Calculate the standard enthalpy change of formation of methane from the following standard enthalpy changes of combustion:

$$\begin{gathered} \mathrm{carbon}=-394 \mathrm{kJ} {\mathrm{mol}}^{-1}. \\ \mathrm{hydrogen}=-286 \mathrm{kJ} {\mathrm{mol}}^{-1}. \\ \mathrm{methane}=-891 \mathrm{kJ} {\mathrm{mol}}^{-1}. \end{gathered}$$

Calculate the standard enthalpy change of combustion of methane using the following bond energies:

$$\begin{gathered} \mathrm{E}\left(\mathrm{C}-\mathrm{H}\right)=+412 \mathrm{kJ} {\mathrm{mol}}^{-1}. \\ \mathrm{E}\left(\mathrm{O}=\mathrm{O}\right)=+496 \mathrm{kJ} {\mathrm{mol}}^{-1}. \\ \mathrm{E}\left(\mathrm{C}=\mathrm{O}\right)=+805 \mathrm{kJ} {\mathrm{mol}}^{-1}. \\ \mathrm{E}\left(\mathrm{O}-\mathrm{H}\right)=+463 \mathrm{kJ} {\mathrm{mol}}^{-1}. \end{gathered}$$

Use the average bond energies that follow to calculate a value for the enthalpy change for the reaction:

$$\begin{gathered} {\mathrm{H}}_2+{\mathrm{I}}_2\to 2\mathrm{HI}. \\ \mathrm{E}\left(\mathrm{H}-\mathrm{H}\right)=+436 \mathrm{kJ} {\mathrm{mol}}^{-1}. \\ \mathrm{E}\left(\mathrm{I}-\mathrm{I}\right)=+151 \mathrm{kJ} {\mathrm{mol}}^{-1}. \\ \mathrm{E}\left(\mathrm{H}-\mathrm{I}\right)=+299 \mathrm{kJ} {\mathrm{mol}}^{-1}. \end{gathered}$$

Given the enthalpy changes $∆{\mathrm{H}}_1$ and $∆{\mathrm{H}}_2$ below, construct Hess's cycle that will enable you to find the enthalpy change,$∆{\mathrm{H}}_{\mathrm{f}}$, for the reaction:

$$\begin{gathered} {\mathrm{MgCO}}_3\left(\mathrm{s}\right)\to \mathrm{MgO}\left(\mathrm{s}\right)+{\mathrm{CO}}_2\left(\mathrm{g}\right); ∆{\mathrm{H}}_{\mathrm{r}}. \\ {\mathrm{MgCO}}_3\left(\mathrm{s}\right)+2\mathrm{HCl}\left(\mathrm{aq}\right)\to {\mathrm{MgCl}}_2 \left(\mathrm{aq}\right)+{\mathrm{CO}}_2\left(\mathrm{g}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right); ∆{\mathrm{H}}_1. \\ \mathrm{MgO}\left(\mathrm{s}\right)+2\mathrm{HCl}\left(\mathrm{aq}\right)\to {\mathrm{MgCl}}_2\left(\mathrm{aq}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right); ∆{\mathrm{H}}_2. \end{gathered}$$