According to Gibbs free energy, will a spontaneous reaction more likely occur at a higher or lower temperature?

A spontaneous reaction is one that occurs without the need for external energy input, which is indicated by a negative change in Gibbs free energy (ΔG < 0). The relationship between Gibbs free energy, enthalpy (ΔH), entropy (ΔS), and temperature (T) is given by the equation:

ΔG = ΔH - TΔS

This equation shows that the spontaneity of a reaction is influenced by both enthalpy and entropy changes, as well as the temperature at which the reaction occurs.

At higher temperatures, the TΔS term becomes more significant. If a reaction has a positive ΔS (entropy increases, which is often favorable for spontaneity), increasing the temperature can enhance the likelihood that TΔS will outweigh ΔH, thereby ensuring that ΔG remains negative and the reaction is spontaneous. Conversely, for reactions where ΔH is particularly large and negative, increasing the temperature could make ΔG less favorable.

Therefore, for reactions that have a positive change in entropy, a higher temperature increases the chance of these reactions being spontaneous due to the increased influence of the entropy term. This is why in many cases, spontaneous reactions are more likely to occur at higher temperatures.

In contrast, at lower temperatures,