Chapter 17, Problem 17.140MP

Interpretation Introduction

Interpretation:

The value of $K$ for the following reaction is to be calculated.

${\text{Ca}}_{\text{5}}{\left({\text{PO}}_{\text{4}}\right)}_{\text{3}}\text{OH}\left(s\right)+{\text{F}}^{-}\left(aq\right)\rightleftharpoons {\text{Ca}}_{\text{5}}{\left({\text{PO}}_{\text{4}}\right)}_{\text{3}}\text{F}\left(s\right)+{\text{OH}}^{-}\left(aq\right)$

Concept introduction:

Solubility product is the equilibrium constant for a reaction that occurs when an ionic compound is dissolved to produce its constituent ions. It is represented by $K_{\text{sp}}$. Consider ${\text{A}}_x{\text{B}}_y$ to be an ionic compound. Its dissociation occurs as follows:

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

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 an ion that contains a metal cation bonded to one or more small ions. The formation of a complex ion is a stepwise process and each step has its own equilibrium constant. The stability of a complex ion is measured by formation constant $K_{\text{f}}$.

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

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