The heat of formation of methane $C_{(s)} + 2H_{2(g)} \to CH_{4(g)}$ at constant pressure is $-18500 \ cal$ at $25 \ ^oC$. The heat of reaction at constant volume would be (in $cal$)

The standard enthalpy of formation $(\Delta_fH^o)$ of methane $(CH_{4(g)})$ at $298 \, K$ is $-74.8 \, kJ \, mol^{-1}$. What additional information is required to calculate the average bond energy of the $C-H$ bond?

Given:
$(i) \, C(\text{graphite}) + O_{2(g)} \to CO_{2(g)}; \Delta_r H^\ominus = x \, kJ \, mol^{-1}$
$(ii) \, C(\text{graphite}) + \frac{1}{2} O_{2(g)} \to CO_{(g)}; \Delta_r H^\ominus = y \, kJ \, mol^{-1}$
$(iii) \, CO_{(g)} + \frac{1}{2} O_{2(g)} \to CO_{2(g)}; \Delta_r H^\ominus = z \, kJ \, mol^{-1}$
Based on the above thermochemical equations,find out which one of the following algebraic relationships is correct?

If the standard heat of the reaction $Fe_2O_{3(s)} + 3CO_{(g)} = 2Fe_{(s)} + 3CO_{2(g)}$ is $-6.6 \, kcal$,then $\Delta H_f^o$ for $Fe_2O_{3(s)}$ is $...... \, kcal/mol$. [Given: $\Delta H_f^o$ of $CO_{(g)} = -26.4 \, kcal$ and $\Delta H_f^o$ of $CO_{2(g)} = -94 \, kcal$]

The heat of formation of $H_2O$ is $-286 \, kJ/mol$ and $H_2O_2$ is $-188 \, kJ/mol$. The enthalpy change for the reaction $2H_2O_2 \to 2H_2O + O_2$ is......$kJ$.

Identify $I, II, III$ in the given Born-Haber cycle diagram for the dissolution of an ionic solid $AB(s)$:
$AB(s) \xrightarrow{I} A^+(aq) + B^-(aq)$
$AB(s) \xrightarrow{II} A^+(g) + B^-(g)$
$A^+(g) + B^-(g) \xrightarrow{III} A^+(aq) + B^-(aq)$