Consider the following redox reaction :

${\mathrm{MnO}}_4^{-}+{\mathrm{H}}^{+}+{\mathrm{H}}_2{\mathrm{C}}_2{\mathrm{O}}_4\rightleftharpoons {\mathrm{Mn}}^{2+}+{\mathrm{H}}_2\mathrm{O}+{\mathrm{CO}}_2$

The standard reduction potentials are given as below $\left({\mathrm{E}}_{\mathrm{red}}°\right)$

${{\mathrm{E}}^0}_{{\mathrm{MnO}}_4^{-}/{\mathrm{Mn}}^{2+}}=+1.51 \mathrm{V}$

${{\mathrm{E}}^0}_{{\mathrm{CO}}_2/{\mathrm{H}}_2{\mathrm{C}}_2{\mathrm{O}}_4}=-0.49 \mathrm{V}$

If the equilibrium constant of the above reaction is given as ${\mathrm{K}}_{\mathrm{eq}}={10}^{\mathrm{x}}$, then the value of $\mathrm{x}=$ _______ (nearest integer)

The Gibbs energy change (in $\mathrm{J}$) for the given reaction at $\left[{\mathrm{Cu}}^{2+}\right]=\left[{\mathrm{Sn}}^{2+}\right]=1\text{\hspace{0.17em}M}$ and $298 \mathrm{K}$ is :

$\mathrm{Cu}\left(\mathrm{s}\right)+{\mathrm{Sn}}^{2+}\left(\mathrm{aq}.\right)\to {\mathrm{Cu}}^{2+}\left(\mathrm{aq}.\right)+\mathrm{Sn}\left(\mathrm{s}\right)$; 

$\left({\mathrm{E}}_{{\mathrm{Sn}}^{2+}\left|\mathrm{Sn}\right.}^0=-0.16\mathrm{V},{\mathrm{E}}_{\left.{\mathrm{Cu}}^{2+}\right|\mathrm{Cu}}^0=0.34\mathrm{V},\right.$Take $\left.\mathrm{F}=96500\mathrm{C}{\mathrm{mol}}^{-1}\right)$

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

An oxidation-reduction reaction in which 3 electrons are transferred has a ${\mathrm{\Delta G}}^0$ of $17.37 \mathrm{kJ} {\mathrm{mol}}^{-1}$ at $25°\mathrm{C}.$ The value of ${\mathrm{E}}_{\mathrm{cell}}^{\mathrm{o}}$ (in V) is $\_\_\_\_\_\_\_\times {10}^{-2}$.

$\left(1\mathrm{F}=96500 \mathrm{C} {\mathrm{mol}}^{-1}\right)$

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

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 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 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 $\mathrm{F}=96,500 \mathrm{C}\hspace{0.17em}{\mathrm{mol}}^{-1}]$