Determination of the Hydrolysis Constants and Solubility Product of Chromium(III) from Reduction of Dichromate Solutions by ICP-OES and UV–Visible Spectroscopy

Abstract

The determination of equilibrium constants is difficult when several chemical species are simultaneously present in solution. In this investigation, optical emission spectroscopic determinations of chromium(III) concentration in a 10⁻⁴ mol⋅dm⁻³ solution, prepared from K₂Cr₂O₇ reduced in HNO₃ or HCl media, were used to construct the pCr_(aq)–pC _H diagram. This diagram was used to calculate the pC _H borderline of precipitation, to estimate the solubility product $(\log_{10}K_{\mathrm{sp,Cr(OH)}_{3}}^{*})$, and the hydrolysis constants $(\log_{10}\beta_{\mathrm{Cr,H}}^{*},\log_{10}\beta_{\mathrm{Cr,2H}}^{*}$, and $\log_{10}\beta_{\mathrm{Cr,3H}}^{*})$ of Cr(III). The hydrolysis constants were also calculated using the SQUAD and SUPERQUAD software, along with the average ligand number method. UV-Vis absorption data and associated variables were used in SQUAD, SUPERQUAD, and the average ligand calculations. Results are: 9.00±0.04 for the pC _H at the onset of precipitation, 12.40 for $\log_{10}K_{\mathrm{sp,Cr(OH)}_{3}}^{*}$, −3.52±0.02 for $\log_{10}\beta_{\mathrm{Cr,H}}^{*}$, −9.30±0.87 for $\log_{10}\beta_{\mathrm{Cr,2H}}^{*}$ and −17.18±0.16 for $\log_{10}\beta_{\mathrm{Cr,3H}}^{*}$, respectively. All methods produced essentially the same values for the hydrolysis constants of Cr(III).