Chapter 18, Problem 55E

Interpretation Introduction

Interpretation:

Whether the given ion concentration can be maintained in the solution without forming any precipitation or not should be explained.

Concept introduction:

The reaction of ${\text{Ag}}^{\text{+}}\text{(aq)}$ and ${\text{2S}}_{\text{2}}{\text{O}}_{\text{3}}{}^{\text{2-}}\text{(aq)}$ is represented as follows:

${\text{Ag}}^{\text{+}}{\text{(aq) + 2S}}_{\text{2}}{\text{O}}_{\text{3}}{}^{\text{2-}}\text{(aq)}\rightleftharpoons {\left(\text{Ag}{\left({\text{S}}_{\text{2}}{\text{O}}_{\text{3}}\right)}_{\text{2}}\right)}^{\text{3-}}\text{(aq)}$

For the above reaction, the expression for ${\text{K}}_f$ can be written as follows:

${\text{K}}_f=\frac{\left[{\left(\text{Ag}{\left({\text{S}}_{\text{2}}{\text{O}}_{\text{3}}\right)}_{\text{2}}\right)}^{\text{3-}}\text{(aq)}\right]}{\left[{\text{Ag}}^{\text{+}}\text{(aq)}\right]{\left[{\text{S}}_{\text{2}}{\text{O}}_{\text{3}}{}^{\text{2-}}\text{(aq)}\right]}^2}$

The dissociation reaction of $\text{AgI(s)}$ is as follows:

$\text{AgI(s)}\rightleftharpoons {\text{Ag}}^{\text{+}}{\text{(aq) + I}}^{\text{-}}\text{(aq)}$

Thus, the value of ${\text{Q}}_{sp}$ will be:

${\text{Q}}_{sp}=\left[{\text{Ag}}^{\text{+}}\text{(aq) }\right]\left[{\text{I}}^{\text{-}}\text{(aq)}\right]$

Precipitation should occur if $Qsp>Ksp.$

Precipitation cannot occur if $Qsp<Ksp.$

A solution is just saturated if $Qsp=Ksp.$