Adsorption and Its Applications: Using Zinc Adsorption on Water Hyacinth to Elaborate the Kinetics and Thermodynamics of Adsorption

Abstract

Adsorption is a technique for removing adsorbate from the liquid or gas phase using adsorbents. The adsorbent is solid while the adsorbate can either be dissolved in liquid or gas. Adsorption has attracted the attention of many researchers because of its wide applicability in water and air purification, environment friendly, effectiveness, and ease to design as compared with the other methods. Activated carbon has been used as an effective adsorbent. However, its application is limited since it’s expensive. This has necessitated research interest in other materials that are safe and economical instead of commercial activated carbon. Some of the materials that have been successfully tested include sawdust, silica gel, zeolites, clay minerals and oxides, nanomaterial, agricultural by-products, biological waste, ion exchange resins and water hyacinth, etc. Although some of these materials are effective, they are not readily available. The kinetics of adsorption is done through testing the adsorption data against standard kinetic models and the model with the best line of fit, based on the values of coefficient of determination (R2) is selected. The adsorption process is described using isotherms such as Freundlich and Langmuir. This chapter sheds more light on adsorption, the most common adsorbents, kinetic models, isotherms, and adsorption applicability.

1. Introduction

Over the last decade, there has been a tremendous increase in industries worldwide. Wastewater released from the industries is contaminated by toxic substances such as heavy metals. Heavy metals are persistent, fairly soluble in water, and hence easily absorbed into living cells [1]. Heavy metal pollution poses health problems such as damage to the liver, kidney, circulatory and nervous system, dermatitis, insomnia, tumor formation, rheumatoid arthritis and respiratory cancer. Heavy metals of great concern are mercury, lead, zinc, nickel, cobalt, chromium, copper, and cadmium. Due to these and many more adverse effects of heavy metals, on humanity and the environment, there is a need for protection and restoration of the environment through the removal of heavy metals from the industrial wastewater before being released into the environment.

Several methods have been used to remove heavy metals from industrial wastewater, which include the use of membranes such as reverse osmosis, electrochemical techniques such as electrolytic extraction and electrodialysis, ion exchange, and chemical precipitation. Although these methods are effective, they are costly in terms of infrastructure, control systems, and energy [2]. There exist cheaper methods of eliminating heavy metals from wastewater such as adsorption [3]. Adsorption is becoming a regular method for the removal of heavy metals from wastewater since its relatively less costly, energy-efficient, environmentally friendly, and inexpensive [4]. Another key advantage of adsorption is the ease of designing and operating [5]. Adsorption is very effective even when the concentration of heavy metal is as low as 1 mg/L, offering metal recovery, metal selectivity and regeneration of the adsorbent material [6].

2. Adsorption mechanism

Adsorption takes place in four definitive stages: Stage 1: The mass transfer of the adsorbate by diffusion from the bulk fluid to the solid–liquid boundary layer surrounding the adsorbent particle. Stage 2: External diffusion. The transportation of the adsorbate through diffusion within the boundary layer to the outer surface of the adsorbent. Stage 3: Internal diffusion. The transfer of the adsorbate from the outer surface of the adsorbent to its inner surface by diffusion. Stage 4: The adsorption of the adsorbate on the active sites by physical (Physisorption) or chemical adsorption (Chemisorption). Physisorption is the interaction between the adsorbate and the active site through the weak van der Waals forces while in the chemical adsorption, the interaction results in the formation of a strong chemical bond. Physisorption is reversible and leads to the formation of multimolecular layers while chemisorptions are irreversible and form a unimolecular layer.

3. Common adsorbents

The applicability of the adsorbent in the removal of pollutants majorly depends on the adsorbent’s characteristics. Some of the major characteristics include porosity, pore configuration, and the general nature of the surface of the adsorbent. The adsorption sites are spread throughout the solid. Adsorption sites’ sizes are categorized into three: macropores, mesopores, and micropores. While macropores’ diameter is larger than 50 nm, mesopores have a diameter that varies between 2 and 50 nm. Micropores’ diameter is less than 2 nm. Many adsorbents are either naturally occurring or manufactured. Some of the common adsorbents include activated carbon, silica gel, zeolites, clay, nanoparticles, biological wastes, exchange resins, and water hyacinth.

3.1 Activated carbon

It is an organic material that forms a porous medium for adsorption. The structure of this medium is composite. The building blocks in this structure are carbon atoms. Activated carbon can be used to remove substances such as dyes and pesticides as well as in the purification of wastewater [7]. This is because it is extremely effective in cadmium, lead, and zinc removal. The removal of pollutants such as chlorinated hydrocarbons, purification of helium, removal of phenols, removal of gas odors, and removal of nitrogen from the air have all utilized activated carbon [8].

3.2 Silica gel, zeolite, clay minerals, and oxides

Silica gel is a porous form of silica. It’s mainly used to control moisture because of its high ability to absorb water vapor [9]. Also, it is used to control moisture in shoe boxes and to remove moisture from transformer oils and gases. Silica gel is widely used since it is cheap and can be regenerated [10]. Zeolite occurs naturally in the form of crystalline alumina that can be used in the adsorption of organic molecules from a gaseous phase. Zeolites have high water uptake since they have extensive surface area. Zeolite is used in industries to purify hydrogen gas and to recover carbon dioxide. In petroleum manufacturing, normal paraffin is separated from branched paraffin by the use of zeolites through adsorption. Clinoptilolite and bentonite, which are forms of zeolite, have been reported as proficient adsorbents in purification since they adsorb heavy metals [11, 12]. Clay minerals and oxides are available in nature and widely used because of their ability to adsorb many species of element. They adsorb cations such Cu²⁺, anions such as N²⁺, and neutral metallic species. Clay can be categorized into four: mica, smectite, kaolinite, and montmorillonite. Although they are readily available, they are less efficient in the adsorption of heavy metals when compared with zeolites.

3.3 Nanomaterial, agricultural by-products, and biological waste

Nanomaterial is a porous material whose pore diameter is less than 200 nm. These materials pose special properties such as distinctive surface and structural properties such as crystallinity and defect. They are used in processes such as ion exchange, catalysis, and separation. Nanomaterials are efficient in adsorption although they are expensive [13]. Most of the nanomaterials that have been used as an adsorbent include carbon nano-tube, activated carbon, and graphene. Agricultural by-products and biological wastes have been utilized in the adsorption of heavy metals. They are readily available, require modest processing, economical, offer selective adsorption and easy to generate. Agricultural by-products such as pecan shells, coconut shells, rice husks, cow dung, and maize cob have all been used effectively [14].

3.4 Ion exchange resins

These are organic materials (polymers) that can substitute ions within them with ions in a solution. This occurs when a solution containing ions is passed through the polymer. Resins can either be anionic or cationic. Anionic resins are negatively charged. As the solution passes through the resin, the positively charged ions in the solution are trapped since the resin is negatively charged [15]. Anionic resins are either weak or strong acids. Cationic resins are positively charged. They trap the negatively charged ions in the solution. The ion exchange resin is used in water softening to substitute Mg²⁺ and Ca²⁺ with Na⁺ converting hard water to soft water [16]. In this case, the resin is regenerated by rinsing it with a solution whose concentration of sodium ions is high. Resins are also used to purify water. In such a case, the poisonous heavy metal ions are replaced with ions such as sodium. Water containing no mineral content is purified using a resin that contains H⁺ and OH⁻ to replace anions and cations.

3.5 Water hyacinth and other low-cost adsorbents

The plant can be grown in contaminated soils to absorb the heavy metal ions [17]. Also, it can be harvested, dried and ground into powder before dispensing it in heavy metal contaminated water. Water hyacinth powder should be allowed sufficient time in the contaminated water for adsorption to occur before the water can be used. The constituents of water hyacinth are cellulose (30–50%), hemicelluloses (20–40%), and lignin (15–30%) [18]. The cellulose contains functional groups such as O-H, which are involved in adsorption through deprotonation [19]. A comparative study on the efficiency of water hyacinth, water lettuce, and vetiver grass showed that the three plants have different abilities to eliminate water contaminants and their capacities are influenced by factors such as climate and temperature etc. [20]. Low-cost adsorbents provide cheap and readily available material to use as adsorbents. Lately, scientists have intensified research on the use of low-cost adsorbents in the removal of heavy metals from wastewater. Biological resources such as the agricultural waste have been put to the test and have proved useful. Rice husks, cow dung, sugarcane bagasse, sawdust, cashew nutshell, soybean hull, coconut shell, cotton hull, orange and banana peel have all successfully been used to remove heavy metals from wastewater. These adsorbents are cleaned and ground to the desired particle sizes before being used for adsorption while others are modified using modification techniques to improve the active sites [21].

4. Adsorption kinetics

During adsorption, equilibrium is not established immediately. The particle transfer from the solution to the adsorption site is restricted by the mass transfer resistance. The graph showing rate of adsorption with time is referred to as adsorption kinetics. It shows the rate of withholding or discharge of adsorbate from the aqueous solution to the adsorbent surface. The rate is influenced by the amount of the adsorbent, temperature, pH and particle size of the adsorbent, among others. The adsorption rate is restricted by resistance to diffusion in the solution (as adsorbate diffuses from the solution to the surface of the adsorbent) and within the adsorbent layers (as the adsorbate diffuses to the active site within the adsorbent) [22]. Kinetics studies are, therefore, important in determining the rate-limiting stage. Kinetics of adsorption is studied using kinetic models such as pseudo-first-order and pseudo-second-order.

4.1 Pseudo-first-order

To be able to analyze adsorption, several models have been applied. One such model is the pseudo-first-order. The linear form of the pseudo-first-order equation is [23]

$$\mathrm{Log}\left({\mathrm{q}}_{\mathrm{e}}-{\mathrm{q}}_{\mathrm{t}}\right)=log\left({\mathrm{q}}_{\mathrm{e}}\right)–\frac{\mathrm{K}1}{2.303}t$$E1

Where q_e (mg/g)—the amount of adsorbate on adsorbent at equilibrium, q_t (mg/g)—the amount of heavy metal adsorbed on water hyacinth at a time t while K₁(Min⁻¹) is a rate constant of adsorption for pseudo-first-order. The values of q_e and q_t are determined using the adsorption capacity Eqs. (2) and (3) respectively [24].

$$\left({\mathrm{q}}_{\mathrm{e}}\right)=\frac{\left(\mathit{C}\mathbf{1}-\mathit{Ce}\right)}{\mathit{M}}\times \mathrm{V}$$E2

$$\left({\mathrm{q}}_{\mathrm{t}}\right)=\frac{\left(\mathit{C}\mathbf{1}-\mathit{C}\mathbf{2}\right)}{\mathit{M}}\times \mathrm{V}$$E3

Where C₁ and C₂ refer to the initial and final concentration, C_e is the concentration of the analyte at equilibrium, M-mass of the adsorbent, V is the volume used. The adsorption rate constant (K₁) for pseudo-first-order is computed from the gradient of a linear plot of log (q_e-q_t) versus t while q_e is the value at the intercept.

4.2 Pseudo-second-order

The linear form of pseudo-second-order is [25];

$$\frac{\mathrm{t}}{\mathrm{qt}}=\frac{1}{\mathrm{qe}}t+\frac{1}{\mathrm{K}2\mathrm{qe}2}$$E4

Where q_e (mg/g)—the amount of adsorbate on adsorbent at equilibrium, q_t (mg/g)—the amount of heavy metal adsorbed on water hyacinth at a time t while K₂(Min⁻¹) is a rate constant of adsorption for pseudo-second-order. The values of q_t are determined using the adsorption capacity Eq. (2). The adsorption rate constant for pseudo-second-order (K₂) and q_e are computed from the gradient and intercept of a linear plot of t/q_t versus t respectively. The linear plot with the highest R² value is considered to describe the reaction best and is taken as the correct reaction order.

4.3 Experimental example

Adsorption studies of water hyacinth powder in the removal of Zn²⁺ (95.5 ppm) from an aqueous solution were conducted, and the data obtained analyzed using both pseudo-first and pseudo-second-order.

To prepare the stock solution, the following procedure was followed [26]:

• The amount of salt dissolved in a liter of distilled water to make 1000 ppm aqueous solutions of zinc was calculated using Eq. (5) [27].

$$\mathrm{m}=\frac{\mathrm{Mw}}{\mathrm{Aw}}\mathrm{x}\frac{\mathrm{100}}{\mathrm{P}}\mathrm{x}\frac{\mathrm{V}}{\mathrm{1000}}$$E5

Where m = mass (g) of analytical grade zinc nitrate, which was weighed, M_W = molecular weight, A_w = Atomic mass, V = volume of the stock solution to be made, P = percentage purity of the salt.

$$\mathrm{m}=\frac{297.48}{\mathrm{65.4}}\mathrm{x}\frac{\mathrm{100}}{\mathrm{95.97}}\mathrm{x}\frac{\mathrm{1000}}{\mathrm{1000}}=4.7396\mathrm{g}$$

• 4.7396 g weighed was transferred into a 1000 ml volumetric flask. 100 ml of distilled water was added, stirred, and made to the mark.

• Working solutions of 95.5 ppm were prepared via serial dilution following the formula indicated in Eq. (6) [28]

$${\mathrm{C}}_{\mathrm{1}}{\mathrm{V}}_{\mathrm{1}}\mathrm{=}{\mathrm{C}}_{\mathrm{2}}{\mathrm{V}}_{\mathrm{2}}$$E6

Water hyacinth stems were collected from the shores of Lake Victoria, cut into smaller pieces, and cleaned vigorously with water to get rid of dust and other contaminants. To further prepare water hyacinth pieces for adsorption, the following procedure was followed

• Thorough cleaning of water hyacinth stems using distilled water followed by sufficient sun drying. Further, oven drying at 110°C to ensure that the moisture was removed totally.

• The dried components were ground and sieved using 300 μm sieves.

4.3.1 Batch experiments

To carry out the batch studies, the following procedure was followed [29]:

• 0.5 g of groundwater hyacinth whose particle size was <300 μm was added in separate 500 ml beakers. To the beakers, a 100 ml aqueous solution of 95.5 ppm for zinc was added. The pH value of the solutions was set at 5 using a benchtop pH meter model HANNA HI 22091 and was adjusted by adding 0.1 M HNO₃ and 0.1 M NaOH.

• The mixtures were stirred continuously using a magnetic stirrer at 300 rpm for 5 min. Adsorption was allowed to occur for 2 h.

• The mixture was gravity filtered using Whatman filter paper no. 40. The residual concentrations (C₂) of selected zinc ions in the filtrate were determined using the AAS (AA-6300 SHIMADZU AAS) after 10 min for 1 h.

Table 1 gives information about the initial and final analyte concentration (C₀, and C_t), the volume of the solution (V), the mass of the adsorbent (M), the amount of adsorbate on water hyacinth at equilibrium (q_{e -} mg/g) and at time t (q_t-mg/g), the quotient t/q_t, the difference between q_e-q_t and their logarithmic difference (log q_e-q_t).

Kinetic data for Zn^2+(95.5 ppm)
time	Ct	Co	V	M	qt	qe	qe-qt	log (qe-qt)	t/qt
0	95.5	95.5	0.1	0.5	0.0000	15.6800	15.6800	1.1953	Error
10	64.1	95.5	0.1	0.5	6.2800	15.6800	9.4000	0.9731	1.5924
20	49.4	95.5	0.1	0.5	9.2200	15.6800	6.4600	0.8102	2.1692
30	42.2	95.5	0.1	0.5	10.6600	15.6800	5.0200	0.7007	2.8143
40	34	95.5	0.1	0.5	12.3000	15.6800	3.3800	0.5289	3.2520
50	21.9	95.5	0.1	0.5	14.7200	15.6800	0.9600	−0.0177	3.3967
60	17.1	95.5	0.1	0.5	15.6800	15.6800	0.0000	Error	3.8265

Table 1.

Kinetic data for Zn²⁺.

Time and logarithmic differences presented between in Table 1 were used to generate Figure 1. Figure 1 shows the variation of the logarithmic difference (log q_e-q_t) with time. The logarithmic difference (log qe-qt) in adsorption capacity at equilibrium and at particular time t decreased linearly as the adsorption time increased as shown between Figure 1.

Figure 1.

Pseudo-first-order for the adsorption of 95.5 ppm zinc ions onto water hyacinth powder.

Time and the quotient t/q_t presented in Table 1 were used to generate Figure 2. Figure 2 demonstrates how the quotient t/q_t changes with time t. The quotient of t /qt increased linearly with the adsorption time as shown in Figure 2.

Figure 2.

Pseudo-second-order for the adsorption of 95.5 ppm zinc ions onto water hyacinth powder.

The essential information presented in Figures 1 and 2 was used in determining the kinetic parameters, which were used in establishing the most suitable model that could be used to describe the adsorption of Zn²⁺ on water hyacinth powder.

4.3.2 Pseudo-first-order and pseudo-second-order kinetic parameters

The pseudo-first-order and pseudo-second-order kinetic parameters include K₁, q_e, and K₂. The initial concentration of Zn²⁺ was 95.5 ppm while the final concentration was 17.1 ppm. Using the Eqs. (1), (4) and the slopes in Figures 1 and 2, the pseudo-first-order and pseudo-second-order kinetic parameters can be calculated as shown:

1. For the pseudo-first-order

   Comparing the slope from Figure 1 with the linear form of pseudo-first-order equation (Eq. (1))

   $$\mathrm{y}=-0.0209\mathrm{x}+1.2253$$
   $$\mathrm{Log}\left({\mathrm{q}}_{\mathrm{e}}-{\mathrm{q}}_{\mathrm{t}}\right)=–\frac{\mathrm{K}1}{2.303}t+log\left({\mathrm{q}}_{\mathrm{e}}\right)$$
   $${\mathrm{q}}_{\mathrm{e}}=16.7996,\text{while}{\mathrm{k}}_1=-2.303\mathrm{x}-0.0209=0.0481$$

2. For the pseudo-second-order

   Comparing the equation from Figure 2 with the linear form of pseudo-second-order

$$\mathrm{y}=0.0578\mathrm{x}+0.7033$$

$$\frac{\mathrm{t}}{\mathrm{qt}}=\frac{1}{\mathrm{qe}}t+\frac{1}{\mathrm{K}2\mathrm{qe}2.}$$

q_e = 1/0.0578, hence q_e 17.3010, K₂ = 0.0048. The pseudo-first-order and pseudo-second-order kinetic parameters are presented in Table 2 which provides information about K₁, qe, R², and K₂.

Pseudo –first-order				Pseudo –second-order
Metal ions	K1(min^−1)	qe (mg/g)	R^2	K2(g/mg.min)	qe (mg/g)	R^2
Zinc ions	0.0481	16.7996	0.944	0.0048	17.3010	0.8995

Table 2.

The pseudo-first-order and pseudo second-order kinetic parameters of adsorption of zinc ions on powdered water hyacinth.

The adsorption kinetics pointed out that the pseudo-first-order kinetic model expressed better the adsorption technique of zinc on water hyacinth with the regression coefficient R² = 0.944 being higher than that of the pseudo-second-order (R² = 0.8995).

5. Adsorption isotherms

Adsorption isotherm refers to a graph showing a relationship between adsorbate in the bulk and that on the surface of the adsorbent at a constant temperature. The adsorbate adsorption or release in an aqueous solution could be represented as follows [30]:

$${\mathrm{S}}_{\mathrm{f}}\left(\mathrm{Me}\right)+{\mathrm{H}}^{+}\left(\text{solution}\right)\leftrightarrow {\mathrm{S}}_{\mathrm{f}}\left(\text{adsorbent}\right)+\mathrm{Me}\left(\text{solution}\right)$$E7

where S_f represents the different adsorption sites on the adsorbent where the metal, Me can be retained. The adsorption of the metal on the sites could be enhanced by both the physical and chemical characteristics of the medium [31]. Langmuir and Freundlich’s isotherms have been applied to heavy metal adsorption studies. The Langmuir isotherm assumes that adsorption is a reversible process and the adsorbing material has a definite number of active spots, which are evenly distributed [32]. The Freundlich isotherm describes multilayer adsorption [33]. The adsorption isotherms and modeling are very important in determining the accuracy of the adsorption process.

5.1 Langmuir isotherms

Langmuir adsorption was intended to illustrate gas–solid adsorption. However, it is also used to compute and compare the adsorption capacities of various adsorbents. Langmuir isotherm balances both adsorption and desorption rates. Adsorption is the measure of the portion of the adsorbent’s surface that is open while desorption accounts for the portion of the surface of the adsorbent that is occupied [33]. The linear form of Langmuir isotherm that was used is shown in Eq. (8) [34]

$$\frac{1}{\mathit{qe}}=\left(\frac{1}{\mathit{qmb}}\right).\frac{1}{\mathit{Ce}}+\frac{1}{\mathit{qm}}$$E8

where: q_e (mg/g)—equilibrium adsorption capacity, C_e (mg/l)—the amount of adsorbed adsorbate at equilibrium, q_m (mg/g)—the highest amount of the adsorbate for every unit weight of adsorbent while b (l/mg)—Langmuir constant (binding affinity). The q_m and b values are determined graphically from a plot of 1/q_e against 1/C_e. The dimensionless factor R_L, also known as the separation factor, is used to describe the Langmuir isotherm. It is determined using Eq. (9) [35]

$${\mathrm{R}}_{\mathrm{L}}=\frac{1}{b\mathit{Co}+1}$$E9

where; R_L < 1—adsorption is favorable,

R_L > 1—adsorption is unfavorable

R_L = 1—linear

R_L > 1—adsorption is irreversible

5.2 Freundlich isotherms

Freundlich isotherm equation is based on the fact that adsorption occurs on a heterogeneous surface. It is an experiential model, which takes into account the adsorptive active sites and their energy exponentially. The expression also considers the heterogeneity of the adsorbent’s surface. It is expressed as shown in Eq. (10) [36]

$${\mathrm{q}}_{\mathrm{e}}={\mathrm{K}}_{\mathrm{F}}{{\mathrm{C}}_{\mathrm{e}}}^{1/\mathrm{n}}$$E10

The linear form of the Freundlich isotherm equation is shown in Eq. (11) [37].

$$\mathit{log}{\mathrm{q}}_{\mathrm{e}}=\frac{1}{n}\mathit{log}{\mathrm{C}}_{\mathrm{e}}+\mathit{log}{\mathrm{K}}_{\mathrm{f}}$$E11

Where qe (mg/g)—the amount of the adsorbate adsorbed per unit weight of water hyacinth bio-material, Ce (mg/L)—the amount of unadsorbed adsorbent in the solution, K_f—a constant indicating adsorption capacity while n—adsorption intensity. Adsorption studies of zinc ions conducted using synthesized magnetite and baobab composite showed that the equilibrium data were suitably expressed by Freundlich because of the high correlation coefficient [38].

5.3 Experimental example

Equilibrium adsorption studies of water hyacinth powder in the removal of Zn²⁺ from aqueous solution were performed, and the data obtained were analyzed using both Langmuir and Freundlich isotherms. The working solutions of concentrations 0.5, 1.0, 10, 20, 40, 50, 60, 80, 100 ppm were prepared through serial dilution of the stock solution prepared in Section 4.3 following the formula indicated in Eq. (6).

5.3.1 Batch experiments

100 ml of aqueous solutions containing zinc metal ion (0.5–100 ppm) were added to 0.5 g of water hyacinth powder (<300 μm) in separate 500 ml beakers. The pH of the solutions was set at 5, and the solutions were stirred for 5 minutes. Adsorption was allowed to occur for 120 minutes. These experiments were performed at room temperature until the equilibrium was established. The mixture was filtered using gravity filtration (using Whatman Filter Paper no. 40 and plastic filter funnels). The residual concentrations of zinc ions in the filtrate were determined using the Atomic Absorption Spectrometer (AA-6300 SHIMADZU AAS). The data obtained from the adsorption studies were computed using Eqs. (2), (8) and (11), and tabulated in Table 3. Table 3 gives information about the initial and equilibrium analyte concentration (C₀, and C_e), reciprocal of equilibrium concentration (1/C_e), the amount of zinc ion on water hyacinth at equilibrium (q_{e -} mg/g) and its reciprocal (1/q_e), and the logarithmic values of both q_e and C_e (log q_e, log C_e).

Equilibrium data for Zn^2+
Co	Ce	1/Ce	qe	1/qe	log qe	log Ce
0.5	0	Error	0.1000	10.0000	Error	−1.0000
1	0	Error	0.2000	5.0000	Error	−0.6990
10	0	Error	2.0000	0.5000	Error	0.3010
20	2.4	0.4167	3.5200	0.2841	0.3802	0.5465
40	4.9	0.2041	7.0200	0.1425	0.6902	0.8463
50	9.4	0.1064	8.1200	0.1232	0.9731	0.9096
60	11.1	0.0901	9.7800	0.1022	1.0453	0.9903
80	16.4	0.0610	12.7200	0.0786	1.2148	1.1045
100	20.7	0.0483	15.8600	0.0631	1.3160	1.2003

Table 3.

Equilibrium data for Zn²⁺.

The logarithmic values of C_e and q_e accessible in Table 3 were used to generate Figure 3 which demonstrates demonstrates the variation of log q_e with log C_e. The logarithm of q_e (adsorption capacity at equilibrium) increased linearly to the logarithm of C_e (concentration at equilibrium) as shown in Figure 3.

Figure 3.

Linearized Freundlich plot for the adsorption of Zinc ions onto water hyacinth powder.

The quotients 1/C_e and 1/q_e presented in Table 3 were used to generate Figure 4 which illustrates how the quotient 1/C_e varies with 1/q_e. The reciprocal of q_e (adsorption capacity at equilibrium) increased linearly with the reciprocal of C_e (concentration at equilibrium) as shown in Figure 4.

Figure 4.

Linearized Langmuir plot for the adsorption of Zinc ions onto water hyacinth powder.

The information presented in Figures 3 and 4 was used in computing the Freundlich and Langmuir parameters essential in determining the most suitable isotherm for explaining the adsorption of Zn²⁺ on water hyacinth powder.

5.3.2 Freundlich and Langmuir parameters

The Freundlich and Langmuir parameters include q_m, b, n, and K_f. The initial concentration of Zn²⁺ was 100 ppm while the equilibrium concentration was 20.7 ppm. Using the Eqs. (8), (11) and the slopes from Figures 3 and 4, the Langmuir and Freundlich parameters were calculated as shown;

1. Freundlich parameters

   Comparing Eq. (11) with the equation from Figure 3

   $$\mathrm{y}=1.4944\mathrm{x}-0.4575$$
   $$\mathit{log}{\mathrm{q}}_{\mathrm{e}}=\frac{1}{n}\mathit{log}{\mathrm{C}}_{\mathrm{e}}+\mathit{log}{\mathrm{K}}_{\mathrm{f}}$$
   $$\mathit{log}{\mathrm{K}}_{\mathrm{f}}=0.3276\text{hence}{\mathrm{K}}_{\mathrm{f}}=0.3487$$
   $$1/\mathrm{n}=1.4944\text{hence}\mathrm{n}=0.6692$$

2. Langmuir parameters

   Comparing Eq. (8) with equation from Figure 4;

$$\mathrm{y}=0.5636\mathrm{x}+0.0452$$

$$\frac{1}{\mathrm{qe}}=\left(\frac{1}{\mathrm{qmb}}\right).\frac{1}{\mathrm{Ce}}+\frac{1}{\mathrm{qm}}$$

$$\frac{1}{\mathrm{qm}}=0.0452\text{hence}{\mathrm{q}}_{\mathrm{m}}=22.1239$$

$$\frac{1}{\mathrm{qm}.\mathrm{b}}=0.5636\text{replacing}{\mathrm{q}}_{\mathrm{m}}\text{we get}\mathrm{b}=0.0802$$

From Eq. (9), R_L=$\frac{1}{b\mathit{Co}+1}.$ The value of R_{L =}$\frac{1}{\left(0.0802\mathrm{x}100\right)+1}$= 0.1109.

The Freundlich and Langmuir adsorption parameters are presented in Table 4 which provides information about n, b, K_f, q_m, and the regression coefficient of Figures 3 and 4.

Freundlich isotherm	Langmuir isotherm
n = 0.6692	b (L/mg) =0.0802
Kf = 0.3487	qm (mg/g) =22.1239
R^2 = 0.9659	R^2 = 0.975

Table 4.

Langmuir and Freundlich isotherms parameters for adsorption of zinc ions from aqueous solution ground using water hyacinth powder.

The use of water hyacinth powder in the adsorption of zinc ions correlated well with the Langmuir model in contrast to the Freundlich model since it had the highest regression coefficient (R² = 0.975). The linearity of Figure 4 demonstrates the validity of the Langmuir isotherm whose basis is the formation of a monolayer on the surface of water hyacinth powder. Results similar to these were obtained by [39] where the equilibrium data during adsorption of Zinc (II) ions from aqueous solution using functionalized lignocelluloses derived from waste biomass was suitably represented by Langmuir isotherm due to high correlation coefficients. The adsorption process was favorable since the separation factor R_L (0.1109) is less than 1. The Freundlich parameter n (n = 0.6692) indicates that the adsorption (physical adsorption) of zinc is unfavorable since 2 < n < 10 indicates favorable adsorption. The Langmuir constant b is important in establishing the adsorption affinity that relates the bond energy between adsorbent and adsorbate [40].

6. Thermodynamics of adsorption

To evaluate the adsorption process further, it is imperative to examine the adsorbate’s binding thermodynamics on the adsorbent. Thermodynamics include changes in entropy$\left(∆S°\right)$, enthalpy$\left(∆H°\right),$ and Gibbs free energy ($∆G°)$, which are computed using Eqs. (12)–(14).

The Gibbs free energy$∆\mathrm{G}°$is given by [41];

$$∆\mathrm{G}°=-\mathrm{R}\mathrm{T}\mathit{ln}\mathrm{Kc}$$E12

Where $∆\mathrm{G}°$ (kJ/mol) is the change in the Gibbs free energy of adsorption, R is the gas constant (8.314 J/ (Kmol)), T is the temperature in Kelvin, K_c is the equilibrium constant. Equilibrium constant K_c can be stated with reference to Gibbs free energy $∆\mathrm{G}°$and entropy $∆\mathrm{S}°$ as indicated in the Van’t Hoffs reaction given in Eq. (13) [42].

$$\mathit{ln}\mathrm{Kc}=-\frac{∆\mathrm{H}°}{\mathrm{R}}\left(\frac{1}{\mathrm{T}}\right)+\frac{∆\mathrm{S}°}{\mathrm{R}}$$E13

Where is $∆\mathrm{H}°$ (kJ/mol) enthalpy change while $∆\mathrm{S}°$ (J/ (mol K) is entropy change.

K_c is computed by following Eq. (14) [43].

$$\mathrm{Kc}=\frac{\mathrm{Qe}}{\mathrm{Ce}}$$E14

Where Qe is the equilibrium adsorption capacity while Ce is the equilibrium concentration of the heavy metal under investigation.

To determine thermodynamic parameters of adsorption, the following procedure is followed;

1. Preparation of stock solution from soluble heavy metal salt. The working solution is prepared through serial dilution of the stock solution.

2. Batch experiments studies should be carried out at a specified temperature until equilibrium is established. The procedure should be repeated with other temperatures under study (Batch studies can be carried out at temperatures such as 298,303,313,323 K). The residual adsorbate concentration at equilibrium (Ce) should be determined for each temperature. The equilibrium adsorption capacity (Qe) should then be computed using Eq. (2).

3. The values of Qe and Ce obtained for each temperature should be used to compute Kc values.

4. Further, the ln of Kc values obtained should be calculated for each temperature.

5. Using ln Kc and 1/T values obtained, a plot showing how ln Kc (y-axis) varies with 1/T (x-axis) should be drawn using excel.

6. The straight-line graph equation (y = Mx + c) obtained from the plot should be compared with Eq. (13). With the slope and R (gas constant), the values of $∆\mathrm{H}°$can be calculated. With the Y-intercept (Value of C in the straight-line graph) and the R (gas constant), the values of $∆\mathrm{S}°$can be computed easily

7. The Gibbs free energies for each temperature are finally calculated and results interpreted.

Negative values of $∆\mathrm{G}°$indicate that the process is spontaneous and will support the forward reaction while positive values show the process is nonspontaneous, hence will support the reverse reaction [44]. The spontaneity of the adsorption process depends on the values of $∆\mathrm{H}°\text{and}∆\mathrm{S}°$ as outlined in Table 5. Table 5 outlines information about Gibbs free energy (Δ$\mathrm{G}°$) and how the spontaneity of an adsorption process is influenced by both enthalpy ($∆\mathrm{H}°$ and entropy (Δ$\mathrm{S}°$).

Gibbs free energy (∆G°)	Enthalpy(∆H°)	Entropy (∆S°)	Spontaneity
ΔG <0	ΔH < 0	ΔS > 0	Spontaneous at all Temperatures
ΔG <0	ΔH >0	ΔS > 0	Spontaneous at high Temperatures
ΔG <0	ΔH <0	ΔS < 0	Spontaneous at low Temperatures
ΔG <0	ΔH > 0	ΔS <0	Non Spontaneous at all Temperatures

Table 5.

Gibbs free energy (ΔG°), enthalpy (∆H°), entropy (ΔS°) and spontaneity of an adsorption process.

When $∆\mathrm{H}°$ >0, then the adsorption process is endothermic and requires to absorb heat from the environment. When $∆\mathrm{H}°$ < 0, the adsorption process is exothermic and releases heat into the surroundings [45]. If $∆\mathrm{S}°$ < 0, it indicates that the adsorption is orderly but if $∆\mathrm{S}°$ > 0 shows adsorption is disorderly at the surface of the adsorbent [46].

7. Application of adsorption

1. Getting rid of colors—Juice obtained from sugar cane is treated with animal charcoal to eliminate the coloring agent to get a clear liquid.

2. Separation of inert gases—A stream of inert gases can be separated into constituent gases through the use of coconut charcoal since the noble gases are adsorbed at different degrees.

3. Controlling humidity—Silica and aluminum gels are applied as adsorbents in the removal of moisture.

4. Gas mask—In coal mines, gas masks are worn to aid staff in breathing. A gas mask consists of activated charcoal that adsorbs impurities.

5. Dyeing cloth—Mordants are applied in dyeing. The mordant, e.g., alum adsorbs the dye elements, hence the dye does not cling to the cloth material.

8. Conclusion

In the review, we have examined the adsorption process, adsorbent, adsorption mechanism, and some of the common adsorption applications. Also, we have scrutinized essential kinetic and thermodynamic parameters of adsorption. Kinetic models and isotherms described include pseudo-first-order, pseudo-second-order, Langmuir, and Freundlich. Kinetic parameters explained include adsorption capacity, pseudo-first and pseudo-second constants while the isotherm parameters described herein include adsorption intensity (n), binding affinity (b), Freundlich constant (K_f), adsorption capacity (q_m), separation factor (R_L). We have used the adsorption of zinc ions to illustrate how kinetic and isotherm parameters are computed during adsorption studies. The adsorption data for zinc from the aqueous solution using water hyacinth fitted well in the Langmuir model (R² = 0.975) in comparison to the Freundlich model (R² = 0.9659) based on the correlation coefficients. Additionally, the study showed that zinc adsorption obeys the pseudo-first-order reaction kinetic model. The adsorption of zinc ions using water hyacinth powder was favorable since the separation factor R_L was less than 1. The Freundlich parameter n an indicator of the probability of physical adsorption taking place showed that physisorption was unfavorable since n < 2. Further, this chapter clearly describes how thermodynamics parameters (entropy$\left(∆S°\right)$, enthalpy$\left(∆H°\right)$, and Gibbs free energy ($∆G°)$) are evaluated during adsorption studies. Also, the chapter details the meaning of entropy$\left(∆S°\right)$, enthalpy$\left(∆H°\right)$, and Gibbs free energy ($∆G°)$ concerning the spontaneity of the adsorption process.

Acknowledgments

I am deeply obliged to my supervisors, Dr. John Onam Onyatta and Prof. Amir O. Yusuf, for the invaluable comments, suggestions, corrections, patience, and constructive criticisms that went a long way to refine this work. Without whose help, this work would not have been a success. Thank you very much for making sure I kept my focus.

Conflict of interest

The author declares no conflict of interest.

Originality/declaration

The author declares that this work is their original work and has not been submitted elsewhere for examination or publication.