The difference between the reaction enthalpy change $(\Delta _r H)$ and reaction internal energy change $(\Delta _r U)$ for the reaction $2C_6H_{6(l)} + 15O_{2(g)} \longrightarrow 12CO_{2(g)} + 6H_2O_{(l)}$ at $300 \ K$ is $....$ $J \ mol^{-1}$ $(R = 8.314 \ J \ mol^{-1} \ K^{-1})$

The $C_p$ of an ideal gas is $10.314 \ J \ mol^{-1} \ K^{-1}$. One mole of this gas is expanded against a constant pressure of $p \ atm$. The change in temperature during expansion is $1.0 \ K$. The values of $q$ (in $J$) and $\Delta H$ (in $J \ mol^{-1}$) are respectively

One mole of an ideal gas is allowed to expand freely and adiabatically into vacuum until its volume has doubled. Which of the following statements is $NOT$ true concerning this expansion?

Match the conditions and the temperature for the 'fusion' process of $H_2O_{(s)}$ at $1 \ atm$ pressure.

Condition	Temperature
$(1)$. Spontaneous	$(p)$. $273 \ K$
$(2)$. At equilibrium	$(q)$. $260 \ K$
$(3)$. Non-spontaneous	$(r)$. $280 \ K$

The combustion of one mole of benzene takes place at $298 \, K$ and $1 \, atm$. After combustion,$CO_{2(g)}$ and $H_2O_{(l)}$ are produced and $3267.0 \, kJ$ of heat is liberated. Calculate the standard enthalpy of formation,$\Delta_f H^{\ominus}$ of benzene. Standard enthalpies of formation of $CO_{2(g)}$ and $H_2O_{(l)}$ are $-393.5 \, kJ \, mol^{-1}$ and $-285.83 \, kJ \, mol^{-1}$ respectively.

The heat of reaction for $C_6H_{12}O_{6(s)} + 6O_{2(g)} \to 6CO_{2(g)} + 6H_2O_{(l)}$ at constant pressure is $-651 \, kcal$ at $17 \, ^oC$. Calculate the heat of reaction at constant volume at $17 \, ^oC$ in $kcal$.