Chapter 17, Problem 17.131QP

Interpretation Introduction

Interpretation:

The precipitation of silver compounds have to be explained using the given data has to be explained.

Concept introduction:

• The solubility product constant ( ${\text{K}}_{\text{sp}}$) is defined as the equilibrium between compound and its ions in an aqueous solution.
• Solubility product is the multiplication of concentration of dissolved ion,  raised to the power of coefficients.
• Formation of solid from solution is called precipitation

To determine: The concentration of silver ion in $\text{AgBr}$

Answer to Problem 17.131QP

${\text{AgBr}}_{\text{(s)}}$ can precipitate first due to least solubility product constant ( ${\text{K}}_{\text{sp}}$) followed by ${\text{Ag}}_{\text{2}}{\text{CO}}_{\text{3}}$ and then last ${\text{Ag}}_{\text{2}}{\text{SO}}_{\text{4}}$ (high ${\text{K}}_{\text{sp}}$).

Explanation of Solution

The concentration of silver ion in $\text{AgBr}$ is determined below.

Solubility product constant ( ${\text{K}}_{\text{sp}}$) of $\text{AgBr}$ is $7.7\times {10}^{-13}$

$\begin{array}{l}{\text{AgBr}}_{\text{(s)}}\to {\text{Ag}}^{\text{+}}{}_{\text{(aq)}}{\text{ + Br}}^{\text{-}}{}_{\text{(aq)}}\\ \text{Initial (M): }\text{0 }\text{0}\text{.1}\\ \text{Change (M):}\text{-x}\text{+x}\text{+x}\\ \text{Equilibrium (M): }\text{x }\text{0}\text{.1 + x}\\ {\text{K}}_{\text{sp}}\text{ = (x)(0}\text{.1+x)}\approx \text{ 0}\text{.1x}\\ \text{7}\text{.7}\text{×}{\text{10}}^{\text{-13}}\text{=}\text{0}\text{.1x}\\ \text{x}\text{=}\text{7}\text{.7}\text{×}{\text{10}}^{\text{-12}}\text{M}\\ [{\text{Ag}}^{\text{+}}]\text{=}\text{7}\text{.7}\text{×}{\text{10}}^{\text{-12}}\text{M}\end{array}$

To determine: The concentration of silver ion in ${\text{Ag}}_{\text{2}}{\text{CO}}_{\text{3}}$

The concentration of silver ion in ${\text{Ag}}_{\text{2}}{\text{CO}}_{\text{3}}$ is determined below.

Solubility product constant ( ${\text{K}}_{\text{sp}}$) of ${\text{Ag}}_{\text{2}}{\text{CO}}_{\text{3}}$ is $8.1\times {10}^{-12}$

$\begin{array}{l}{\text{Ag}}_{\text{2}}{\text{CO}}_{\text{3}}{}_{\text{(s)}}\to 2{\text{Ag}}^{\text{+}}{}_{\text{(aq)}}{\text{ + CO}}_{\text{3}}{{}^{\text{2-}}}_{\text{(aq)}}\\ \text{Initial (M): }\text{0 }\text{0}\text{.1}\\ \text{Change (M):}\text{-x}\text{+2x}\text{+x}\\ \text{Equilibrium (M): }2\text{x }\text{0}\text{.1 + x}\\ {\text{K}}_{\text{sp}}{\text{ = (2x)}}^{\text{2}}\text{(0}\text{.1+x)}\approx \text{ 0}{\text{.4x}}^{\text{2}}\\ 8.1\text{×}{\text{10}}^{\text{-12}}\text{=}\text{0}{\text{.4x}}^{\text{2}}\\ \text{x}\text{=}4.5\text{×}{\text{10}}^{\text{-6}}\text{M}\\ {\text{[Ag}}^{\text{+}}\text{]}\text{=}\text{2x}\text{=}9.0\text{×}{\text{10}}^{\text{-6}}\text{M}\end{array}$

To determine: The concentration of silver ion in ${\text{Ag}}_{\text{2}}{\text{SO}}_{\text{4}}$.

The concentration of silver ion in ${\text{Ag}}_{\text{2}}{\text{SO}}_{\text{4}}$ is determined below.

Solubility product constant ( ${\text{K}}_{\text{sp}}$) of ${\text{Ag}}_{\text{2}}{\text{SO}}_{\text{4}}$ is $1.5\times {10}^{-5}$

$\begin{array}{l}{\text{Ag}}_{\text{2}}{\text{SO}}_{\text{4}}{}_{\text{(s)}}\to 2{\text{Ag}}^{\text{+}}{}_{\text{(aq)}}{\text{ + SO}}_{\text{4}}{{}^{\text{2-}}}_{\text{(aq)}}\\ \text{Initial (M): }\text{0 }\text{0}\text{.1}\\ \text{Change (M):}\text{-x}\text{+2x}\text{+x}\\ \text{Equilibrium (M): }2\text{x }\text{0}\text{.1 + x}\\ {\text{K}}_{\text{sp}}{\text{ = (2x)}}^{\text{2}}\text{(0}\text{.1+x)}\approx \text{ 0}{\text{.4x}}^{\text{2}}\\ 1.5\text{×}{\text{10}}^{\text{-5}}\text{=}\text{0}{\text{.4x}}^{\text{2}}\\ \text{x}\text{=}6.1\text{×}{\text{10}}^{\text{-3}}\\ {\text{[Ag}}^{\text{+}}\text{]}\text{=}\text{2x}\text{=}1.2\text{×}{\text{10}}^{\text{-2}}\text{M}\end{array}$

${\text{AgBr}}_{\text{(s)}}$ can precipitate first due to least solubility product constant ( ${\text{K}}_{\text{sp}}$) followed by ${\text{Ag}}_{\text{2}}{\text{CO}}_{\text{3}}$ and then last ${\text{Ag}}_{\text{2}}{\text{SO}}_{\text{4}}$ (high ).

Conclusion

The precipitation of silver compounds have to be explained using the given data was explained.