We can use Hess's law to calculate enthalpy changes that...

We can use Hess's law to calculate enthalpy changes that cannot be measured. One such reaction is the conversion of methane to ethane: $$ 2 \mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2}(g) $$ Calculate the $\Delta H^{\circ}$ for this reaction using the following thermochemical data: $$ \begin{aligned} \mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) & \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) & \Delta H^{\circ} &=-890.3 \mathrm{~kJ} \\ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) & \Delta H^{\circ} &=-571.6 \mathrm{~kJ} \\ 2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{O}_{2}(g) & \longrightarrow 4 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) & \Delta H^{\circ} &=-3120.8 \mathrm{~kJ} \end{aligned} $$

We can use Hess's law to calculate enthalpy changes that cannot be measured. One such reaction is the conversion of methane to ethane:
$$
2 \mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2}(g)
$$
Calculate the $\Delta H^{\circ}$ for this reaction using the following thermochemical data:
$$
\begin{aligned}
\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) & \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) & \Delta H^{\circ} &=-890.3 \mathrm{~kJ} \\
2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) & \Delta H^{\circ} &=-571.6 \mathrm{~kJ} \\
2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{O}_{2}(g) & \longrightarrow 4 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) & \Delta H^{\circ} &=-3120.8 \mathrm{~kJ}
\end{aligned}
$$

Key Concepts

Hess's Law

Hess’s Law states that the total enthalpy change for a reaction is the same, no matter how many intermediate steps are taken. This principle is based on the conservation of energy and allows the calculation of reaction enthalpies by breaking a reaction into a series of steps with known enthalpy changes, even if the overall reaction cannot be measured directly.

Enthalpy Change

Enthalpy change (?H) is a measure of the heat absorbed or released during a chemical reaction at constant pressure. It is an extensive property that can be added up for sequential chemical processes, making it possible to calculate the overall energy change when reactions are combined or manipulated according to Hess's Law.

Thermochemical Equations

Thermochemical equations are balanced chemical equations that include the enthalpy change of the reaction. They provide essential information about the energy transfer in a chemical process and are used in calculating unknown enthalpy changes by systematically combining, reversing, or scaling various reactions.

Reaction Manipulation

Reaction manipulation involves reversing, scaling, or adding chemical equations to achieve a desired overall reaction. When manipulating these reactions, the corresponding enthalpy changes must be adjusted appropriately (inverting the sign when the reaction is reversed and multiplying the enthalpy when the reaction is scaled) to maintain consistency with the conservation of energy, as dictated by Hess’s Law.

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