At $298 \mathrm{K}$, a $1$ litre solution containing $10 \mathrm{mmol}$ of ${\mathrm{Cr}}_2{\mathrm{O}}_7^{2-}$ and $100\mathrm{mmol}$ of ${\mathrm{Cr}}^{3+}$ shows a $\mathrm{pH}$ of $3.0$.

Given : ${\mathrm{Cr}}_2{\mathrm{O}}_7{}^{2-}\to {\mathrm{Cr}}^{3+};{\mathrm{E}}^0=1.330 \mathrm{V}$ and $\frac{2.303\mathrm{RT}}{\mathrm{F}}=0.059 \mathrm{V}$

The potential for the half cell reaction is $\mathrm{x}\times {10}^{-3} \mathrm{V}$ . The value of $\mathrm{x}$ is _____ .

Consider the cell $\mathrm{Pt}\left(\mathrm{s}\right)\left|{\mathrm{H}}_2( \mathrm{s})\left(\mathrm{latm}\right)\right|{\mathrm{H}}^{+}\left(\mathrm{aq},\left[{\mathrm{H}}^{+}\right]=1\right)\left|\right|{\mathrm{Fe}}^{3+}\left(\mathrm{aq}\right),{\mathrm{Fe}}^{2+}\left(\mathrm{aq}\right)\mid Pt\left(\mathrm{s}\right)$

Given: ${\mathrm{E}}_{{\mathrm{Fe}}^{3+}/{\mathrm{Fe}}^{2+}}°=0.771 \mathrm{V}$ and ${\mathrm{E}}_{{\mathrm{H}}^{+}/\frac{1}{2}{\mathrm{H}}_2}°=0 \mathrm{V}, \mathrm{T}=298 \mathrm{K}$

If the potential of the cell is $0.712 \mathrm{V}$ the ratio of concentration of ${\mathrm{Fe}}^{2+}$ to ${\mathrm{Fe}}^{3+}$ is
(Nearest integer)

$Pt\left(\mathrm{s}\right){\mathrm{H}}_2( \mathrm{g})\left(1\mathrm{bar}\right)\left|{\mathrm{H}}^{+}\left(\mathrm{aq}\right)\left(1\mathrm{M}\right)\right|\left|{\mathrm{M}}^{3+}\left(\mathrm{aq}\right),{\mathrm{M}}^{+}\left(\mathrm{aq}\right)\right|\mathrm{Pt}\left(\mathrm{s}\right)$

The ${\mathrm{E}}_{\text{cell }}$ for the given cell is $0.1115 \mathrm{V}$ at $298 \mathrm{K}$

When $\frac{\left[{\mathrm{M}}^{+}\left(\mathrm{aq}\right)\right]}{\left[{\mathrm{M}}^{3+}\left(\mathrm{aq}\right)\right]}={10}^{\mathrm{a}}$

The value of a is ___________

Given : ${\mathrm{E}}^{\theta }{}_{{\mathrm{M}}^{3+}/{\mathrm{M}}^{+}}=0.2 \mathrm{V}$

$\frac{2.303\mathrm{RT}}{\mathrm{F}}=0.059 \mathrm{V}$

Following figure shows dependence of molar conductance of two electrolytes on concentration. ${\mathrm{\Lambda }}_{\mathrm{m}}^0$ is the limiting molar conductivity.

The number of Incorrect statement(s) from the following is _____

(A) ${\mathrm{\Lambda }}_{\mathrm{m}}^0$ for electrolyte $\mathrm{A}$ is obtained by extrapolation
(B) For electrolyte $\mathrm{B}, {\mathrm{\Lambda }}_{\mathrm{m}} \mathrm{Vs} \sqrt{\mathrm{c}}$  graph is a straight line with intercept equal to ${\mathrm{\Lambda }}_{\mathrm{m}}^0$
(C) At infinite dilution, the value of degree of dissociation approach zero for electrolyte $\mathrm{B}$.
(D) ${\mathrm{\Lambda }}_{\mathrm{m}}$ for any electrolyte $\mathrm{A}$ or $\mathrm{B}$ can be calculated using $\mathrm{\lambda }°$ for individual ions.

The equilibrium constant for the reaction $\mathrm{Zn}\left(\mathrm{s}\right)+{\mathrm{Sn}}^{2+}\left(\mathrm{aq}\right)\rightleftharpoons {\mathrm{Zn}}^{2+}\left(\mathrm{aq}\right)+\mathrm{Sn}\left(\mathrm{s}\right)$ is $1\times {10}^{20}$ at $298 \mathrm{K}$. The magnitude of standard electrode potential of $\mathrm{Sn}/{\mathrm{Sn}}^{2+}$ if ${\mathrm{E}}_{{\mathrm{Zn}}^{2*}/\mathrm{Zn}}^0=-0.76 \mathrm{V}$ is _____ $\times {10}^{-2} \mathrm{V}$. (Nearest integer)

Given : $\frac{2.303\mathrm{RT}}{\mathrm{F}}=0.059 \mathrm{V}$

Consider the cell

${\mathrm{Pt}}_{\left(\mathrm{s}\right)}\left|{\mathrm{H}}_2\left(\mathrm{g},1\mathrm{atm}\right)\right|{\mathrm{H}}^{+}\left(\mathrm{aq},1\mathrm{M}\right)|\left|{\mathrm{Fe}}^{3+}\left(\mathrm{aq}\right),{\mathrm{Fe}}^{2+}\left(\mathrm{aq}\right)\right|Pt\left(\mathrm{s}\right)$

When the potential of the cell is $0.712 \mathrm{V}$ at $298 \mathrm{K}$, the ratio $\left[{\mathrm{Fe}}^{2+}\right]/\left[{\mathrm{Fe}}^{3+}\right]$ is
(Nearest integer)
Given: $\overline{){\mathrm{Fe}}^{3+}+{\mathrm{e}}^{-}={\mathrm{Fe}}^{2+},\mathrm{E}°{\mathrm{Fe}}^{3+},{\mathrm{Fe}}^{2+}}\mathrm{Pt}=0.771 \frac{2.303\mathrm{RT}}{\mathrm{F}}=0.06 \mathrm{V}$

The electrode potential of the following half cell at $298 \mathrm{K}$

$\mathrm{X}\left|{\mathrm{X}}^{2+}\left(0.001\mathrm{M}\right)\Vert {\mathrm{Y}}^{2+}\left(0.01\mathrm{M}\right)\right|\mathrm{Y}$ is _____ $\times {10}^{-2} \mathrm{V}$ (Nearest integer)

Given : ${\mathrm{E}}_{{\mathrm{X}}^{2+}\mid \mathrm{X}}^0=-2.36 \mathrm{V}$

${\mathrm{E}}_{{\mathrm{Y}}^{2+}\mathrm{Y}}^0=+0.36 \mathrm{V}$

$\frac{2.303\mathrm{RT}}{\mathrm{F}}=0.06 \mathrm{V}$

Which one of the following statements is correct for electrolysis of brine solution?