Hess's law can be used to calculate reaction enthalpies for...

Hess's law can be used to calculate reaction enthalpies for hypothetical processes that can't be carried out in the laboratory. Set up a Hess's law cycle that will let you calculate $\Delta H^{\circ}$ for the conversion of methane to ethylene: $$ 2 \mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(g)+2 \mathrm{H}_{2}(g) $$ You can use the following information: $$ 2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) $$ $$ \Delta H^{\circ}=-3120.8 \mathrm{kJ} $$ $$ \mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) $$ $$ \begin{array}{l}{\Delta H^{\circ}=-890.3 \mathrm{kJ}} \\ {\Delta H^{\circ}=-136.3 \mathrm{kJ}}\end{array} $$ $$ \begin{array}{l}{\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)} \\ {\mathrm{H}_{2} \mathrm{O}(l) \quad \Delta H_{\mathrm{f}}^{\circ}=-285.8 \mathrm{kJ} / \mathrm{mol}}\end{array} $$

Hess's law can be used to calculate reaction enthalpies for hypothetical processes that can't be carried out in the laboratory. Set up a Hess's law cycle that will let you calculate $\Delta H^{\circ}$ for the conversion of methane to ethylene:
$$
2 \mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(g)+2 \mathrm{H}_{2}(g)
$$
You can use the following information:
$$
2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l)
$$
$$
\Delta H^{\circ}=-3120.8 \mathrm{kJ}
$$
$$
\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)
$$
$$
\begin{array}{l}{\Delta H^{\circ}=-890.3 \mathrm{kJ}} \\ {\Delta H^{\circ}=-136.3 \mathrm{kJ}}\end{array}
$$
$$
\begin{array}{l}{\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)} \\ {\mathrm{H}_{2} \mathrm{O}(l) \quad \Delta H_{\mathrm{f}}^{\circ}=-285.8 \mathrm{kJ} / \mathrm{mol}}\end{array}
$$

Key Concepts

Hess's Law

Hess's Law states that the total enthalpy change for a chemical reaction is the same regardless of the path taken from reactants to products. This principle allows one to calculate the enthalpy change for a reaction that may not be directly measurable by using a series of steps with known enthalpy changes.

Thermochemical Cycles

A thermochemical cycle is a diagram that represents the different pathways between the same reactants and products. By constructing a cycle, you can combine and rearrange known reactions so that their cumulative enthalpy changes sum to the desired reaction’s enthalpy change. This cycle illustrates energy conservation in chemical reactions.

Standard Enthalpy of Reaction

The standard enthalpy of reaction is the heat change that occurs when reactants in their standard states are converted to products in their standard states. It is typically calculated by summing the standard enthalpies of formation of the products and subtracting those of the reactants, or by using Hess’s Law with known reaction enthalpies.

Manipulation of Thermochemical Equations

When using Hess's Law, individual thermochemical equations may be reversed, multiplied, or added together. It is crucial to properly adjust the sign and magnitude of the enthalpy change associated with each manipulated equation to ensure that the overall enthalpy change is correctly calculated.

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