Chapter 17, Problem 17.120SP

Interpretation Introduction

Interpretation:

The fraction of uncomplexed ${\text{Cr}}^{3+}$ in a solution is to be calculated.

Concept introduction:

Solubility product is equilibrium constant for reactions that occur when an ionic compound is dissolved to produce ions. It is denoted by $K_{\text{sp}}$. Consider ${\text{A}}_x{\text{B}}_y$ is an ionic compound. Its dissociation occurs as:

${\text{A}}_x{\text{B}}_y\rightleftharpoons x{\text{A}}^{y+}+y{\text{A}}^{x-}$

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

$K_{\text{sp}}={\left[{\text{A}}^{y+}\right]}^x{\left[{\text{B}}^{x-}\right]}^y$

A complex ion is ion that contains a metal cation bonded to one or more small ions. The formation of complex ion is generally a stepwise procedure and each step has its equilibrium constant. The stability of complex ion is measured by formation constant $\left(K_{\text{f}}\right)$.

The relation between $K_{\text{f}}$, $K_{\text{sp}}$ and $K$ is as follows:

$K=K_{\text{f}}\cdot K_{\text{sp}}$