At 298 K , the molar conductivity of $x \%(\mathrm{w} / \mathrm{w}) \mathrm{MX}$ solution (aqueous) is $123.5 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$. The conductance of same solution is $1.9 \times 10^{-3} \mathrm{~S}$. The value of $x$ is $\_\_\_\_$ $\times 10^{-2}$.

(Given: cell constant $=1.3 \mathrm{~cm}^{-1}$; molar mass of MX is $75 \mathrm{~g} \mathrm{~mol}^{-1}$, density of aqueous solution of MX at 298 K is $1.0 \mathrm{~g} \mathrm{~mL}^{-1}$ )

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

$\left[\begin{array}{ll}\text { Given: } & E_{Sn\left( {OH} \right)_6^{2 - } |HSnO_2^ -}^o = - 0.9V \\ & \mathrm{E}^{\mathrm{o}}{ }_{\mathrm{Bi}_2 \mathrm{O}_3 \mid \mathrm{Bi}}=-0.44 \mathrm{~V} \\ & \mathrm{pKa}_{\left(\mathrm{H}_2 \mathrm{CO}_3\right)}=6.11 \\ & \frac{2.303 \mathrm{RT}}{\mathrm{F}}=0.059 \mathrm{~V} \\ & \text { Antilog }(1.29)=19.5\end{array}\right]$