When ΔH is positive and small, and ΔS is positive and large, the reaction will be

The spontaneity of a reaction is determined by the Gibbs free energy change, given by:

\[\Delta G = \Delta H - T\Delta S\]

A reaction is spontaneous when \(\Delta G\) is negative.

In this question:

• \(\Delta H\) is positive and small (slightly endothermic).
• \(\Delta S\) is positive and large (significant increase in disorder).

Substituting into the equation:

\[\Delta G = (\text{small positive}) - T \times (\text{large positive})\]

Since \(T\) (absolute temperature in Kelvin) is always positive, the term \(T\Delta S\) will be a large positive number. Subtracting this large positive value from a small positive \(\Delta H\) gives:

\[\Delta G = \text{small positive} - \text{large positive} = \text{negative}\]

A negative \(\Delta G\) means the reaction is spontaneous.

Exam tip: When \(\Delta H\) is positive but \(\Delta S\) is also positive and large, the entropy term dominates, and the reaction is spontaneous, especially at higher temperatures. This is called an entropy-driven reaction.