Chapter 13, Problem 13.39PAE

Calculate the standard free energy change for the following reactions using the standard cell potentials for the half-reactions that are involved.

(a) $\text{Fe}\left(\text{s}\right)+{\text{Hg}}_{\text{2}}{}^{\text{2+}}\left(\text{aq}\right)\to {\text{Fe}}^{\text{2+}}\left(\text{aq}\right)+\text{2}\text{Hg}\left(\mathcal{l}\right)$

(b ${\text{Fe}}^{3+}\left(\text{aq}\right)+\text{Ag}\left(\text{s}\right)+{\text{Cl}}^{\text{-}}\left(\text{aq}\right)\to {\text{Fe}}^{2+}\left(\text{aq}\right)+\text{AgCl}\left(\text{s}\right)$

(c) $2{\text{MnO}}_4{}^{-}\left(\text{aq}\right)+5\text{Zn}\left(\text{s}\right)+16{\text{H}}_{\text{3}}{\text{O}}^{+}\left(\text{aq}\right)\to 2{\text{Mn}}^{\text{2+}}\left(\text{aq}\right)+5{\text{Zn}}^{\text{2+}}\left(\text{aq}\right)+24{\text{H}}_{\text{2}}\text{O}\left(\mathcal{l}\right)$

Interpretation Introduction

To determine:

To find the standard free energy for reaction:

${\text{Fe(s)+Hg}}_{\text{2}}{}^{\text{2+}}\text{(aq)}\to {\text{Fe}}^{\text{2+}}\text{(aq)+2Hg(l)}$.

Explanation of Solution

$\begin{array}{l}{\text{Fe(s)+Hg}}_{\text{2}}{}^{\text{2+}}\text{(aq)}\to {\text{Fe}}^{\text{2+}}\text{(aq)+2Hg(l)}\\ {\text{E}}^{\text{0}}{\text{cell=E}}^{\text{0}}{}_{{\text{Hg}}_2^{2+}\text{/Hg}}{\text{-E}}^{\text{0}}{}_{{\text{Fe}}^{\text{2+}}\text{/Fe}}\\ \text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{ = 0}\text{.80-(-0}\text{.44)}\\ \text{ =1}\text{.24 V}\\ {\text{ΔG}}^{\text{0}}{\text{=-nFE}}_{\text{cell}}^{\text{o}}\\ \text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{ = -2 x 96500 x 1}\text{.24}\\ \text{ = -239320 J}\\ \text{ = -239}\text{.3 kJ}\end{array}$

Interpretation Introduction

To determine:

To find the standard free energy for reaction:

${\text{Fe}}^{3+}{\text{(aq)+Ag(s)+Cl}}^{-}\text{(aq)}\to {\text{Fe}}^{\text{2+}}\text{(aq)+AgCl(s)}$.

Explanation of Solution

$\begin{array}{l}{\text{Fe}}^{3+}{\text{(aq)+Ag(s)+Cl}}^{-}\text{(aq)}\to {\text{Fe}}^{\text{2+}}\text{(aq)+AgCl(s)}\\ {\text{E}}^{\text{0}}{\text{cell=E}}^{\text{0}}{}_{{\text{Fe}}^{\text{3+}}{\text{/Fe}}^{\text{2+}}}{\text{-E}}^{\text{0}}{}_{{\text{AgCl}}^{\text{+}}{\text{, Cl}}^{\text{-}}}\\ \text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{ = 0}\text{.77-0}\text{.22}\\ \text{ =0}\text{.55 V}\end{array}$

$\begin{array}{l}{\text{ΔG}}^{\text{0}}{\text{=-nFE}}_{\text{cell}}^{\text{o}}\\ \text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{ = -1 x 96500 x 0}\text{.55}\\ \text{ = -53075 J}\\ \text{ = -53}\text{.07 kJ}\end{array}$

Interpretation Introduction

To determine:

To find the standard free energy for the reaction:

${\text{2MnO}}_{\text{4}}{}^{\text{-}}{\text{(aq)+5 Zn(s)+16 H}}_{\text{3}}{\text{O}}^{+}\text{(aq)}\to 2{\text{Mn}}^{\text{2+}}{\text{(aq)+5Zn}}^{\text{2+}}{\text{(aq)+24 H}}_2\text{O(l)}$.

Explanation of Solution

$\begin{array}{l}{\text{2MnO}}_{\text{4}}{}^{\text{-}}{\text{(aq)+5 Zn(s)+16 H}}_{\text{3}}{\text{O}}^{+}\text{(aq)}\to \\ 2{\text{Mn}}^{\text{2+}}{\text{(aq)+5Zn}}^{\text{2+}}{\text{(aq)+24 H}}_2\text{O(l)}\\ {\text{E}}^{\text{0}}{\text{cell=E}}^{\text{0}}{}_{{\text{MnO}}^{\text{4-}}{\text{/Mn}}^{\text{2+}}}{\text{-E}}^{\text{0}}{}_{{\text{Zn}}^{\text{2+}}\text{/Zn}}\\ \text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{ = 1}\text{.51-(-0}\text{.76)}\\ \text{ =2}\text{.27 V}\\ {\text{ΔG}}^{\text{0}}{\text{=-nFE}}_{\text{cell}}^{\text{o}}\\ \text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{ = -10 x 96500 x 2}\text{.27}\\ \text{ = -2190550 J}\\ \text{ = -2190}\text{.6 kJ}\end{array}$

Conclusion

The standard free energy for ${\text{Fe(s)+Hg}}_{\text{2}}{}^{\text{2+}}\text{(aq)}\to {\text{Fe}}^{\text{2+}}\text{(aq)+2Hg(l)}$ is -239.3 kJ. The standard free energy for ${\text{Fe}}^{3+}{\text{(aq)+Ag(s)+Cl}}^{-}\text{(aq)}\to {\text{Fe}}^{\text{2+}}\text{(aq)+AgCl(s)}$ is -53.07 kJ. The standard free energy for ${\text{2MnO}}_{\text{4}}{}^{\text{-}}{\text{(aq)+5 Zn(s)+16 H}}_{\text{3}}{\text{O}}^{+}\text{(aq)}\to 2{\text{Mn}}^{\text{2+}}{\text{(aq)+5Zn}}^{\text{2+}}{\text{(aq)+24 H}}_2\text{O(l)}$ is -2190.6 kJ.