When $2.0 \ g$ of sucrose is oxidized to form $CO_{2(g)}$ and $H_2O(\ell)$,the internal energy changes by $-24 \ kJ$. Calculate the value of $\Delta H$ at $298 \ K$ in $kJ \ mol^{-1}$. (Molar mass of sucrose $= 342 \ g \ mol^{-1}$)

For the reaction $2A_{(g)} + B_{(g)} \to 2D_{(g)}$,given $\Delta U^{\theta} = -10.5 \ kJ$ and $\Delta S^{\theta} = -44.1 \ J \ K^{-1}$. Calculate $\Delta G^{\theta}$ for the reaction at $298 \ K$ and predict whether the reaction may occur spontaneously.

What is the value of $\Delta S_{\text{total}}$ for the following reaction at $300 \ K$:
$Fe_{2}O_{3(s)} + 3CO_{(g)} \longrightarrow 2Fe_{(s)} + 3CO_{2(g)}$
$\Delta H^{\circ} = -25 \ kJ, \Delta S^{\circ} = 15 \ J \ K^{-1}$ (in $J \ K^{-1}$)

Consider the $P-V$ (pressure-volume) diagram given below,where an ideal gas is reversibly converted from state $X$ to state $Y$. Among the following,which is the correct $T-S$ (temperature-entropy) diagram corresponding to this process?

For the reaction $2X_{(s)} + 2Y_{(s)} \to 2C_{(\ell)} + D_{(g)}$,the value of $q_p$ is $-28 \, \text{kcal mol}^{-1}$ at $2700 \, ^\circ\text{C}$. Calculate the value of $q_v$ in $\text{kcal mol}^{-1}$.

$0.3 \ g$ 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]