Both $\mathrm{E}{°}_{\mathrm{cell}}$ and $∆\mathrm{G}°$ for the cell reaction are intensive properties.

Relation between Gibb's Free Energy and EMF of a Cell Consider a $70\%$ efficient hydrogen-oxygen fuel cell working under standard conditions at $1$ bar and $298 \mathrm{K}$. Its cell reaction is

${\mathrm{H}}_2\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)\to {\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)$

The work derived from the cell on the consumption of $1.0\times {10}^{-3 }\mathrm{mol}$ of ${\mathrm{H}}_2\left(\mathrm{g}\right)$ is used to compress $1.00 \mathrm{mol}$ of a monoatomic ideal gas in a thermally insulated container. What is the change in the temperature (in $\mathrm{K}$ ) of the ideal gas?

The standard reduction potentials for the two half-cells are given below.

${\mathrm{O}}_2\left(\mathrm{g}\right)+4{\mathrm{H}}^{+}\left(\mathrm{aq}\right)+4{\mathrm{e}}^{-}\to 2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right), {\mathrm{E}}^0=1.23 \mathrm{V}$,

$2{\mathrm{H}}^{+}\left(\mathrm{aq}\right)+2{\mathrm{e}}^{-}\to {\mathrm{H}}_2\left(\mathrm{g}\right), {\mathrm{E}}^0=0.00 \mathrm{V}$

Use $\mathrm{F}=96500 \mathrm{C} {\mathrm{mol}}^{-1},\mathrm{R}=8.314 \mathrm{J} {\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}$.

For the cell reaction

$2\mathrm{F}{\mathrm{e}}^{3+}\left(\mathrm{a}\mathrm{q}\right)+2{\mathrm{I}}^{-}\left(\mathrm{a}\mathrm{q}\right)\to 2\mathrm{F}{\mathrm{e}}^{2+}\left(\mathrm{a}\mathrm{q}\right)+{\mathrm{I}}_2\left(\mathrm{a}\mathrm{q}\right)$

${\mathrm{E}}_{\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{l}}^0=0.24\mathrm{V}$ at $298\mathrm{ }\mathrm{K}.$ The standard Gibbs energy $\left({\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{G}}^{\mathrm{o}}\right)$ of the cell reaction is:

[Given that Faraday constant $\mathrm{F}=96500\mathrm{ }\mathrm{C}\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}$ ]

The standard e.m.f. of the cell, $\mathrm{Cd}\left(\mathrm{s}\right)\left|{\mathrm{CdCl}}_2\left(\mathrm{aq}\right)\left(0.1\mathrm{M}\right)\right|\left|\mathrm{AgCl}\left(\mathrm{s}\right)\right|\mathrm{Ag}\left(\mathrm{s}\right)$ in which the cell reaction is $\mathrm{Cd}\left(\mathrm{s}\right)+2\mathrm{AgCl}\left(\mathrm{s}\right)⟶2\mathrm{Ag}\left(\mathrm{s}\right)+{\mathrm{Cd}}^{2+}\left(\mathrm{aq}\right)+2{\mathrm{Cl}}^{-}\left(\mathrm{aq}\right)$ is $0.6915 \mathrm{V}$ at $0°\mathrm{C}$ and $0.6753 \mathrm{V}$ at $25°\mathrm{C}$. The enthalpy change of the reaction at $25°\mathrm{C}$ is

The standard electrode potential ${\mathrm{E}}^o$ and its temperature coefficient $\left(\frac{\mathrm{dE}}{\mathrm{dT}}\right)$ for a cell are $2\hspace{0.17em}\mathrm{V}$ and $-5{\times 10}^{-4}\mathrm{\hspace{0.17em}} \mathrm{V} {\mathrm{K}}^{-1}$ at $\mathrm{300\hspace{0.17em}}\mathrm{K}$, respectively. The reaction is $\mathrm{Zn} \left(\mathrm{s}\right)+{\mathrm{Cu}}^{2+} \left(\mathrm{aq}\right)\to {\mathrm{Zn}}^{2+} \left(\mathrm{aq}\right)+\mathrm{Cu} \left(\mathrm{s}\right)$. The standard reaction enthalpy $\left({\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{H}}^{-}\right)$ at $300\hspace{0.17em}\mathrm{K}$ in $\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}$ is 

$[$Use $\mathrm{R}=8 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$ and $\mathrm{F}=96,500 \mathrm{C}\hspace{0.17em}{\mathrm{mol}}^{-1}]$

The value of ${\mathrm{E}}_1^{\mathrm{o}}$ is

The emf of the following cell is $1.229 \mathrm{V}$ at $298 \mathrm{K}$.

$\mathrm{Pt},{\mathrm{H}}_2\left(1\mathrm{atm}\right)\left|{\mathrm{H}}^{+}\left(1\mathrm{M}\right)\right|{\mathrm{O}}_2\left(1\mathrm{atm}\right),\mathrm{Pt}$ 

${\mathrm{H}}_2+\frac{1}{2}{\mathrm{O}}_2\rightleftharpoons {\mathrm{H}}_2\mathrm{O}$

The standard free energy change for the cell reaction is________ $\left[\mathrm{F}=9.649\times {10}^4 \mathrm{C} {\mathrm{mol}}^{-1}\right]$

For the disproportionation reaction $2{\mathrm{Cu}}^{+}\left(\mathrm{aq}\right)\rightleftharpoons \mathrm{Cu}\left(\mathrm{s}\right)+{\mathrm{Cu}}^{2+}\left(\mathrm{aq}\right)$ at $298\mathrm{K},$ $\ln \left(\mathrm{K}\right)$  (where $\mathrm{K}$ is the equilibrium constant) is _______$\times {10}^{-1}$

Given $:\left(\mathrm{E}{°}_{{\mathrm{Cu}}^{2+}/{\mathrm{Cu}}^{+}}=0.16V E{°}_{{\mathrm{Cu}}^{+}/\mathrm{Cu}}=0.52\mathrm{V}\frac{\mathrm{RT}}{\mathrm{F}}=0.025\right)$

The standard emf of the cell $\left({\mathrm{E}}_{\text{cell }}°\right.$ and equilibrium constant $\left({\mathrm{K}}_{\mathrm{eq}}\right)$ of the following reaction of $298 \mathrm{K}$

${\mathrm{Cd}}^{2+}+4{\mathrm{NH}}_3\rightleftharpoons \mathrm{Cd}{\left({\mathrm{NH}}_3\right)}_4^{2+}$

Calculate $∆{\mathrm{G}}^{°}$ for the reaction $\mathrm{Zn} \left(\mathrm{s}\right) + {\mathrm{Cu}}^{2+} \left(\mathrm{aq}\right) \to {\mathrm{Zn}}^{2+} \left(\mathrm{aq}\right) + \mathrm{Cu} \left(\mathrm{s}\right)$

Given:

$$\begin{gathered} {\mathrm{E}}^{°} \mathrm{for} {\mathrm{Zn}}^{2+}/\mathrm{Zn} = -0.76\mathrm{V} \\ {\mathrm{E}}^{°} \mathrm{for} {\mathrm{Cu}}^{2+}/\mathrm{Cu} = +0.34\mathrm{V} \\ \mathrm{R} = 8.314 {\mathrm{JK}}^{-1} {\mathrm{mol}}^{-1} \\ \mathrm{F} = 96500 \mathrm{C} {\mathrm{mol}}^{-1} \end{gathered}$$