An electrochemical cell, consist of the following two redox couples, $\mathrm{M}^{x+} (\mathrm{aq}) / \mathrm{M}(\mathrm{s})\left[\mathrm{E}_{\text {red }}^{\Theta}=+0.15 \mathrm{~V}\right]$ and $\mathrm{Fe}^{3+}(\mathrm{aq}) / \mathrm{Fe}(\mathrm{s})\left[\mathrm{E}_{\text {red }}^{\Theta}=-0.036 \mathrm{~V}\right]$. The cell EMF $\left(\mathrm{E}_{\text {cell }}\right)$ is recorded to be 0.2057 V . If the reaction quotient of the electrochemical reaction is found to be $10^{-2}$, then the value of $x$ is

$\_\_\_\_$ .(Nearest integer)

[Given : M is a p-block metal and $\frac{2.303 R T}{F}=0.059 \mathrm{~V}$ ]

Consider the following two half-cell reactions along with the standard reduction potential given :

$\mathrm{CO}_2 + 6\mathrm{H}^+ + 6e^- \longrightarrow \mathrm{CH}_3\mathrm{OH} + \mathrm{H}_2\mathrm{O}\qquad E_{\text{red}}^{\circ} = 0.02\ \mathrm{V}$

$\dfrac{1}{2} \mathrm{O}_2 + 2\mathrm{H}^+ + 2e^- \longrightarrow \mathrm{H}_2\mathrm{O}\qquad E_{\text{red}}^{\circ} = 1.23\ \mathrm{V}$

A fuel cell was set up using the above two reactions such that the cell operates under the standard condition of 1 bar pressure and 298 K temperature. The fuel cell works with 80% efficiency. If the work derived from the cell using 1 mol of $\mathrm{CH}_3\mathrm{OH}$ is used to compress an ideal gas isothermally against a constant pressure of 1 kPa, then the change in the volume of the gas,

$\Delta V = \underline{\hspace{2cm}}$ m$^3$. (nearest integer)

Given : $\mathrm{F} = 96500~\mathrm{C~mol}^{-1}$

A volume of x mL of 5 M NaHCO₃ solution was mixed with 10 mL of 2 M H₂CO₃ solution to make an electrolytic buffer. If the same buffer was used in the following electrochemical cell to record a cell potential of 235.3 mV, then the value of x = ______ mL (nearest integer).

Sn(s) | Sn(OH)₆²⁻ (0.5 M) | HSnO₂⁻ (0.05 M) | OH⁻ | Bi₂O₃(s) | Bi(s)

Consider up to one place of decimal for intermediate calculations

For strong electrolyte $\Lambda_m$ increases slowly with dilution and can be represented by the equation

$$\Lambda_m = \Lambda_m^\circ - A c^{1/2}$$

Molar conductivity values of the solutions of strong electrolyte AB at 18°C are given below :

The value of constant A based on the above data [in S cm² mol^-1/(mol/L)^1/2] unit is ________.