Calculate the work done for the following reaction at $27^{\circ}C$: $C_2H_4(g) + H_2(g) \rightarrow C_2H_6(g)$ $(R = 8.314 \text{ J K}^{-1} \text{mol}^{-1})$ (in $\text{ J}$)

$A$ liquid confined inside an adiabatic container is taken from state $1$ to state $2$ by a single-stage process as shown in the $P-V$ diagram. Then,$\Delta H$ is:

In a reversible process,under what condition does the heat exchanged become a state function?

$0.3 \ g$ of ethane undergoes combustion at $27^{\circ} C$ in a bomb calorimeter. The temperature of the calorimeter system (including the water) is found to rise by $0.5^{\circ} C$. The heat evolved during combustion of ethane at constant pressure is $....... kJ \ mol^{-1}$. (Nearest integer) [Given: The heat capacity of the calorimeter system is $20 \ kJ \ K^{-1}$,$R = 8.3 \ J \ K^{-1} \ mol^{-1}$. Assume ideal gas behaviour. Atomic mass of $C$ and $H$ are $12$ and $1 \ g \ mol^{-1}$ respectively]

$A$ gas expands from $3\, dm^3$ to $5.8\, dm^3$ against a constant external pressure of $3\, bar$. The work done during expansion is used to heat $2\, moles$ of water from $290\, K$ to a final temperature of $T\, K$. If the specific heat of water is $4.2\, J\, g^{-1}\, K^{-1}$,then $T = ......\, K$. (in $.6$)

The heat evolved in the combustion of methane is given by the following equation: $CH_{4(g)} + 2O_{2(g)} \to CO_{2(g)} + 2H_2O_{(l)}$; $\Delta H = -890.3 \ kJ$. How many grams of methane would be required to produce $445.15 \ kJ$ of heat of combustion?