Methanol, a potential replacement for gasoline as an...

Methanol, a potential replacement for gasoline as an automotive fuel, can be made from $\mathrm{H}_{2}$ and $\mathrm{CO}$ by the reaction $$ \mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(g) $$ At $500.0 \mathrm{~K},$ this reaction has $K_{\mathrm{p}}=6.25 \times 10^{-3}$ . Calculate $\Delta G_{500}^{\circ}$ for this reaction in units of kilojoules.

Methanol, a potential replacement for gasoline as an automotive fuel, can be made from $\mathrm{H}_{2}$ and $\mathrm{CO}$ by the reaction
$$
\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(g)
$$
At $500.0 \mathrm{~K},$ this reaction has $K_{\mathrm{p}}=6.25 \times 10^{-3}$ . Calculate $\Delta G_{500}^{\circ}$ for this reaction in units of kilojoules.

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Key Concepts

Gibbs Free Energy

Gibbs free energy is a thermodynamic potential that measures the maximum reversible work a system can perform at constant temperature and pressure. It indicates the spontaneity of a reaction: a negative ?G means that a process is spontaneous under constant conditions, while a positive ?G implies non-spontaneity.

Equilibrium Constant

The equilibrium constant, commonly denoted as K, expresses the ratio of the concentrations or partial pressures of products to reactants when a chemical reaction is at equilibrium. Its value indicates the extent to which a reaction proceeds and is fundamentally linked to the reaction’s thermodynamic properties.

Relationship between ?G° and Equilibrium Constant

The connection between standard Gibbs free energy change (?G°) and the equilibrium constant is given by the equation ?G° = -RT ln K, where R is the gas constant and T is the absolute temperature. This equation allows one to relate the thermodynamic favorability of a reaction directly to its equilibrium constant.

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