Given the following data: 2 H2(g)+C(s) ⟶CH4(g) ΔG^∘=-51 kJ 2 H2(g)+O2(g) ⟶2 H2 O(

step 1 Okay, problem 57, we have this final reaction here and we're just asked to calculate the delta G

Given the following data: 2 H2(g)+C(s) ⟶CH4(g) ...

Given the following data: $$\begin{aligned}2 \mathrm{H}_{2}(g)+\mathrm{C}(s) \longrightarrow \mathrm{CH}_{4}(g) & & \Delta G^{\circ}=-51 \mathrm{~kJ} \\ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) & & \Delta G^{\circ}=-474 \mathrm{~kJ} \\ \mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) & & \Delta G^{\circ}=-394 \mathrm{~kJ} \end{aligned}$$ Calculate $\Delta G^{\circ}$ for $\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$.

Given the following data:
$$\begin{aligned}2 \mathrm{H}_{2}(g)+\mathrm{C}(s) \longrightarrow \mathrm{CH}_{4}(g) & & \Delta G^{\circ}=-51 \mathrm{~kJ} \\
2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) & & \Delta G^{\circ}=-474 \mathrm{~kJ} \\
\mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) & & \Delta G^{\circ}=-394 \mathrm{~kJ}
\end{aligned}$$
Calculate $\Delta G^{\circ}$ for $\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$.

Key Concepts

Hess's Law

Hess's Law states that the total enthalpy change (or Gibbs free energy change) for a reaction is the same regardless of the pathway taken, provided the initial and final conditions are identical. This concept is crucial because it allows one to calculate the overall energy change of a reaction by breaking it down into a series of steps whose individual energy changes are known, even if the steps themselves do not occur in the actual reaction mechanism.

Gibbs Free Energy

Gibbs free energy is a thermodynamic potential that measures the maximum reversible work that can be performed by a system at constant temperature and pressure. A negative value of Gibbs free energy indicates a spontaneous process under the given conditions, while a positive value suggests non-spontaneity. Understanding this concept is essential for predicting reaction spontaneity and for performing energy balance calculations in chemical reactions.

Standard Free Energy Change Calculation

The standard free energy change of a reaction can be determined by using the known free energy changes of related reactions, adjusting for reaction stoichiometry and reversing reactions as needed. This method involves mathematically combining reactions to yield the target reaction and then summing the corresponding ?G values. This approach is a practical application of Hess's Law in the context of Gibbs free energy.

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