Why do some reactions have positive entropy changes but are non-spontaneous?

Some reactions have positive entropy changes but are non-spontaneous due to unfavourable enthalpy changes and temperature conditions.

Entropy is a measure of the disorder or randomness of a system. A positive change in entropy (ΔS) indicates an increase in disorder, which is generally favourable for a reaction to occur spontaneously. However, the spontaneity of a reaction is not determined by entropy alone. It is also influenced by the enthalpy change (ΔH) and the absolute temperature (T) of the system. This relationship is described by the Gibbs free energy equation: ΔG = ΔH - TΔS.

For a reaction to be spontaneous, the Gibbs free energy change (ΔG) must be negative. If the enthalpy change is positive (endothermic reaction) and large enough, it can outweigh the positive entropy change, resulting in a positive ΔG. This means the reaction is non-spontaneous under these conditions.

Temperature also plays a crucial role in determining the spontaneity of a reaction. Even if both ΔH and ΔS are positive, the reaction can still be non-spontaneous if the temperature is low. This is because the TΔS term in the Gibbs free energy equation becomes small at low temperatures, reducing its ability to offset a positive ΔH.

In summary, while a positive entropy change tends to favour the spontaneity of a reaction, it does not guarantee it. The enthalpy change and temperature conditions can make a reaction with a positive entropy change non-spontaneous. Understanding these factors and their interplay is key to predicting whether a reaction will occur spontaneously or not.