Question

Methanol is formed by the following gas phase homogeneous reaction:

\[ \mathrm{CO(g) + 2H_2(g) \rightleftharpoons CH_3OH(g)} \]

The standard Gibbs free energies of formation at \(298\ \mathrm{K}\) for CO and \(\mathrm{CH_3OH}\) are \(-137\ \mathrm{kJ\,mol^{-1}}\) and \(-162\ \mathrm{kJ\,mol^{-1}}\), respectively. The value of the universal gas constant is \(8.314\ \mathrm{J\,mol^{-1}\,K^{-1}}\). The equilibrium constant for the given reaction at \(298\ \mathrm{K}\) is ______ \(\times 10^4\) (rounded off to one decimal place).

Hint:

Compute \(\Delta G_{rxn}^\circ\) from the formation energies (remembering \(\Delta G_f^\circ = 0\) for elemental \(\mathrm{H_2}\)), then use \(\Delta G_{rxn}^\circ=-RT\ln K\).

Answer 1

Correct Answer: 2.4

Using base-10 logs: $\log_{10}K=25000/5705.8=4.3813$, $K=10^{4.3813}\approx2.406\times10^4\approx2.4\times10^4$, matching the natural-log approach.