Ion exchange equilibrium for three systems involving monovalent and divalent ions has been investigated over various temperatures (283, 298 and 313 K) using CMX cationic exchange membrane. All experiments were carried out at 0.1 mol/L. Ion exchange isotherms for the binary systems (Na+/K+), (Na+/Ca2+) and (K+/Ca2+) were established at temperatures ranging from 283 to 313 K. The obtained affinity order is: K+>Ca2+>Na+. Selectivity coefficients KK+2Na+, K2Na+Ca2+ and KCa2+2K+ were determined and found to increase with rise in temperature. Thermodynamic equilibrium constants Ki°j were calculated. Wilson and Debye–Hückel equations have been used to calculate activity coefficients in the membrane and solution, respectively. Standard free energy ΔGT°, standard enthalpy change ΔHT° and standard entropy change ΔST° were calculated. The values of ΔHT° were found to be 51.98 kJ/mol, 64.59 kJ/mol and 29.57 kJ/mol, respectively, for (Na+/K+), (Na+/Ca2+) and (K+/Ca2+) binary systems, which indicate that the ion exchange process between the CMX membrane and the studied binary systems is an endothermic process. ΔST° is found to be positive, which means that the increased randomness appeared on the membrane-solution interface during the ion exchange reaction. In addition, the standard free enthalpy change ΔGT° value for all systems is negative, which is an indication that the ion exchange equilibrium is spontaneous in standard conditions.

INTRODUCTION

Ion exchange membrane techniques (electrodialysis, electro-electrodialysis, dialysis) are commonly used due to their many applications in separation processes, water treatment and wastewater treatment, drinking water production, pharmaceutical and chemical industries (Juda & Mcrae 1950; Blaedel et al. 1969; Cui et al. 1998; Balster et al. 2005; Tongwen 2005; Kariduraganavar et al. 2006; Nagarale et al. 2006; Hosseini et al. 2014; Karas et al. 2014).

In this area, electrodialysis represents one of the most important ion exchange membrane methods. It deals with problems of desalination of water, concentration of dilute solutions, separation of electrolytes and production of acids and alkalis.

For accurate selection of an ion exchange membrane in a particular application, it is important to have adequate information concerning their physical and chemical properties, which constitutes a complementary part of an ion exchange membrane characterization study.

Several studies have been carried out to study the properties of the ion exchange membrane and generate thermodynamic data (Valverde et al. 2002; Lee et al. 2007) related to various uni-univalent and uni-bivalent ion systems. Theories explaining ion exchange equilibrium between ion exchange membranes and an electrolyte solution were developed by several researchers (Muraviev et al. 1998; Strathmann 2004; Ivanov et al. 2006). They found that ion exchange process can be influenced by several factors including type of membranes, temperature, concentration and pH.

Attempts were made to study the temperature effect on ion exchange equilibrium for computing the thermodynamic equilibrium constants (Lee et al. 2007; Lokhande et al. 2008; Guesmi et al. 2010).

An experimental study was conducted by Lee et al. (2007) on the ion exchange isotherms for the systems , and using a cation exchange resin Amberlite IR 120 at 283 and 303 K. They showed that the affinity order of the resin for the metal ions increases with increasing temperature. In the same context, Guesmi et al. (2010) investigated the influence of temperature on the ion exchange equilibrium between the AMX anion exchange membrane and electrolyte solutions containing a binary mixture of and ) at 283, 298 and 313 K, and they concluded that increasing the temperature reflects an increase in affinity. In addition, Lokhande et al. (2008) studied the effect of temperature on ion exchange equilibrium for uni-univalent systems and , and uni-divalent systems and using Duolite ion exchange resin A-102 D, and they showed that the affinity of the resin for the metal ions increases with increasing temperature.

Therefore in the present investigation attempts were made to study the temperature effect on the uni-univalent and uni-divalent cation exchange equilibrium between the CMX membrane and binary systems , and . The affinity order and the values of the selectivity coefficients at different temperatures were determined. All experiments were maintained at a constant concentration of 0.1 mol/L. Thermodynamic parameters such as standard free energy , standard enthalpy change and standard entropy change were calculated. Ion analysis was performed using ionic chromatography.

EXPERIMENTAL PROCEDURE

Reagents

Solutions were prepared using an analytical grade of , and . All chemicals of analytical grade were purchased from Sigma–Aldrich. Ultrapure water was used for the preparation of solutions.

Characteristics of the CMX membrane

The membrane used in all experiments was a Neosepta CMX cation exchange membrane purchased from Tokuyama Soda Co., Japan. The base polymer of this membrane is styrene and divinylbenzene, and the ionic fixed sites are sulfonic acid groups. The main characteristics of the CMX membrane are given in Table 1.

Table 1

Main characteristics of the CMX membrane

CMX membrane characteristics 
Matrix Polystyrene-DVB 
Transport number > 0.98 
Thickness (mm) 0.16–0.20 
Electric resistance (Ω.Cm22.5–3.5 
Humidity percentage (%) 23 
Ion exchange capacity (meq/g) 1.69 
CMX membrane characteristics 
Matrix Polystyrene-DVB 
Transport number > 0.98 
Thickness (mm) 0.16–0.20 
Electric resistance (Ω.Cm22.5–3.5 
Humidity percentage (%) 23 
Ion exchange capacity (meq/g) 1.69 

Ion exchange equilibrium

Five samples of CMX membranes (5 × 5 cm) in the ionic form were immersed in 250 mL of different solutions of binary mixtures ( and ) at constant total concentrations equal to 0.1 mol/L. The samples were maintained at a fixed temperature under vigorous stirring. At the end of equilibrium, the concentration of ionic species in the solution was determined by ion chromatography. The concentration of ions present in the membrane phase was derived from the following equations: 
formula
1
 
formula
2
where is the initial concentration of A ions in the solution (meq/L); is the initial concentration of B ions in the solution (meq/L); is the equilibrium concentration of A ions in the solution (meq/L); is the equilibrium concentration of B ions in the solution (meq/L); is the concentration of A ions in the membrane (meq/g); is the concentration of B ions in the membrane (meq/g); ms is the dray mass of the membrane (g); is the ion exchange capacity of the membrane (meq/g); V is the volume of solution (L).
The equivalent molar fractions of A and B ions in the solution , and in the membrane phase and , can also be defined using the following equations: 
formula
3
 
formula
4
where and are the charge of the A and B ions, respectively.

The determination of these fractions allows us to establish the ion exchange isotherms at studied temperatures.

RESULTS AND DISCUSSION

Effect of temperature on ion exchange equilibrium

The ion exchange isotherms (Figures 13) were established for the three binary systems , and at different temperatures (283, 298 and 313 K). These isotherms allow the affinity order of the CMX membrane to be determined.
Figure 1

Ion exchange isotherms for the system (K+/Ca2+), C0 = 0.1 mol/L.

Figure 1

Ion exchange isotherms for the system (K+/Ca2+), C0 = 0.1 mol/L.

Figure 2

Ion exchange isotherms for the system (Na+/K+), C0 = 0.1 mol/L.

Figure 2

Ion exchange isotherms for the system (Na+/K+), C0 = 0.1 mol/L.

Figure 3

Ion exchange isotherms for the system (Na+/Ca2+), C0 = 0.1 mol/L.

Figure 3

Ion exchange isotherms for the system (Na+/Ca2+), C0 = 0.1 mol/L.

The analysis of the ion exchange isotherms given in Figures 13 shows that the CMX membrane is more selective for potassium ions than calcium and sodium ions. The obtained affinity order is: . These results were in agreement with the study of Hannachi et al. (2009), using the same membrane at a total concentration equal to 0.1 mol/L and at a constant temperature of 298 K. Maining & Melshelmer (1983) also found this affinity order for the Nafion cationic exchange membrane type at a total concentration varying from 0.04 to 0.3 mol /L and at a temperature of 298 K.

To explain the CMX membrane selectivity for the system , Bessière et al. (1999) concluded that the cation exchange membranes (CMI, CM2 and Nafion 117) prefer the lowest molar hydrated volume (VH(Na+) = 51 cm3/mol > VH(K+) = 18 cm3/mol).

For the system, the CMX membrane is more selective for the calcium ions than sodium ions at 283, 298 and 313 K. Poilbout et al. (2000) and Ersoz et al. (2001) explained this behavior by the fact that for sufficiently dilute solutions the affinity of the membrane increases when the charge (z) of the counter ion increases, because the attractive electrostatic attraction between the functional groups and counter ions is important as the valence of the ions is higher. This phenomenon is called electroselectivity. These results were observed by Lee et al. (2007) when they studied the ion exchange equilibrium between Amberlite IR 120 resin and binary systems , and at 283 and 303 K. They concluded that the affinity of this resin for the metal ions increases with increasing temperature. Guesmi et al. (2010) studied the effect of temperature on ion exchange equilibrium between the AMX anion exchange membrane and binary systems , and at 283, 298 and 313 K. They found that the affinity of the AMX membrane increases with temperature.

While the ion exchange membrane usually prefers the highly charged ions at dilute solution, an anomaly in the affinity order is observed and a selectivity reversal has taken place for the system, and the CMX membrane presents more selectivity for potassium than calcium. This result is in agreement with the study of Maining & Melshelmer (1983) and Hannachi et al. (2009).

Selectivity coefficients

For the binary ion exchange equilibrium given by Equation (5): 
formula
5

where and are the valences of the ionic species A and B, respectively, and the notations m and s indicate the ion in the solution and in the membrane phase, respectively.

According to this equilibrium, the selectivity coefficients can be determined at different temperatures as given in Equation (6): 
formula
6
where and are the valences of the ionic species A and B,

The calculated values of selectivity coefficient for the studied systems are illustrated in Table 2.

Table 2

Values of the selectivity coefficients

Temperature (K) KK+Na+ KCa2+2Na+ KCa2+2K+ 
283 1.245 1.66 0.101 
298 2.679 2.31 0.400 
313 3.705 3.58 0.800 
Temperature (K) KK+Na+ KCa2+2Na+ KCa2+2K+ 
283 1.245 1.66 0.101 
298 2.679 2.31 0.400 
313 3.705 3.58 0.800 

The obtained values show that the selectivity coefficients are related to the temperature and they increase when it increases. This is due to the endothermic ion exchange reactions as concluded by Guesmi et al. (2010).

Thermodynamic equilibrium constant

The thermodynamic equilibrium constant for the ion exchange equilibrium is usually defined as: 
formula
7
where and are the activities of ionic species in solution and in the membrane.
The thermodynamic equilibrium constant is related to the selectivity coefficient by: 
formula
8
where and are the activity coefficient of different species in the solution and the membrane, respectively.
Activity coefficients of different species in the solution can be calculated using the Debye–Hückel equation (Hamrouni & Dhahbi 2001): 
formula
9
where Zi is the ion charge; ai is the hydrated radius of the ion i; bi is the correction coefficient; I is the ionic strength of the solution; A and B are the constants for the solvent and essentially depend on the temperature.
The activity coefficients in the membrane phase were calculated using the Wilson equations (Petrus & Warchol 2003): 
formula
10
 
formula
11
ΛAB and ΛBA are the Wilson binary interaction parameters.

The calculated values of thermodynamic equilibrium constants are given in Table 3. The results show that for all systems at different temperatures.

Table 3

Experimental values of thermodynamic equilibrium constants for the CMX membrane

Temperature (K) 283 298 313 
Systems A-B KA°B KA°B KA°B 
 7.49 26.32 61.99 
 0.027 0.061 0.169 
 26.33 44.12 88.201 
Temperature (K) 283 298 313 
Systems A-B KA°B KA°B KA°B 
 7.49 26.32 61.99 
 0.027 0.061 0.169 
 26.33 44.12 88.201 

Thermodynamic parameters of the ion exchange equilibrium

At equilibrium, the variation of standard free enthalpy change of the ion exchange system reaction CMX membrane/system (A/B) is defined by the following equation: 
formula
12
where R is the the universal gas constant; T is the absolute temperature (Kelvin).
can also be defined as: 
formula
13
where is the standard enthalpy change of the reaction; is the standard entropy change of the reaction.
The combination of Equations (12) and (13) gives the following equation which can be used to determine the thermodynamic parameters and : 
formula
14
The standard enthalpy change and standard entropy change were determined from the curve giving the variation of versus presented in Figure 4. The obtained results are given in Table 4.
Figure 4

Graphical representation of the Van't Hoff equation.

Figure 4

Graphical representation of the Van't Hoff equation.

Table 4

Standard thermodynamic parameters for the binary systems (Na+/K+), (K+/Ca2+) and (Na+/Ca2+)

System A-B T (K) ΔGT° (kJ/mol) ΔHT° (kJ/mol) ΔST° (J/mol K) 
 283 –4.73 51.98 200.78 
298 –8.10 
313 –10.73 
 283 2.09 29.57 131.3612 
298 –1.9 
313 –4.5 
 283 –7.69 64.59 221.56 
298 –9.38 
313 –11.65 
System A-B T (K) ΔGT° (kJ/mol) ΔHT° (kJ/mol) ΔST° (J/mol K) 
 283 –4.73 51.98 200.78 
298 –8.10 
313 –10.73 
 283 2.09 29.57 131.3612 
298 –1.9 
313 –4.5 
 283 –7.69 64.59 221.56 
298 –9.38 
313 –11.65 

The analysis of the data presented in Table 4 shows that the value of are positive, this indicates that the ion exchange process between the CMX membrane and the studied binary systems , and is an endothermic process.

The standard entropy in this study is found to be positive; it means that an increase in the randomness appeared on the membrane/solution interface during the ion exchange reaction.

CONCLUSIONS

The effect of temperature on ion exchange equilibrium for the binary systems , and was studied. The affinity order for the CMX membrane for the studied temperatures was . The selectivity coefficients , and were determined. Obtained results show that these coefficients increase with the rise of temperature. Thermodynamic equilibrium constants and the thermodynamic parameters of the ion exchange equilibrium were calculated. Ion exchange equilibrium at temperatures 283, 298 and 313 K of the studied binary systems were found to be an endothermic process, as the positive enthalpy indicates. The negative values of the standard free enthalpy change confirm that the ion exchange process is spontaneous in the standard conditions.

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