Find the enthalpy of formation of the $OH^-$ ion in $KJ$ at $25^\circ C$ from the following data:
$H_2O_{(l)} \to H^+_{(aq)} + OH^-_{(aq)} ; \Delta H = 57.32 \ KJ$
$H_{2(g)} + \frac{1}{2} O_{2(g)} \to H_2O_{(l)} ; \Delta H = -286.20 \ KJ$

Given: $H_2 + 1/2 O_2 \rightarrow H_2O : \Delta H = -68.4 \ \text{kcal}$,$C + O_2 \rightarrow CO_2 : \Delta H = -94.0 \ \text{kcal}$,and $C_2H_5OH + 3O_2 \rightarrow 2CO_2 + 3H_2O : \Delta H = -327.0 \ \text{kcal}$. Calculate the heat of formation of $C_2H_5OH$ in $\text{kcal}$.

Given that $C + O_{2} \longrightarrow CO_{2} ; \Delta H^{\circ} = -x \ kJ$ and $2 CO + O_{2} \longrightarrow 2 CO_{2} ; \Delta H^{\circ} = -y \ kJ$. The heat of formation of carbon monoxide will be

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?

Given that $\Delta H_f(H) = 218 \ kJ/mol$, express the $H-H$ bond energy in $kcal/mol$.

Calculate the heat of combustion (in $kJ$) of methane from the following data:
$(i)$ $C_{\text{(graphite)}} + 2H_{2(g)} \rightarrow CH_{4(g)} \quad \Delta H = -74.8 \ kJ$
(ii) $C_{\text{(graphite)}} + O_{2(g)} \rightarrow CO_{2(g)} \quad \Delta H = -393.5 \ kJ$
(iii) $H_{2(g)} + 1/2 O_{2(g)} \rightarrow H_2O_{(l)} \quad \Delta H = -286.2 \ kJ$