For the reaction $CaCO_{3(s)} \rightleftharpoons CaO_{(s)} + CO_{2(g)}$ at $977 \ ^oC$,given $\Delta H = 176 \ kJ \ mol^{-1}$,the value of $\Delta E$ is ............. $kJ$.

For a dimerization reaction,$2 A_{(g)} \rightarrow A_{2(g)}$ at $298 \ K$,$\Delta U^{\ominus} = -20 \ kJ \ mol^{-1}$,$\Delta S^{\ominus} = -30 \ J \ K^{-1} \ mol^{-1}$,then the $\Delta G^{\ominus}$ will be........ $J$

The heats of combustion of $C_2H_4, C_2H_6$ and $H_2$ are $-1409.5 \, kJ, -1558.3 \, kJ$ and $-285.6 \, kJ$ respectively. The heat of hydrogenation of ethene is ...... $kJ$.

$5 \, mol$ of an ideal gas at $100 \, K$ are allowed to undergo reversible compression till its temperature becomes $200 \, K$. If $C_v = 28 \, J \, K^{-1} \, mol^{-1}$,calculate $\Delta U$ and $\Delta pV$ for this process. $(R = 8.0 \, J \, K^{-1} \, mol^{-1})$

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?

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 $\text{kcal mol}^{-1}$.