Chapter 17, Problem 1PE

What are the ion product expressions for the following salts: (a) lead(II) bromide, (b) aluminum hydroxide? (Hint: Remember that they are heterogeneous equilibria.)

Interpretation Introduction

Interpretation:

The expression for the ionic product of the given salts is to be determined.

Concept Introduction:

Electrolytes have the ability to dissociate themselves into their respective ions. If the product of the concentration of these ions is raised to their coefficients, according to their balanced chemical equation, then the resultant expression called the ionic product of the electrolyte and is denoted as $K_{\text{sp}}$.

Answer to Problem 1PE

Solution:

a) $K_{\text{sp}}=\left[{\text{Pb}}^{2+}\right]{\left[{\text{Br}}^{-}\right]}^2$

b) $K_{\text{sp}}=\left[{\text{Al}}^{3+}\right]{\left[{\text{OH}}^{-}\right]}^3$

Explanation of Solution

a) Lead (II) Bromide.

The dissociation of ${\text{PbBr}}_2$ is:

${\text{PbBr}}_2\left(s\right)\rightleftharpoons {\text{Pb}}^{2+}\left(aq\right)+2{\text{Br}}^{-}\left(aq\right)$

The ionic product expression is:

$K_{\text{sp}}=\left[{\text{Pb}}^{2+}\right]{\left[{\text{Br}}^{-}\right]}^2$

The above expression gives information about the ions and their coefficients that are present in the respective compound. Proper balanced equation of the dissociation of the compound must be known for determining the expression for its ionic product. The ionic product of Lead (II) Bromide explains that the ${\text{PbBr}}_2$ consists of one lead ion $\left({\text{Pb}}^{2+}\right)$ and two bromide ions $\left(2{\text{Br}}^{-}\right)$

b) Aluminum Hydroxide

The dissociation of $\text{Al}{\left(\text{OH}\right)}_3$ is:

$\text{Al}{\left(\text{OH}\right)}_3\left(s\right)\rightleftharpoons {\text{Al}}^{3+}\left(aq\right)+2{\text{OH}}^{-}\left(aq\right)$

The ionic product expression is:

$K_{\text{sp}}=\left[{\text{Al}}^{3+}\right]{\left[{\text{OH}}^{-}\right]}^3$

The above expression gives information about the ions and their coefficients that are present in the respective compound. Proper balance equation of the dissociation of the compound must be known for determining the expression of its ionic product. The ionic product of Aluminum Hydroxide explains that the $\text{Al}{\left(\text{OH}\right)}_3$ consists of one aluminum ion $\left({\text{Al}}^{3+}\right)$ and three hydroxide ions $\left(3{\text{OH}}^{-}\right)$