In order to get maximum calorific output, a burner should have an optimum fuel-to-oxygen ratio which corresponds to $3 \mathrm{times}$ as much oxygen as is required theoretically for complete combustion of the fuel. A burner which has been adjusted for methane as fuel (with $\mathrm{X} \mathrm{litre} {\mathrm{hour}}^{-1}$ of ${\mathrm{CH}}_4$ and $6\mathrm{X} \mathrm{litre} {\mathrm{hour}}^{-1}$ of ${\mathrm{O}}_2$) is to be readjusted for butane, ${\mathrm{C}}_4{\mathrm{H}}_{10}$. In order to get the same calorific output, what should be the rate of supply of butane and oxygen? Assume that losses due to incomplete combustion, etc, are the same for both fuels and that the gases behave ideally. Heat of combustion: ${\mathrm{CH}}_4=809 \mathrm{kJ} {\mathrm{mole}}^{-1}, {\mathrm{C}}_4{\mathrm{H}}_{10}=2878 \mathrm{kJ} {\mathrm{mole}}^{-1}$.

$0.16 \mathrm{g}$ of methane was subjected to combustion at $27°\mathrm{C}$ in a bomb calorimeter. The temperature of the calorimeter system (including water) was found to rise by $0.5°\mathrm{C}$. Calculate the heat of combustion of methane in terms of $\mathrm{kJ} {\mathrm{mol}}^{-1}$ at constant volume with a proper sign either $+/-$.

[Given: The thermal capacity of the calorimeter system is $17.7 \mathrm{kJ} {\mathrm{K}}^{-1}, \mathrm{R}=8.314 \mathrm{J} {\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}$]

$0.16 \mathrm{g}$ of methane was subjected to combustion at $27°\mathrm{C}$ in a bomb calorimeter. The temperature of the calorimeter system (including water) was found to rise by $0.5°\mathrm{C}$. Calculate the heat of combustion of methane in terms of $\mathrm{kJ} {\mathrm{mol}}^{-1}$ at constant pressure with a proper sign either $+/-$ and please correct up to three decimal places. The thermal capacity of the calorimeter system is $17.7 \mathrm{kJ} {\mathrm{K}}^{-1}· \left(\mathrm{R}=8.31 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}\right)$.

At what temperature (in Kelvin) does the average translational kinetic energy of a molecule in a gas becomes equal to the kinetic energy of an electron accelerated from rest through a potential difference of $1 \mathrm{volt}$? Answer has to be rounded-off to the nearest integer.

$1 \mathrm{eV}=1.602\times {10}^{-12} \mathrm{erg}, \mathrm{k}=1.38\times {10}^{-23} {\mathrm{m}}^2 \mathrm{kg} {\mathrm{s}}^{-2} {\mathrm{K}}^{-1}$

The ${\mathrm{K}}_{\mathrm{p}}$ value for the reaction equilibrium: ${\mathrm{H}}_2\left(\mathrm{g}\right)+{\mathrm{I}}_2\left(\mathrm{g}\right)\rightleftharpoons 2\mathrm{HI}\left(\mathrm{g}\right)$ is $871$ at $25°\mathrm{C}$. If the vapour pressure of iodine is $4\times {10}^{-4} \mathrm{atm}$, The equilibrium constant in terms of partial pressures is $\mathrm{x} \times {10}^{-2}$ at the same temperature for the reaction equilibrium ${\mathrm{H}}_2\left(\mathrm{g}\right)+{\mathrm{I}}_2\left(\mathrm{s}\right)\rightleftharpoons 2\mathrm{HI}\left(\mathrm{g}\right)$ . The value of $\mathrm{x}$ should be given to the nearest interger value.

Solid ${\mathrm{NH}}_4\mathrm{HS}$ is taken in an evacuated vessel and allowed to dissociate at a certain temperature until the total gas pressure is $0.66 \mathrm{atm}$. What would be the value of ${\mathrm{K}}_{\mathrm{p}}$ for the following reaction?

${\mathrm{NH}}_4\mathrm{HS}\left(\mathrm{s}\right)\rightleftharpoons {\mathrm{NH}}_3\left(\mathrm{g}\right)+{\mathrm{H}}_2\mathrm{S}\left(\mathrm{g}\right)$

What would be the partial pressure of ${\mathrm{H}}_2\mathrm{S}$, if additional ${\mathrm{NH}}_3$ is introduced into the equilibrium mixture at the same temperature, until the partial pressure of ${\mathrm{NH}}_3$ is $0.921 \mathrm{atm}?$ (Answer to be rounded up to three places of decimals)

Solid ammonium carbamate, ${\mathrm{NH}}_2{\mathrm{COONH}}_4,$ dissociates on heating to ${\mathrm{NH}}_3$ and ${\mathrm{CO}}_2$.

${\mathrm{NH}}_2{\mathrm{COONH}}_4\left(\mathrm{s}\right)\rightleftharpoons 2{\mathrm{NH}}_3\left(\mathrm{g}\right)+{\mathrm{CO}}_2\left(\mathrm{g}\right)$

When pure carbamate is put into a closed container and allowed to attain equilibrium with the gaseous products at a constant temperature, $35°\mathrm{C}$, the total pressure is found to be $0.30 \mathrm{atm}$. Determine ${\mathrm{K}}_{\mathrm{p}}$ $\left(\mathrm{in} {10}^{-3} {\mathrm{atm}}^3\right)$ for this reaction at $35°\mathrm{C}$.