JEE Main - 12th January 2019 Shift 1

The enthalpy change for the conversion of $\frac{1}{2}{\mathrm{Cl}}_2$ (g) to ${\mathrm{Cl}}^{-}\left(\mathrm{aq}\right)$ is $(-)$
${\mathrm{kJmol}}^{-1}$ (Nearest integer)
Given : ${\Delta }_{\text{dis }}{\mathrm{H}}_{{\mathrm{Cl}}_{2( \mathrm{g})}}^0=240{\mathrm{kJmol}}^{-1}$.
${\Delta }_{\mathrm{eg}}{\mathrm{H}}_{\mathrm{Cl}\left(\mathrm{g}\right)}^{\mathrm{o}}=-350{\mathrm{kJmol}}^{-1}$,
${\Delta }_{\mathrm{hyd}}{\mathrm{H}}_{{\mathrm{Cl}}_{\left(\mathrm{g}\right)}^{-}}^{\mathrm{o}}=-380{\mathrm{kJmol}}^{-1}$

At $25°\mathrm{C}$, the enthalpy of the following processes are given:

${\mathrm{H}}_2( \mathrm{g})+{\mathrm{O}}_2( \mathrm{g})\to 2\mathrm{OH}\left(\mathrm{g}\right)\Delta {\mathrm{H}}^{\mathrm{o}}=78 \mathrm{kJ} {\mathrm{mol}}^{-1}$

${\mathrm{H}}_2( \mathrm{g})+1/2{\mathrm{O}}_2( \mathrm{g})\to {\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)\Delta {\mathrm{H}}^0=-242 \mathrm{kJ} {\mathrm{mol}}^{-1}$

${\mathrm{H}}_2( \mathrm{g})\to 2\mathrm{H}\left(\mathrm{g}\right)\Delta {\mathrm{H}}^{\mathrm{o}}=436 \mathrm{kJ} {\mathrm{mol}}^{-1}$

$1/2{\mathrm{O}}_2( \mathrm{g})\to \mathrm{O}\left(\mathrm{g}\right)\Delta {\mathrm{H}}^0=249 \mathrm{kJ} {\mathrm{mol}}^{-1}$

What would be the value of X for the following reaction? (Nearest integer)

${\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)\to \mathrm{H}\left(\mathrm{g}\right)+\mathrm{OH}\left(\mathrm{g}\right) ∆{\mathrm{H}}^{\mathrm{o}}=\mathrm{X} {\mathrm{kJmol}}^{-1}$

$0.3 \mathrm{g}$ of ethane undergoes combustion at $27°\mathrm{C}$ in a bomb calorimeter. The temperature of calorimeter system (including the water) is found to rise by $0.5°\mathrm{C}$. The heat evolved during combustion of ethane at constant pressure is ${\mathrm{kJmol}}^{-1}$.
(Nearest integer)

[Given : The heat capacity of the calorimeter system is $20 \mathrm{kJ} {\mathrm{K}}^{-1},\mathrm{R}=8.3{\mathrm{JK}}^{-1} {\mathrm{mol}}^{-1}$.
Assume ideal gas behaviour.

Assume ideal gas behaviour.

Atomic mass of $\mathrm{C}$ and $\mathrm{H}$ are $12$ and $1 \mathrm{g} {\mathrm{mol}}^{-1}$ respectively]

$28.0$ L of ${\mathrm{CO}}_2$ is produced on complete combustion of $16.8 \mathrm{L}$ gaseous mixture of ethene and methane at $25°\mathrm{C}$ and $1$ atm. Heat evolved during the combustion process is $\mathrm{kJ}$

Given$:{\mathrm{\Delta H}}_{\mathrm{C}}\left({\mathrm{CH}}_4\right)=-900 \mathrm{kJ} {\mathrm{mol}}^{-1}$

${\mathrm{\Delta H}}_{\mathrm{C}}\left({\mathrm{C}}_2{\mathrm{H}}_4\right)=-1400 \mathrm{kJ} {\mathrm{mol}}^{-1}$.

Which of the following relations are correct?
(A) $\mathrm{\Delta U}=\mathrm{q}+\mathrm{p\Delta V}$
(B) $\mathrm{\Delta G}=\mathrm{\Delta H}-\mathrm{T\Delta S}$
(C) $\mathrm{\Delta S}=\frac{{\mathrm{q}}_{\mathrm{rev}}}{\mathrm{T}}$
(D) $\mathrm{\Delta H}=\mathrm{\Delta U}-\mathrm{\Delta nRT}$
Choose the most appropriate answer from the options given below :

When 2 litre of ideal gas expands isothermally into vacuum to a total volume of $6$ litre, the change in internal energy is _____ J. (Nearest integer)

$1$ mole of ideal gas is allowed to expand reversibly and adiabatically from a temperature of $27°\mathrm{C}$. The work done is $3 \mathrm{kJ} {\mathrm{mol}}^{-1}$. The final temperature of the gas is _____ $\mathrm{K}$ (Nearest integer). Given ${\mathrm{C}}_{\mathrm{v}}=20 \mathrm{J} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}$

Enthalpies of formation of ${\mathrm{CCl}}_4( \mathrm{g}),{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right),{\mathrm{CO}}_2( \mathrm{g})$ and $\mathrm{HCl}$ are $-105,-242,-394$ and $-92 \mathrm{kJ} {\mathrm{mol}}^{-1}$ respectively. The magnitude of enthalpy of the reaction given below is ${\mathrm{kJmol}}^{-1}$. (nearest integer) ${\mathrm{CCl}}_4( \mathrm{g})+2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)\to {\mathrm{CO}}_2( \mathrm{g})+4\mathrm{HCl}\left(\mathrm{g}\right)$