Embibe Experts Solutions for Chapter: Electrochemistry, Exercise 1: JEE Advanced Paper 1 - 2015

Some standard electrode potentials at $298 \mathrm{K}$ are given below:

$\begin{array}{ll}{\mathrm{Pb}}^{2+}/\mathrm{Pb}& -0.13 \mathrm{V}\end{array}$

$\begin{array}{ll}{\mathrm{Ni}}^{2+}/\mathrm{Ni}& -0.24 \mathrm{V}\end{array}$

$\begin{array}{ll}{\mathrm{Cd}}^{2+}/\mathrm{Cd}& -0.40 \mathrm{V}\end{array}$

$\begin{array}{ll}{\mathrm{Fe}}^{2+}/\mathrm{Fe}& -0.44 \mathrm{V}\end{array}$

To a solution containing $0.001 \mathrm{M}$ of ${\mathbf{X}}^{2+}$ and $0.1 \mathrm{M}$ of ${\mathbf{Y}}^{2+}$, the metal rods $\mathbf{X}$ and $\mathbf{Y}$ are inserted $($at $298 \mathrm{K})$ and connected by a conducting wire. This resulted in dissolution of $\mathbf{X}$. The correct combination(s) of $\mathbf{X}$ and $\mathbf{Y}$, respectively, is(are)

(Given: Gas constant, $\mathrm{R}=8.314 \mathrm{J}{ \mathrm{K}}^{-1}{ \mathrm{mol}}^{-1}$, Faraday constant, $\mathrm{F}=96500 \mathrm{C} {\mathrm{mol}}^{-1}$)

For the cell $\mathrm{Zn} \left(\mathrm{s}\right)\left|{\mathrm{ZnSO}}_4 \left(\mathrm{aq}\right)\right|\left|{\mathrm{CuSO}}_4 \left(\mathrm{aq}\right)\right|\mathrm{Cu} \left(\mathrm{s}\right)$, when the concentration of ${\mathrm{Zn}}^{2+}$ is $10$ times the concentration of ${\mathrm{Cu}}^{2+}$, the expression for $\mathrm{\Delta G} \left(\mathrm{in}\mathrm{ }\mathrm{J}\mathrm{ }{\mathrm{mol}}^{-1}\right)$ is

$[\mathrm{F}=$Faraday's constant, $\mathrm{R}=$universal gas constant, $\mathrm{T}=$temperature, ${\mathrm{E}}^{\mathrm{o}}\mathrm{cell}=1.1\mathrm{V}]$

For the following electrochemical cell at $\text{289 K,}$

$\text{Pt}\left(\text{s}\right)\left|{\text{H}}_2\left(\text{g},1\text{ bar}\right) \right|{\text{H}}^{+}\left(\text{aq},1\text{M}\right)\left|\right|{\text{ M}}^{4+}\left(\text{aq}.\right){\text{, M}}^{\text{2+}}(\text{aq}.)|\text{ Pt}(\text{s})$

${\mathrm{E}}_{\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{l}}=0.092\mathrm{ }\mathrm{V}$ when $\frac{\left[{\mathrm{M}}^{2+}\left(\mathrm{a}\mathrm{q}.\right)\right]}{\left[{\mathrm{M}}^{4+}\left(\mathrm{a}\mathrm{q}.\right)\right]}={10}^{\mathrm{x}}$

Given: ${\mathrm{E}}_{{\mathrm{M}}^{4+}/{\mathrm{M}}^{2+}}^0=0.151\mathrm{ }\mathrm{V}\mathrm{ };2.303\frac{\mathrm{R}\mathrm{T}}{\mathrm{F}}=0.059$

The value of $\text{x}$ is -

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 electrochemical cell, $\text{Mg(s)}\left|{\text{Mg}}^{\text{2+}}\left(\text{aq,1}\text{M}\right)\right|\left|{\text{Cu}}^{\text{2+}}\left(\text{aq,1}\text{M}\right)\right|\text{Cu }\left(\text{s}\right)$ the standard emf of the cell is $\text{2}\text{.70 V}$ at $\text{300 K}\text{.}$ When the concentration of ${\text{Mg}}^{\text{2+}}$ is changed to $\text{x M,}$ the cell potential changes to $\text{2}\text{.67 V}$ at $\text{300 K}\text{.}$ The value of $\text{x}$ is ________.

(given, $\frac{\text{F}}{\text{R}}{\text{=11500 K V}}^{-\text{1}}\text{,}$ where $\text{F}$ is the Faraday constant and $\text{R}$ is the gas constants, $\text{ln}\left(\text{10}\right)\text{=}\text{2}\text{.30}$ )

In a galvanic cell, the salt bridge