Chapter 17, Problem 17.133SP

Interpretation Introduction

Interpretation:

Whether ${\text{Co}}^{2+}$ can be separated from ${\text{Zn}}^{2+}$ or not should be determined.

Concept introduction:

Solubility product in acid is equilibrium constant for reaction that occurs in acid solution when an ionic compound is dissolved to produce ions. It is represented by $K_{\text{spa}}$. Consider $\text{MS}$ an ionic compound dissolved in acidic solution. Its dissociation occurs as:

$\text{MS}\left(s\right)+{\text{2H}}_{\text{3}}{\text{O}}^{+}\left(aq\right)\rightleftharpoons {\text{M}}^{2+}\left(aq\right)+{\text{H}}_{\text{2}}\text{S}\left(aq\right)+{\text{2H}}_{\text{2}}\text{O}\left(l\right)$

The expression for its $K_{\text{spa}}$ is as follows:

$K_{\text{spa}}=\frac{\left[{\text{M}}^{2+}\right]\left[{\text{H}}_{\text{2}}\text{S}\right]}{\left[{\text{H}}_{\text{3}}{\text{O}}^{+}\right]}$

A precipitate of an ionic compound will form when solutions that contain respective ions are mixed. The precipitation depends on value of reaction quotient ${\text{Q}}_{\text{c}}$. ${\text{Q}}_{\text{c}}$ is defined in same way as $K_{\text{spa}}$. Also, concentrations in the expression for ${\text{Q}}_{\text{c}}$ are concentration at time t and not equilibrium concentrations. Consider $\text{MS}$ to be an ionic compound. Its dissociation occurs as:

$\text{MS}\left(s\right)+{\text{2H}}_{\text{3}}{\text{O}}^{+}\left(aq\right)\rightleftharpoons {\text{M}}^{2+}\left(aq\right)+{\text{H}}_{\text{2}}\text{S}\left(aq\right)+{\text{2H}}_{\text{2}}\text{O}\left(l\right)$

The expression for ${\text{Q}}_{\text{c}}$ is as follows:

${\text{Q}}_{\text{c}}=\frac{\left[{\text{M}}^{2+}\right]\left[{\text{H}}_{\text{2}}\text{S}\right]}{\left[{\text{H}}_{\text{3}}{\text{O}}^{+}\right]}$

Metal cations can be separated into two groups by the precipitation of metal sulfide. The cations which form very insoluble sulfides can be separated from cations which form soluble sulfides. The separation takes place in an acidic solution and use solubility equilibrium.

The separation depends on the ${\text{H}}_{\text{3}}{\text{O}}^{+}$ concentration so that reaction quotient ${\text{Q}}_{\text{c}}$ exceeds $K_{\text{spa}}$ for insoluble sulfides but not for soluble sulfide. As a result, insoluble sulfides precipitate under acidic condition but soluble sulfides remain in solution.