Dissociation Constants for Citric Acid in NaCl and KCl Solutions and their Mixtures at 25 °C

Abstract

The constants for the dissociation of citric acid (H₃C) have been determined from potentiometric titrations in aqueous NaCl and KCl solutions and their mixtures as a function of ionic strength (0.05–4.5 mol-dm⁻³) at 25 °C. The stoichiometric dissociation constants (K _i ^*)

$$\eqalign{ & {\text{H}}_3 {\text{C}} \rightleftharpoons {\text{H}}^ + + {\text{H}}_2 {\text{C}}^ - ,\quad {\text{K}}_{\text{1}}^{\text{*}} = {{{\text{K}}_1 \gamma ({\text{H}}_3 {\text{C}})} \mathord{\left/ {\vphantom {{{\text{K}}_1 \gamma ({\text{H}}_3 {\text{C}})} {\left\{ {\gamma ({\text{H}}^ + )\gamma ({\text{H}}_2 {\text{C}}^ - )} \right\}}}} \right. \kern-\nulldelimiterspace} {\left\{ {\gamma ({\text{H}}^ + )\gamma ({\text{H}}_2 {\text{C}}^ - )} \right\}}} \cr & {\text{H}}_2 {\text{C}}^ - \rightleftharpoons {\text{H}}^ + + {\text{HC}}^{2 - } ,\quad {\text{K}}_{\text{2}}^{\text{*}} = {{{\text{K}}_2 \gamma ({\text{H}}_2 {\text{C}}^ - )} \mathord{\left/ {\vphantom {{{\text{K}}_2 \gamma ({\text{H}}_2 {\text{C}}^ - )} {\left\{ {\gamma ({\text{H}}^ + )\gamma ({\text{HC}}^{2 - } )} \right\}}}} \right. \kern-\nulldelimiterspace} {\left\{ {\gamma ({\text{H}}^ + )\gamma ({\text{HC}}^{2 - } )} \right\}}} \cr & {\text{HC}}^{2 - } \rightleftharpoons {\text{H}}^ + + {\text{C}}^{3 - } ,\quad {\text{K}}_{\text{3}}^{\text{*}} = {{{\text{K}}_3 \gamma ({\text{HC}}^{2 - } )} \mathord{\left/ {\vphantom {{{\text{K}}_3 \gamma ({\text{HC}}^{2 - } )} {\left\{ {\gamma ({\text{H}}^ + )\gamma ({\text{C}}^{3 - } )} \right\}}}} \right. \kern-\nulldelimiterspace} {\left\{ {\gamma ({\text{H}}^ + )\gamma ({\text{C}}^{3 - } )} \right\}}} \cr}$$

were used to determine Pitzer parameters for citric acid (H₃C), and the anions, H₂C⁻, HC²⁻, and C³⁻. The thermodynamic constants (K _i ) needed for these calculations were taken from the work of R. G. Bates and G. D. Pinching (J. Amer. Chem. Soc. 71, 1274; 1949) to fit to the equations (T/K):

$$\eqalign{ & {\rm{ln }}K_1 = - 646.52280{\rm{ + }}{{{\rm{14264}}{\rm{.1855}}} \over T}{\rm{ + 115}}{\rm{.34510 ln }}T - 0.2204T{\rm{, }}\;\sigma {\rm{ = 0}}{\rm{.0032}} \cr & {\rm{ln }}K_2 = - 52.19970{\rm{ + }}{{{\rm{1842}}{\rm{.97387}}} \over T}{\rm{ + 11}}{\rm{.19421 ln }}T - 0.05487T{\rm{, }}\;\sigma {\rm{ = 0}}{\rm{.0023}} \cr & {\rm{ln }}K_3 = - 129.89305{\rm{ + }}{{{\rm{394}}{\rm{.04129}}} \over T}{\rm{ + 25}}{\rm{.36088 ln }}T - 0.09394T{\rm{, }}\;\sigma {\rm{ = 0}}{\rm{.0021}} \cr}$$

The values of Pitzer interaction parameters for Na⁺ and K⁺ with H₃C, H₂C⁻, HC²⁻, and C³⁻ have been determined from the measured pK values. These parameters represent the values of pK₁^*, pK₂^*, and pK₃^*, respectively, with standard errors of σ = 0.003–0.006, 0.015–0.016, and 0.019–0.023 for the first, second, and third dissociation constants. A simple mixing of the pK^* values for the pure salts in dilute solutions yield values for the mixtures that are in good agreement with the measured values. The full Pitzer equations are necessary to estimate the values of pK _i ^* in the mixtures at high ionic strengths. The interaction parameters found for the mixtures are Ψ_{Na-K − H2C} = − 0.00823 ± 0.0009; Ψ_{Na-K − HC} = − 0.0233 ± 0.0009, and Ψ_{Na-K − C} = 0.0299 ± 0.0055 with standard errors of σ(pK₁) = 0.011, σ(pK₂) = 0.011, and σ(pK₃) = 0.055.