Copper reduces ${\mathrm{NO}}_3^{-}$ into $\mathrm{NO}$ and ${\mathrm{NO}}_2$ depending upon the concentration of ${\mathrm{HNO}}_3$ in solution. (Assuming fixed $\left[{\mathrm{Cu}}^{2+}\right]$ and ${\mathrm{P}}_{\mathrm{NO}}={\mathrm{P}}_{{\mathrm{NO}}_2}$), the ${\mathrm{HNO}}_3$ concentration at which the thermodynamic tendency for reduction of ${\mathrm{NO}}_3^{-}$ into $\mathrm{NO}$ and ${\mathrm{NO}}_2$ by copper is same is ${10}^x \mathrm{M}$. The value of $2x$ is ___. (Rounded-off to the nearest integer)
[Given, ${\mathrm{E}}_{{\mathrm{Cu}}^{2+}/\mathrm{Cu}}^{\mathrm{o}}=0.34 \mathrm{V},{\mathrm{E}}_{{\mathrm{NO}}_3^{-}/\mathrm{NO}}^{\mathrm{o}}=0.96 \mathrm{V},{\mathrm{E}}_{{\mathrm{NO}}_3^{-}/{\mathrm{NO}}_2}^{\mathrm{o}}=0.79 \mathrm{V}$ and at $298 \mathrm{K}$, $\frac{\mathrm{RT}}{\mathrm{F}}\left(2.303\right)=0.059$]

The magnitude of the change in oxidising power of the ${\mathrm{MnO}}_4^{-}/{\mathrm{Mn}}^{2+}$ couple is $\mathrm{x}\times {10}^{-4} \mathrm{V}$ if the ${\mathrm{H}}^{+}$ concentration is decreased from $1 \mathrm{M}$ to ${10}^{-4}\mathrm{M}$ at $25°\mathrm{C}.$ (Assume concentration of ${\mathrm{MnO}}_4^{-}$ and ${\mathrm{Mn}}^{2+}$ to be same on change in ${\mathrm{H}}^{+}$ concentration). The value of $\mathrm{x}$ is __________.

(Rounded off to the nearest integer)

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

Assume a cell with the following reaction ${\mathrm{Cu}}_{\left(\mathrm{s}\right)}+2{\mathrm{Ag}}^{+}\left(1\times {10}^{-3}\mathrm{M}\right)\to {\mathrm{Cu}}^{2+}(0.250\mathrm{M})+2{\mathrm{Ag}}_{\left(\mathrm{s}\right)}$
${\mathrm{E}}_{\mathrm{cell} }^{\circ }=2.97 \mathrm{V}$

${\mathrm{E}}_{\mathrm{cell} }$ for the above reaction is $\underline{ }$  $\mathrm{V}.$

(Nearest integer)

$[$ Given : $\log 2.5=0.3979, \mathrm{T}=298 \mathrm{K}]$

Potassium chlorate is prepared by electrolysis of $\mathrm{KCl}$ in basic solution as shown by following equation.

$6{\mathrm{OH}}^{-}+{\mathrm{Cl}}^{-}\to {\mathrm{ClO}}_3^{-}+3{\mathrm{H}}_2\mathrm{O}+6{\mathrm{e}}^{-}$

A current of $\mathrm{xA}$ has to be passed for $10 \mathrm{h}$ to produce $10.0 \mathrm{g}$ of potassium chlorate. the value of $\mathrm{x}$ is __________. (Nearest integer)

(Molar mass of ${\mathrm{KClO}}_3=122.6 \mathrm{g}{ \mathrm{mol}}^{-1} \mathrm{F}=96500 \mathrm{C}$)

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