${\mathrm{N}}_2$ gas is assumed to behave ideally. A given volume of ${\mathrm{N}}_2$ originally at $373 \mathrm{K}$ and $0.1013 \mathrm{MPa}$ pressure is adiabatically compressed by irreversible process due to which its temperature rises to $673 \mathrm{K}$. Which of the following is/are correct?

Calculate magnitude of $\mathrm{\Delta U}$ of the reaction in $\mathrm{kcal} {\mathrm{mol}}^{-1}$ for the hydrogenation of acetylene to ethene at constant volume and at $77°\mathrm{C}.$ Given that ${\mathrm{\Delta H}}_{\mathrm{f}}\left({\mathrm{H}}_2\mathrm{O}\right)=-67.8 \mathrm{kcal} {\mathrm{mol}}^{-1}$; ${\mathrm{\Delta H}}_{\text{comb }}\left({\mathrm{C}}_2{\mathrm{H}}_2\right)=-310.1 \mathrm{kcal} {\mathrm{mol}}^{-1}, {\mathrm{\Delta H}}_{\text{comb }}\left({\mathrm{C}}_2{\mathrm{H}}_4\right)=-337.2 \mathrm{kcal} {\mathrm{mol}}^{-1}$.

Round off your answer to the nearest integer.

The thermochemical equation for the dissociation of hydrogen gas into atoms may be written as

${\mathrm{H}}_2\to 2\mathrm{H}; \mathrm{\Delta H}=436 \mathrm{kJ}$

What is the ratio of the energy yield on combustion of hydrogen atoms to steam to the yield on combustion of an equal mass of hydrogen molecules to steam? ${\mathrm{\Delta H}}_{\text{combustion }}\text{ for }{\mathrm{H}}_2=-241.81 \mathrm{kJ}$

Answer correct up to one significant value.

Assuming that $50\%$ of the heat is useful, how many $\mathrm{kgs}$ of water, at $15°\mathrm{C}$, can be heated to $95°\mathrm{C}$ by burning $200 \mathrm{litres}$ of methane at $\mathrm{NTP}? {\mathrm{\Delta H}}_{\text{combustion }}\left({\mathrm{CH}}_4\right)$ $=211 \mathrm{kcal}/\mathrm{mole},\text{ specific heat of water }=1 \mathrm{kcal}/\mathrm{kg} \mathrm{K}.$

Answer after rounding off to the nearest integer value.

Water-gas is produced by the reaction $\mathrm{C}\left(\mathrm{s}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)\to {\mathrm{H}}_2\left(\mathrm{g}\right)+\mathrm{CO}\left(\mathrm{g}\right)$. The heat required for this endothermic reaction may be supplied by adding a limited amount of air and burning some carbon to carbon dioxide. Calculate the amount of carbon to be burnt to ${\mathrm{CO}}_2$ to provide enough heat for the water- gas $\left({\mathrm{H}}_2+\mathrm{CO}\right)$ conversion of $100 \mathrm{g}$ of carbon. $\mathrm{\Delta H}{°}_{\mathrm{f}}$ for $\mathrm{CO}=-110.53 \mathrm{kJ}, \mathrm{\Delta H}{°}_{\mathrm{f}}$ for ${\mathrm{H}}_2\mathrm{O}=-241.81 \mathrm{kJ}$ and ${\mathrm{\Delta H}}_{\text{combustion }}$ for $\mathrm{C}=-393.51 \mathrm{kJ}.$

Final answer has to be given after rounding-off to the nearest integer.

Calculate the $\mathrm{C}-\mathrm{C}$ bond enthalpy from the following data:

$\left(\mathrm{a}\right) \mathrm{C}\left(\mathrm{s}\right)⟶\mathrm{C}\left(\mathrm{g}\right); \mathrm{\Delta H}=170 \mathrm{kcal}$

$\left(\mathrm{b}\right) \frac{1}{2}{\mathrm{H}}_2\left(\mathrm{g}\right)⟶\mathrm{H}\left(\mathrm{g}\right); \mathrm{\Delta H}=52 \mathrm{kcal}$

$\left(\mathrm{c}\right)$ Heat of formation of ethane $=-20 \mathrm{kcal}$

$\left(\mathrm{d}\right) \mathrm{C}-\mathrm{H}$ bond enthalpy$=99 \mathrm{kcal}$