Chapter 5, Problem 5.51P

(a)

Interpretation Introduction

Interpretation:

The expression that shows the solubility’s ratio for $AgCl$ at two different temperatures has to be identified.

Concept Introduction:

The solubility constant $K_s$ is the equilibrium constant expressed for ionic equilibrium since pure solid does not come in equilibrium constant expression as its activity value is 1. The solubility constant expression for one general chemical reaction is as follows,

$\begin{array}{l}Consider,Ca{\left(OH\right)}_2\left(s\right)\rightleftharpoons C{a}^{2+}\left(aq\right)+2O{H}^{-}\left(aq\right)\\ now,K_s=\frac{a_{C{a}^{2+}}{a}^2{}_{O{H}^{-}}}{a_{Ca{\left(OH\right)}_2}}\\ =a_{C{a}^{2+}}{a}^2{}_{O{H}^{-}}\left(here,a_{Ca{\left(OH\right)}_2}=1\right)\end{array}$

The change in equilibrium constant (K) with respect to temperature with standard enthalpy change is described by Van’t Hoff equation. In a chemical reaction the K value changes as T changes since ${\text{-Δ}}_{\text{r}}\text{G/RT}$ changes as T change.

$\begin{array}{c}\text{van't Hoff equation}\Rightarrow {\text{lnK}}^{\text{'}}=\text{lnK+}\frac{{\text{Δ}}_{\text{r}}H}{R}\left(\frac{1}{T}-\frac{1}{T^{\text{'}}}\right)\\ here,K=equilibriumco\text{nstant}\text{at}\text{T}\\ {\text{K}}^{\text{'}}=equilibriumco\text{nstant}\text{at}{\text{T}}^{\text{'}}\\ R=gasco\text{nstant}\\ {\text{Δ}}_{\text{r}}H=enthalpychange\end{array}$

(b)

Interpretation Introduction

Interpretation:

The response for solubility of $AgCl$ towards increase in temperature has to be identified.