It deals between the rate of reaction and what is the mechanism of this metal complex reaction.
As we discuss above in thermodynamic stability, kinetic stability is referred for the complexes at which complex is inert or labile. The term “inert” was used by Tube for the thermally stable complex and for reactive complexes the term ‘labile’ used [16]. The naturally occurring chlorophyll is the example of polydentate ligand. This complex is extremely inert due to exchange of Mg2+ ion in the aqueous media.
The nature of central atom of metal complexes, dimension, its degree of oxidation, electronic structure of these complexes, and so many other properties of complexes are affected by the stability constant. Some of the following factors described are as follows.
In the coordination chemistry, metal complexes are formed by the interaction between metal ions and ligands. For these type of compounds, metal ions are the coordination center, and the ligand or complexing agents are oriented surrounding it. These metal ions mostly are the transition elements. For the determination of stability constant, some important characteristics of these metal complexes may be as given below.
Ligands are oriented around the central metal ions in the metal complexes. The sizes of these metal ions determine the number of ligand species that will be attached or ordinated (dative covalent) in the bond formation. If the sizes of these metal ions are increased, the stability of coordination compound defiantly decreased. Zn(II) metal ions are the central atoms in their complexes, and due to their lower size (0.74A°) as compared to Cd(II) size (0.97A°), metal ions are formed more stable.
Hence, Al3+ ion has the greatest nuclear charge, but its size is the smallest, and the ion N3− has the smallest nuclear charge, and its size is the largest [17]. Inert atoms like neon do not participate in the formation of the covalent or ionic compound, and these atoms are not included in isoelectronic series; hence, it is not easy to measure the radius of this type of atoms.
The properties of stability depend on the size of the metal ion used in the complexes and the total charge thereon. If the size of these metal ions is small and the total charge is high, then their complexes will be more stable. That is, their ratio will depend on the charge/radius. This can be demonstrated through the following reaction:
An ionic charge is the electric charge of an ion which is formed by the gain (negative charge) or loss (positive charge) of one or more electrons from an atom or group of atoms. If we talk about the stability of the coordination compounds, we find that the total charge of their central metal ions affects their stability, so when we change their charge, their stability in a range of constant can be determined by propagating of error [18]. If the charge of the central metal ion is high and the size is small, the stability of the compound is high:
In general, the most stable coordination bonds can cause smaller and highly charged rations to form more stable coordination compounds.
When an electron pair attracts a central ion toward itself, a strong stability complex is formed, and this is due to electron donation from ligand → metal ion. This donation process is increasing the bond stability of metal complexes exerted the polarizing effect on certain metal ions. Li+, Na+, Mg2+, Ca2+, Al3+, etc. are such type of metal cation which is not able to attract so strongly from a highly electronegative containing stable complexes, and these atoms are O, N, F, Au, Hg, Ag, Pd, Pt, and Pb. Such type of ligands that contains P, S, As, Br and I atom are formed stable complex because these accepts electron from M → π-bonding. Hg2+, Pb2+, Cd2+, and Bi3+ metal ions are also electronegative ions which form insoluble salts of metal sulfide which are insoluble in aqueous medium.
Volatile ligands may be lost at higher temperature. This is exemplified by the loss of water by hydrates and ammonia:
The transformation of certain coordination compounds from one to another is shown as follows:
A ligand is an ion or small molecule that binds to a metal atom (in chemistry) or to a biomolecule (in biochemistry) to form a complex, such as the iron-cyanide coordination complex Prussian blue or the iron-containing blood-protein hemoglobin. The ligands are arranged in spectrochemical series which are based on the order of their field strength. It is not possible to form the entire series by studying complexes with a single metal ion; the series has been developed by overlapping different sequences obtained from spectroscopic studies [19]. The order of common ligands according to their increasing ligand field strength is
The above spectrochemical series help us to for determination of strength of ligands. The left last ligand is as weaker ligand. These weaker ligand cannot forcible binding the 3d electron and resultant outer octahedral complexes formed. It is as-
Increasing the oxidation number the value of Δ increased.
Δ increases from top to bottom.
However, when we consider the metal ion, the following two useful trends are observed:
Δ increases with increasing oxidation number.
Δ increases down a group. For the determination of stability constant, the nature of the ligand plays an important role.
The following factors described the nature of ligands.
The size and charge are two factors that affect the production of metal complexes. The less charges and small sizes of ligands are more favorable for less stable bond formation with metal and ligand. But if this condition just opposite the product of metal and ligand will be a more stable compound. So, less nuclear charge and more size= less stable complex whereas if more nuclear charge and small in size= less stable complex. We take fluoride as an example because due to their smaller size than other halide and their highest electro negativity than the other halides formed more stable complexes. So, fluoride ion complexes are more stable than the other halides:
As compared to S2− ion, O22− ions formed more stable complexes.
It is suggested by Calvin and Wilson that the metal complexes will be more stable if the basic character or strength of ligands is higher. It means that the donating power of ligands to central metal ions is high [20].
It means that the donating power of ligands to central metal ions is high. In the case of complex formation of aliphatic diamines and aromatic diamines, the stable complex is formed by aliphatic diamines, while an unstable coordination complex is formed with aromatic diamines. So, from the above discussion, we find that the stability will be grater if the e-donation power is greater.
Thus it is clear that greater basic power of electron-donating species will form always a stable complex. NH3, CN−, and F− behaved as ligands and formed stable complexes; on the other hand, these are more basic in nature.
We know that if the concentration of coordination group is higher, these coordination compounds will exist in the water as solution. It is noted that greater coordinating tendency show the water molecules than the coordinating group which is originally present. SCN− (thiocynate) ions are present in higher concentration; with the Co2+ metal ion, it formed a blue-colored complex which is stable in state, but on dilution of water medium, a pink color is generated in place of blue, or blue color complex is destroyed by [Co(H2O)6]2+, and now if we added further SCN−, the pink color will not appear:
Now it is clear that H2O and SCN− are in competition for the formation of Co(II) metal-containing complex compound. In the case of tetra-amine cupric sulfate metal complex, ammonia acts as a donor atom or ligand. If the concentration of NH3 is lower in the reaction, copper hydroxide is formed but at higher concentration formed tetra-amine cupric sulfate as in the following reaction:
For a metal ion, chelating ligand is enhanced and affinity it and this is known as chelate effect and compared it with non-chelating and monodentate ligand or the multidentate ligand is acts as chelating agent. Ethylenediamine is a simple chelating agent (Figure 1).
Structure of ethylenediamine.
Due to the bidentate nature of ethylenediamine, it forms two bonds with metal ion or central atom. Water forms a complex with Ni(II) metal ion, but due to its monodentate nature, it is not a chelating ligand (Figures 2 and 3).
Structure of chelating configuration of ethylenediamine ligand.
Structure of chelate with three ethylenediamine ligands.
The dentate cheater of ligand provides bonding strength to the metal ion or central atom, and as the number of dentate increased, the tightness also increased. This phenomenon is known as chelating effect, whereas the formation of metal complexes with these chelating ligands is called chelation:
or
Some factors are of much importance for chelation as follows.
The sizes of the chelating ring are increased as well as the stability of metal complex decreased. According to Schwarzenbach, connecting bridges form the chelating rings. The elongated ring predominates when long bridges connect to the ligand to form a long ring. It is usually observed that an increased a chelate ring size leads to a decrease in complex stability.
He interpreted this statement. The entropy of complex will be change if the size of chelating ring is increased, i.e., second donor atom is allowed by the chelating ring. As the size of chelating ring increased, the stability should be increased with entropy effect. Four-membered ring compounds are unstable, whereas five-membered are more stable. So the chelating ring increased its size and the stability of the formed metal complexes.
The number of chelating rings also decides the stability of complexes. Non-chelating metal compounds are less stable than chelating compounds. These numbers increase the thermodynamic volume, and this is also known as an entropy term. In recent years ligands capable of occupying as many as six coordination positions on a single metal ion have been described. The studies on the formation constants of coordination compounds with these ligands have been reported. The numbers of ligand or chelating agents are affecting the stability of metal complexes so as these numbers go up and down, the stability will also vary with it.
For the Ni(II) complexes with ethylenediamine as chelating agent, its log K1 value is 7.9 and if chelating agents are trine and penten, then the log K1 values are 7.9 and 19.3, respectively. If the metal ion change Zn is used in place of Ni (II), then the values of log K1 for ethylenediamine, trine, and penten are 6.0, 12.1, and 16.2, respectively. The log βMY values of metal ions are given in Table 1.
Metal ion | log βMY (25°C, I = 0.1 M) |
---|---|
Ca2+ | 11.2 |
Cu2+ | 19.8 |
Fe3+ | 24.9 |
Metal ion vs. log βMY values.
Ni(NH3)62+ is an octahedral metal complex, and at 25 °C its log β6 value is 8.3, but Ni(ethylenediamine)32+ complex is also octahedral in geometry, with 18.4 as the value of log β6. The calculated stability value of Ni(ethylenediamine)32+ 1010 times is more stable because three rings are formed as chelating rings by ethylenediamine as compared to no such ring is formed. Ethylenediaminetetraacetate (EDTA) is a hexadentate ligand that usually formed stable metal complexes due to its chelating power.
A special effect in molecules is when the atoms occupy space. This is called steric effect. Energy is needed to bring these atoms closer to each other. These electrons run away from near atoms. There can be many ways of generating it. We know the repulsion between valence electrons as the steric effect which increases the energy of the current system [21]. Favorable or unfavorable any response is created.
For example, if the static effect is greater than that of a product in a metal complex formation process, then the static increase would favor this reaction. But if the case is opposite, the skepticism will be toward retardation.
This effect will mainly depend on the conformational states, and the minimum steric interaction theory can also be considered. The effect of secondary steric is seen on receptor binding produced by an alternative such as:
Reduced access to a critical group.
Stick barrier.
Electronic resonance substitution bond by repulsion.
Population of a conformer changes due to active shielding effect.
The macrocyclic effect is exactly like the image of the chelate effect. It means the principle of both is the same. But the macrocyclic effect suggests cyclic deformation of the ligand. Macrocyclic ligands are more tainted than chelating agents. Rather, their compounds are more stable due to their cyclically constrained constriction. It requires some entropy in the body to react with the metal ion. For example, for a tetradentate cyclic ligand, we can use heme-B which forms a metal complex using Fe+2 ions in biological systems (Figure 4).
Structure of hemoglobin is the biological complex compound which contains Fe(II) metal ion.
The n-dentate chelating agents play an important role for the formation of more stable metal complexes as compared to n-unidentate ligands. But the n-dentate macrocyclic ligand gives more stable environment in the metal complexes as compared to open-chain ligands. This change is very favorable for entropy (ΔS) and enthalpy (ΔH) change.
There are so many parameters to determination of formation constants or stability constant in solution for all types of chelating agents. These numerous parameters or techniques are refractive index, conductance, temperature, distribution coefficients, refractive index, nuclear magnetic resonance volume changes, and optical activity.
Solubility products are helpful and used for the insoluble salt that metal ions formed and complexes which are also formed by metal ions and are more soluble. The formation constant is observed in presence of donor atoms by measuring increased solubility.
To determine the solubility constant, it involves the distribution of the ligands or any complex species; metal ions are present in two immiscible solvents like water and carbon tetrachloride, benzene, etc.
In this method metal ions or ligands are present in solution and on exchanger. A solid polymers containing with positive and negative ions are ion exchange resins. These are insoluble in nature. This technique is helpful to determine the metal ions in resin phase, liquid phase, or even in radioactive metal. This method is also helpful to determine the polarizing effect of metal ions on the stability of ligands like Cu(II) and Zn(II) with amino acid complex formation.
At the equilibrium free metal and ions are present in the solution, and using the different electrometric techniques as described determines its stability constant.
This method is based upon the titration method or follows its principle. A stranded acid-base solution used as titrate and which is titrated, it may be strong base or strong acid follows as potentiometrically. The concentration of solution using 103− M does not decomposed during the reaction process, and this method is useful for protonated and nonprotonated ligands.
This is the graphic method used to determine the stability constant in producing metal complex formation by plotting a polarograph between the absences of substances and the presence of substances. During the complex formation, the presence of metal ions produced a shift in the half-wave potential in the solution.
If a complex is relatively slow to form and also decomposes at measurable rate, it is possible, in favorable situations, to determine the equilibrium constant.
This involves the study of the equilibrium constant of slow complex formation reactions. The use of tracer technique is extremely useful for determining the concentrations of dissociation products of the coordination compound.
This method is based on the study of the effect of an equilibrium concentration of some ions on the function at a definite organ of a living organism. The equilibrium concentration of the ion studied may be determined by the action of this organ in systems with complex formation.
The solution of 25 ml is adopted by preparing at the 1.0 × 10−5 M ligand or 1.0 × 10−5 M concentration and 1.0 × 10−5 M for the metal ion:
The solutions containing the metal ions were considered both at a pH sufficiently high to give almost complete complexation and at a pH value selected in order to obtain an equilibrium system of ligand and complexes.
In order to avoid modification of the spectral behavior of the ligand due to pH variations, it has been verified that the range of pH considered in all cases does not affect absorbance values. Use the collected pH values adopted for the determinations as well as selected wavelengths. The ionic strengths calculated from the composition of solutions allowed activity coefficient corrections. Absorbance values were determined at wavelengths in the range 430–700 nm, every 2 nm.
For a successive metal complex formation, use this method. If ligand is protonate and the produced complex has maximum number of donate atoms of ligands, a selective light is absorbed by this complex, while for determination of stability constant, it is just known about the composition of formed species.
Bjerrum (1941) used the method stepwise addition of the ligands to coordination sphere for the formation of complex. So, complex metal–ligand-n forms as the following steps [22]. The equilibrium constants, K1, K2, K3, … Kn are called stepwise stability constants. The formation of the complex metal-ligandn may also be expressed by the following steps and equilibrium constants.
Where:
M = central metal cation
L = monodentate ligand
N = maximum coordination number for the metal ion M for the ligand
If a complex ion is slow to reach equilibrium, it is often possible to apply the method of isotopic dilution to determine the equilibrium concentration of one or more of the species. Most often radioactive isotopes are used.
This method was extensively used by Werner and others to study metal complexes. In the case of a series of complexes of Co(III) and Pt(IV), Werner assigned the correct formulae on the basis of their molar conductance values measured in freshly prepared dilute solutions. In some cases, the conductance of the solution increased with time due to a chemical change, e.g.,
It is concluded that the information presented is very important to determine the stability constant of the ligand metal complexes. Some methods like spectrophotometric method, Bjerrum’s method, distribution method, ion exchange method, electrometric techniques, and potentiometric method have a huge contribution in quantitative analysis by easily finding the stability constants of metal complexes in aqueous solutions.
All the authors thank the Library of University of Delhi for reference books, journals, etc. which helped us a lot in reviewing the chapter.
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