Calculate the enthalpy of formation of ethylene $(C_2H_4)$ from the following data:
$I. C_{(graphite)} + O_{2(g)} \rightarrow CO_{2(g)}; \Delta H = -393.5 \ kJ$
$II. H_{2(g)} + \frac{1}{2}O_{2(g)} \rightarrow H_2O_{(l)}; \Delta H = -286.2 \ kJ$
$III. C_2H_{4(g)} + 3O_{2(g)} \rightarrow 2CO_{2(g)} + 2H_2O_{(l)}; \Delta H = -1410.8 \ kJ$ (in $kJ$)

The heats of formation of two compounds $X$ and $Y$ are $-84 \ kJ$ and $-156 \ kJ$ respectively. Which of the following statements is correct?

Calculate the heat of reaction for the process: $NH_3(g) + HCl(g) \rightarrow NH_4Cl(s)$ given the following data:
$(i)$ $NH_3(g) + aq \rightarrow NH_3(aq)$,$\Delta H = -8.4 \, Kcal$
$(ii)$ $HCl(g) + aq \rightarrow HCl(aq)$,$\Delta H = -17.3 \, Kcal$
$(iii)$ $NH_3(aq) + HCl(aq) \rightarrow NH_4Cl(aq)$,$\Delta H = -12.5 \, Kcal$
$(iv)$ $NH_4Cl(s) + aq \rightarrow NH_4Cl(aq)$,$\Delta H = +3.9 \, Kcal$ (in $, Kcal$)

If the enthalpies of formation of $Al_2O_3$ and $Cr_2O_3$ are $-1596 \, kJ/mol$ and $-1134 \, kJ/mol$ respectively,then calculate $\Delta H$ for the following reaction in $kJ$:
$2Al + Cr_2O_3 \to Al_2O_3 + 2Cr$

Given the reactions:
$C + \frac{1}{2}O_2 \to CO : \Delta H = -12 \ kJ$
$CO + \frac{1}{2}O_2 \to CO_2 : \Delta H = -10 \ kJ$
For the reaction $C + O_2 \to CO_2 : \Delta H = x \ kJ$,the value of $x$ is: (in $kJ$)

Which of the following equations correctly represents the standard heat of formation $(\Delta H_f^o)$ of methane?