The Examination of the Activity Coefficients of Cu(II) Complexes with OH⁻ and Cl⁻ in NaClO₄ Using Pitzer Equations: Application to Other Divalent Cations

Abstract

The stability constants for the hydrolysis of Cu(II) and formation of chloride complexes in NaClO₄ solution, at 25 °C, have been examined using the Pitzer equations. The calculated activity coefficients of CuOH⁺, Cu(OH)₂, Cu₂(OH)³⁺, Cu₂(OH) ²⁺₂ , CuCl⁺ and CuCl₂ have been used to determine the Pitzer parameter (β ⁽⁰⁾ _i , β ⁽¹⁾ _i , and C _i ) for these complexes. These parameters yield values for the hydrolysis constants (log ₁₀ β ^*₁ , log ₁₀ β ^*₂ , log ₁₀ β ^*_2,1 and log ₁₀ β ^*_2,2 ) and the formation of the chloride complexes (log ₁₀ β ^*_CuCl and $\log_{10}\beta_{\mathrm{CuCl}_{2}}^{\mathrm{*}})$ that agree with the experimental measurements, respectively to ±0.01,±0.02,±0.03,±0.06,±0.03 and ±0.07.

The stability constants for the hydrolysis and chloride complexes of Cu(II) were found to be related to those of other divalent metals over a wide range of ionic strength. This has allowed us to use the calculated Pitzer parameters for copper complexes to model the stability constants and activity coefficients of hydroxide and chloride complexes of other divalent metals. The applicability of the Pitzer Cu(II) model to the ionic strength dependence of hydrolysis of zinc and cadmium is presented. The resulting thermodynamic hydroxide and chloride constants for zinc are $\log_{10}\beta_{\mathrm{ZnOH}^{+}}=-9.04\pm0.04$ and $\log_{10}\beta_{\mathrm{Zn(OH)}_{2}}=-16.90\pm0.02$ . For cadmium the thermodynamic hydrolysis constants are $\log_{10}\beta_{\mathrm{CdOH}^{+}}=-10.24\pm0.05$ and $\log_{10}\beta_{\mathrm{Cd(OH)}_{2}}=-20.42\pm0.07$ . The Cu(II) model allows one to determine the stability of other divalent metal complexes over a wide range of concentration when little experimental data are available. More reliable stepwise stability constants for divalent metals are needed to test the linearity found for the chloro complexes.