1 mole of ideal gas is allowed to expand reversibly and adiabatically from a temperature of $27^{\circ} \mathrm{C}$. The work done is $3 \mathrm{~kJ} \mathrm{~mol}^{-1}$. The final temperature of the gas is ________ $\mathrm{K}$ (Nearest integer).

Given $\mathrm{C_V}=20 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$

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

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

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

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

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

Consider the following equation:

$2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g), \Delta H=-190 \mathrm{~kJ}$

The number of factors which will increase the yield of $\mathrm{SO}_{3}$ at equilibrium from the following is _______.

A. Increasing temperature

B. Increasing pressure

C. Adding more $\mathrm{SO}_{2}$

D. Adding more $\mathrm{O}_{2}$

E. Addition of catalyst

Lead storage battery contains $38 \%$ by weight solution of $\mathrm{H}_{2} \mathrm{SO}_{4}$. The van't Hoff factor is $2.67$ at this concentration. The temperature in Kelvin at which the solution in the battery will freeze is ________. (Nearest integer).

Given $\mathrm{K}_{f}=1.8 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$