J. Chem. Soc., Faraduy Trans. I, 1982, 78, 283-287 Enthalpies of Mixing of Simple Electrolyte Solutions with Sodium Carboxymethylcellulose BY PHILIP W. HALES AND GEOFFREY PASS* Department of Chemistry and Applied Chemistry, University of Salford, Salford M5 4WT Received 26th February, I98 1 The enthalpies of mixing have been determined for the reaction between aqueous solutions of two samples of sodium carboxymethylcellulose with different degrees of substitution and aqueous solutions of lithium chloride, sodium chloride, and potassium chloride. The effect of temperature on the enthalpy of mixing has also been investigated. The results are compared with the predictions of the line-charge theory. Mixing solutions containing lithium and sodium ions gives an additional endothermic contribution to the reaction, while mixing solutions containing potassium and sodium ions gives an additional exothermic contribution to the reaction. The enthalpy change occurring when solutions containing a polyelectrolyte and a simple electrolyte containing the same cation are mixed does not obey a simple additivity rule.Although the enthalpies of dilution of the polyelectrolyte and the simple electrolyte are negative, corresponding to an exothermic process, the enthalpy of mixing of the two solutions is found to be p0sitive.l Good agreement was found between experimental values and values calculated from an expression derived from the line-charge theory.2 More recent measurements have shown a dependence of the enthalpy of mixing on the nature of the ~ a t i o n .~ The line-charge theory assumes that as the charge on a polyelectrolyte is increased a critical value is reached, above which counter-ions are condensed on to the polyelectrolyte and limit the increase in effective charge. The results so far reported for the enthalpies of mixing of polyelectrolytes refer to polystyrenesulphonates, in which a considerable proportion of the counter-ions is taken to be condensed on to the polyanion. Measurement of the enthalpy of mixing of a polyelectrolyte with low linear charge would not only extend the range of polyelectrolyte charge over which the expression might apply but comparison with a similar polyelectrolyte with a linear charge above the critical value may help to establish the validity of the assumption regarding c~ndensation.~-~ The enthalpies of mixing of two samples of sodium carboxymethylcellulose, with different degrees of substitutions above and below the critical value, have been measured.The influence of the cation has been investigated by using solutions containing like cations and solutions containing unlike cations. The influence of temperature was also investigated. EX P E R I M E N T A I, Two samples of sodium carboxymethylcellulose, (4M6F) and (7L2P) were supplied by the Hercules Co. The samples were dialysed for 48 h against distilled water before use. Lithium chloride, sodium chloride and potassium chloride were dried at 105 O C for 48 h before use. A stock solution of each chloride was prepared containing 16 x lop2 mol dm-3. Aliquots of these solutions were diluted as required.Since the enthalpies of mixing were found to depend on the 283 10-2284 ENTHALPIES OF MIXING OF SIMPLE ELECTROLYTES initial concentration of the p~lyelectrolyte,~ all the enthalpies of mixing in the present work were determined by mixing equal volumes of polyelectrolyte solutions of constant concentration (1 x mol dm-3). Enthalpies of dilution of the salt solutions were also determined. Calorimetric measurements were made using a flow calorimeter (LKB Produkter, Bromma, Sweden, model 2107) and the procedure previously described.' mol dm-3) and salt solutions with a range of concentrations (16 x 1OP2-1 x RESULTS AND DISCUSSION A theoretical model2 has been developed to explain the behaviour of polyelectrolytes in aqueous solution in terms of a linear charge parameter, <, defined for monovalent charged groups and counter-ions as e2 ' = 4m,DkTb where e is the charge on the proton, D is the bulk dielectric constant of water, b is the average distance between charged groups, k is Boltzmann's constant and T is the thermodynamic temperature.An expression for the enthalpy change when a polyelectrolyte is mixed with a salt solution containing the same counter-ion has been derivedl from the line-charge model : (1) where in addition to the terms defined above n = 1 when 5 < 1 and n = - 1 when < > 1 , mE, is the final polyelectrolyte concentration, ma is the initial polyelectrolyte concentration, mi is the final salt concentration, a = 1 when < < 1 and a = < when 5 > 1.According to the charge model, when < > 1 a sufficient proportion of counter-ions will condense on to the polyelectrolyte to give an effective linear charge -2.303RTr"( 1 +-- TdD) log,, m; + 2am; 2 D d T mT, AHmi, = FIG. 1.-Enthalpy of mixing of NaCMC with alkali metal chlorides at 25 OC: 0, LiCI+NaCMC 4M; x , LiClfNaCMC 7L; a, NaCl+NaCMC 4M; ., NaCl+NaCMC 7L; 0, KCl+NaCMC 4M; A, KCI + NaCMC 7L. Broken line shows calculated values.P. W. HALES AND G. PASS 285 parameter of unity. Condensation results in a smaller fraction of the counter-ions, c-l, having Debye-Huckel interactions with the polyion. Two samples of sodium carboxymethylcellulose (NaCMC) were selected with different degrees of substitution (d.s.). One sample, NaCMC 4M6F, had d.s. = 0.45. The second sample, NaCMC 7L2P, had d.s.= 0.83. Taking the lengths of an anhydroglucose unit in the poly- electrolyte as 0.5 15 nm, eqn (1) gives values of 5 = 0.64 and 5 = 1.15 for NaCMC 4M6F and NaCMC 7L2P, respectively. The enthalpy changes occurring when aqueous solutions of the two samples of NaCMC were mixed with solutions of simple electrolyte at 25 "C have been measured and the results are plotted in fig. 1. The experimental values are corrected for the enthalpy of dilution of the simple electrolyte. In order to compare the results for the two samples of NaCMC different ordinate scales are used; these are suitably selected so that the theoretical values calculated from eqn (1) for the two values of 4: fit the same straight line. When plotted in this way the enthalpies of mixing of the different NaCMC samples with the same simple electrolyte give overlapping plots.Since one of the samples of NaCMC has a value of 5 > I , when condensation of a proportion of counter-ions is assumed to occur and is allowed for in eqn (l), the good agreement with the other sample where 5 < 1 and no condensation occurs appears to confirm the predictions of theory with regard to condensation and the dependence of the enthalpy of mixing on the linear charge parameter. The results in fig. 1 suggest that even when simple electrolyte and polyelectrolyte containing the same cation are mixed interactions occur which are not covered by the theoretical assumptions. The effects become more pronounced when simple electrolyte and polyelectrolyte containing different cations are mixed, as shown by the results of mixing lithium chloride and potassium chloride with the two samples of NaCMC.The different effects produced by the three cations are shown in fig. 2 where the additional molar enthalpy change of added cation is plotted against the amount of added cation. If the mixing behaviour was fully interpreted by eqn (1) all the FIG. 2.-Excess enthalpy of mixing of NaCMC with alkali metal chlorides at 25 OC: 0, LiCl+NaCMC 4M; x , LiCl+NaCMC 7L; 0 , NaCl+NaCMC 4M; W, NaCl+NaCMC 7L; 0, KClfNaCMC 4M; A, KCl+NaCMC 7L.286 ENTHALPIES OF M I X I N G OF SIMPLE ELECTROLYTES experimental points should lie on the abscissa. Mixing of sodium chloride with NaCMC shows an exothermic shift from the theoretical value which has only a small dependence on the amount of added sodium chloride.The effect is slightly increased when the linear charge parameter is increased. In the case of lithium chloride mixed with NaCMC, where an endothermic effect is observed, and potassium chloride mixed with NaCMC, where an exothermic effect is observed, there is a greater dependence of the additional enthalpy change on the concentration of the simple salt, and the influence of the linear charge parameter also increases at the lower concentration of simple salt. The enthalpies of mixing simple electrolyte with NaCMC 4M6F were also determined at 40 O C and the results are plotted in fig. 3. The enthalpy of mixing of sodium chloride with NaCMC gives greatly improved agreement with the theoretical values compared with fig.I . The results obtained from mixing potassium chloride with NaCMC a t the higher temperature are also shifted towards the theoretical line but the results obtained with lithium chloride and NaCMC at the higher temperature show greater divergence from the theoretical values. log,, [(mi i- 2CX/?Z~)/t??b ] FIG. 3.-Enthalpy of mixing of NaCMC 4M with alkali metal chlorides at 40 OC: 0, LiCl; x , NaC1; 0, KCl. Broken line shows calculated values. The results for the mixing of sodium chloride with the samples of NaCMC are similar to the results recently reported for the mixing of sodium chloride with sodium poly(styrene sulphonate), which also show an exothermic shift from the calculated value^.^ Investigation of the volume changes occurring in the interaction between counter-ions and polyions has led to the conclusion that only counter-ions which are condensed onto the polyanion undergo a change in hydration.9+ The enthalpy changes observed when solutions of simple electrolytes are mixed have been interpretedP.W. HALES AND G. P A S S 287 in terms of a contribution to the overall enthalpy change from changes in the water structure associated with the different ions.ll Thus for the mixing of sodium chloride with NaCMC 4M6F, where 5 = 0.64 and there is no counter-ion condensation, a change in the overall water structure when the cations move from bulk solution into the ion atmosphere of the polyanion is a possible cause of the additional enthalpy effect. In this respect it is significant that additional enthalpy effects have the opposite sign for dilution of the ion atmosphere of the polyion.12 The greatly improved agreement between experimental and calculated values for the mixing of sodium chloride with NaCMC 4M6F at 40 "C is consistent with a decreased contribution from water-structure effects at the higher temperature.When polyelectrolyte and simple salt containing unlike cations are mixed a contribution from changes in water structure is again to be expected. There is also the further possibility of a mixing or exchange reaction between the sodium ions in the ion atmosphere of the polyanion and lithium or potassium ions in the bulk solution. An exchange reaction of this type might be responsible for the cmcentration dependence of the additional enthalpy effects shown in fig.2. The molar enthalpy contribution of added cation showing a marked decrease as equilibrium is established between mixed cations in the ion atmosphere of the polyanion and mixed cations in the bulk solution. The results in fig. 3 are also consistent with such a reaction scheme. Thus the extent of the endothermic reaction involving lithium chloride is increased and the extent of the exothermic reaction involving potassium chloride is decreased as the reaction temperature is increased. As the concentration of added cation is increased the molar enthalpy change decreases and approaches the values obtained for mixing of simple salts with unlike cations.ll G. E. Boyd, D. P. 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