Methanol (CH₃OH) is made industrially in two steps from CO and H₂. It is so cheap to make that it is being considered for use as a precursor to hydrocarbon fuels, such as methane (CH₄):
Step 1. CO(g) + 2 H₂(g) S CH₃OH(l) ΔS° = - 332 J/K
Step 2. CH₃OH₁l₂ → CH₄(g) + 1/2 O₂(g) ΔS° = 162 J/K
(l) Is the overall reaction spontaneous at 298 K?

Verified step by step guidance

1. Calculate the overall change in entropy (\(\Delta S^\circ_{\text{total}}\)) for the reaction by adding the \(\Delta S^\circ\) values for each step: \(\Delta S^\circ_{\text{total}} = \Delta S^\circ_{\text{Step 1}} + \Delta S^\circ_{\text{Step 2}}\).
2. Determine the change in enthalpy (\(\Delta H^\circ\)) for each step if provided, or use standard enthalpy values to calculate it.
3. Use the Gibbs free energy equation \(\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ\) to find the overall \(\Delta G^\circ\) at 298 K.
4. Evaluate the sign of \(\Delta G^\circ\): if \(\Delta G^\circ < 0\), the reaction is spontaneous; if \(\Delta G^\circ > 0\), it is non-spontaneous.
5. Conclude whether the overall reaction is spontaneous at 298 K based on the sign of \(\Delta G^\circ\).

Key Concepts

Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that helps predict the spontaneity of a reaction at constant temperature and pressure. A reaction is spontaneous if the change in Gibbs Free Energy (ΔG) is negative. It is calculated using the equation ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy.

Entropy (ΔS)

Entropy (S) is a measure of the disorder or randomness in a system. The change in entropy (ΔS) during a reaction indicates how the distribution of energy changes. A positive ΔS suggests an increase in disorder, while a negative ΔS indicates a decrease. In the context of the given reactions, the values of ΔS will influence the spontaneity of the overall process.

Spontaneity of Reactions

The spontaneity of a chemical reaction refers to its ability to proceed without external intervention. It is determined by the balance between enthalpy (ΔH) and entropy (ΔS) changes. A reaction is spontaneous if the overall ΔG is negative, which can occur when the enthalpy decrease outweighs the entropy decrease, or vice versa, depending on the temperature and the magnitudes of ΔH and ΔS.