Chapter 14, Problem 14.80QE

Interpretation Introduction

Interpretation:

Whether the precipitate would form if $20\text{ mL}$ of $1.0\times {10}^{-6}M{\text{ MgCl}}_{\text{2}}$ is added to $80\text{ mL}$ of $1.0\times {10}^{-6}M\text{ KF}$ or not has to be determined.

Concept Introduction:

Solubility product is the equilibrium constant for the 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:

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

The general equilibrium reaction is as follows:

  $a\text{A}+b\text{B}\rightleftharpoons c\text{C}+d\text{D}$

Here,

$\text{A}$ and $\text{B}$ are the reactants.

$\text{C}$ and $\text{D}$ are products.

$a$ and $b$ are the stoichiometric coefficients of reactants.

$c$ and $d$ are the stoichiometric coefficients of products.

The expression of the reaction quotient for the above reaction is as follows:

  $Q=\frac{{\left[\text{C}\right]}^c{\left[\text{D}\right]}^d}{{\left[\text{A}\right]}^a{\left[\text{B}\right]}^b}$

Here,

$Q$ is the reaction quotient.

$\left[\text{C}\right]$ is the concentration of $\text{C}$.

$\left[\text{D}\right]$ is the concentration of $\text{D}$.

$\left[\text{A}\right]$ is the concentration of $\text{A}$.

$\left[\text{B}\right]$ is the concentration of $\text{B}$.

The prediction of precipitate formation occurs as follows:

(1) If $Q$ is less than $K_{\text{sp}}$ then precipitation will not occur and no precipitates are formed.

(2) If $Q$ is greater than $K_{\text{sp}}$ then precipitation occurs and therefore precipitates are formed.

(3) If $Q$ is equal to $K_{\text{sp}}$ then the solution is saturated and no change takes place in it.