How much $kJ$ energy is released when $6 \ mol$ of octane is burnt in air? Given $\Delta H_f^o$ for $CO_{2(g)}$,$H_2O_{(g)}$ and $C_8H_{18(l)}$ respectively are $-490$,$-240$,and $+160 \ kJ/mol$.

For the reaction $\frac{1}{2}X_2 + \frac{3}{2}Y_2 \to XY_3$,$\Delta H = -30 \ kJ/mol$. Given $\Delta S_{X_2} = 60 \ J/mol \cdot K$,$\Delta S_{Y_2} = 40 \ J/mol \cdot K$,and $\Delta S_{XY_3} = 50 \ J/mol \cdot K$,calculate the temperature at equilibrium in $K$.

Water vapor is an ideal gas. Calculate the internal energy change $(\Delta U)$ when $1 \, \text{mol}$ of water is vaporized at $1 \, \text{bar}$ pressure and $100 \, ^{\circ}C$. (Given: Molar enthalpy of vaporization of water at $1 \, \text{bar}$ and $373 \, K = 41 \, kJ \, \text{mol}^{-1}$ and $R = 8.3 \, J \, \text{mol}^{-1} \, K^{-1}$)

An ideal gas is expanded from $(p_1, V_1, T_1)$ to $(p_2, V_2, T_2)$ under different conditions. The correct statement$(s)$ among the following is(are):
[$A$] The work done on the gas is maximum when it is compressed irreversibly from $(p_2, V_2)$ to $(p_1, V_1)$ against constant pressure $p_1$.
[$B$] The work done by the gas is less when it is expanded reversibly from $V_1$ to $V_2$ under adiabatic conditions as compared to that when expanded reversibly from $V_1$ to $V_2$ under isothermal conditions.
[$C$] The change in internal energy of the gas is $(i)$ zero,if it is expanded reversibly with $T_1=T_2$,and $(ii)$ positive,if it is expanded reversibly under adiabatic conditions with $T_1 \neq T_2$.
[$D$] If the expansion is carried out freely,it is simultaneously both isothermal as well as adiabatic.

For the reaction: $A_{(g)} + B_{(s)} \rightleftharpoons 2C_{(g)} + D_{(g)}$,given $\Delta U = 5.0 \ kcal$ and $\Delta S = 50 \ cal \ K^{-1}$ at $400 \ K$. Calculate $\Delta G$ for the reaction. (in $kcal$)

$\Delta H_f^o$ of water is $-285.5\, kJ\, mol^{-1}$. If enthalpy of neutralisation of monoacidic strong base is $-57.3\, kJ\, mol^{-1}$,$\Delta H_f^o$ of $OH^{-}$ ion will be $.....\, kJ\, mol^{-1}$.