Calculate the enthalpy change in $kJ$ for the reaction: $2C_{(graphite)} + 2H_{2(g)} \to C_2H_{4(g)}$
$C_{(graphite)} + O_{2(g)} \to CO_{2(g)} \quad \Delta H = -393.5 \ kJ$
$C_2H_{4(g)} + 3O_{2(g)} \to 2CO_{2(g)} + 2H_2O_{(l)} \quad \Delta H = -1410.9 \ kJ$
$H_{2(g)} + 1/2O_{2(g)} \to H_2O_{(l)} \quad \Delta H = -285.8 \ kJ$

State and prove Hess's law of constant heat summation.

Based on Hess's law calculations,what is the average bond energy of $S-O$ in $SO_3$ if $\Delta H_f^o$ of $SO_3$ is $-270 \ kJ \ mol^{-1}$. The bond energy of $O=O$ is $495 \ kJ \ mol^{-1}$ and the heat of sublimation for $S_{(s)}$ is $277 \ kJ \ mol^{-1}$? (Given: Bond energy of $S=O$ is not provided,assume the reaction $S_{(s)} + \frac{3}{2} O_2(g) \rightarrow SO_3(g)$). Note: The provided values in the prompt were inconsistent with standard chemical data; using standard values: $\Delta H_{sub}(S) = 277 \ kJ \ mol^{-1}$,$BE(O=O) = 495 \ kJ \ mol^{-1}$,$BE(S-O) = 330 \ kJ \ mol^{-1}$ is not the goal,we calculate based on the provided logic.

The standard enthalpies of formation for $CH_{4(g)}$,$CO_{2(g)}$,and $H_2O_{(l)}$ are $-75$,$-393.5$,and $-286 \ kJ \ mol^{-1}$ respectively. The enthalpy change for the reaction $CH_{4(g)} + 2O_{2(g)} \rightarrow CO_{2(g)} + 2H_2O_{(l)}$ is ......... $kJ$.

While performing a thermodynamics experiment,a student made the following observations:
$HCl + NaOH \rightarrow NaCl + H_{2}O$ $\Delta H = -57.3 \ kJ \ mol^{-1}$
$CH_{3}COOH + NaOH \rightarrow CH_{3}COONa + H_{2}O$ $\Delta H = -55.3 \ kJ \ mol^{-1}$
The enthalpy of ionization of $CH_{3}COOH$ as calculated by the student is $kJ \ mol^{-1}$. (nearest integer)

Calculate the standard heat of formation of carbon disulphide $(l)$,given that the standard heat of combustion of carbon $(s)$,sulphur $(s)$ and carbon disulphide $(l)$ are $-393.3, -293.72$ and $-1108.76 \text{ kJ mol}^{-1}$ respectively.