For combustion of one mole of magnesium in an open container at $300 \mathrm{K}$ and $1$ bar pressure, ${\mathrm{\Delta }}_{\mathrm{C}}{\mathrm{H}}^{\ominus }=-601.70 \mathrm{kJ}{ \mathrm{mol}}^{-1}$, the magnitude of change in internal energy for the reaction is $\mathrm{kJ}$. (Nearest integer)
(Given : $\mathrm{R}=8.3 \mathrm{J}{ \mathrm{K}}^{-1}{ \mathrm{mol}}^{-1}$)

$2.2 \mathrm{g}$ of nitrous oxide $\left({\mathrm{N}}_2\mathrm{O}\right)$ gas is cooled at a constant pressure of $1$ atm from $310 \mathrm{K}$ to $270 \mathrm{K}$ causing the compression of the gas from $217.1 \mathrm{mL}$ to $167.75 \mathrm{mL}$. The change in internal energy of the process, $△\mathrm{U}$ is $\text{'}-\mathrm{x}\text{'}\mathrm{J}$. The value of $\text{'}x\text{'}$ is _____.

[nearest integer]

(Given: atomic mass of $\mathrm{N}=14 \mathrm{g}{ \mathrm{mol}}^{-1}$ and of $\mathrm{O}=16 \mathrm{g}{ \mathrm{mol}}^{-1}$. Molar heat capacity of ${\mathrm{N}}_2\mathrm{O}$ is $100 {\mathrm{JK}}^{-1}{ \mathrm{mol}}^{-1}$)

While performing a thermodynamics experiment, a student made the following observations, $\mathrm{HCl}+\mathrm{NaOH}\to \mathrm{NaCl}+{\mathrm{H}}_2\mathrm{O}\Delta \mathrm{H}=-57.3 \mathrm{kJ}{ \mathrm{mol}}^{-1}$

${\mathrm{CH}}_3\mathrm{COOH}+\mathrm{NaOH}\to {\mathrm{CH}}_3\mathrm{COONa}+{\mathrm{H}}_2\mathrm{O}$

$\mathrm{\Delta H}=-55.3 \mathrm{kJ}{ \mathrm{mol}}^{-1}$.

The enthalpy of ionization of ${\mathrm{CH}}_3\mathrm{COOH}$ as calculated by the student is $\mathrm{kJ} {\mathrm{mol}}^{-1}$. 

$2.4 \mathrm{g}$ coal is burnt in a bomb calorimeter in excess of oxygen at $298 \mathrm{K}$ and $1 \mathrm{atm}$ pressure.

The temperature of the calorimeter rises from $298 \mathrm{K}$ to $300 \mathrm{K}$. The enthalpy change during the combustion of coal is $-\mathrm{x} \mathrm{kJ}{ \mathrm{mol}}^{-1}$. The value of $\mathrm{x}$ is_____(Given : Heat capacity of bomb calorimeter $20.0 {\mathrm{kJK}}^{-1}$. Assume coal to be pure carbon)

For the reaction ${\mathrm{H}}_2{\mathrm{F}}_2\left(\mathrm{g}\right)\to {\mathrm{H}}_2\left(\mathrm{g}\right)+{\mathrm{F}}_2\left(\mathrm{g}\right)$

$\mathrm{\Delta U}=-59.6 \mathrm{kJ} {\mathrm{mol}}^{-1}$ at $27 °\mathrm{C}$

The enthalpy change for the above reaction is $\left(-\right)$____ ${\mathrm{kJmol}}^{-1}$ (nearest integer)

(Given : $\mathrm{R}=8.314{\mathrm{JK}}^{-1}{ \mathrm{mol}}^{-1}$) .

The molar heat capacity for an ideal gas at constant pressure is $20.785 \mathrm{J}{ \mathrm{K}}^{-1}{ \mathrm{mol}}^{-1}$. The change in internal energy is $5000 \mathrm{J}$ upon heating it from $300 \mathrm{K}$ to $500 \mathrm{K}$. The number of moles of the gas at constant volume is____

(Given: $\mathrm{R}=8.314 \mathrm{J}{ \mathrm{K}}^{-1}{ \mathrm{mol}}^{-1}$)