What determines the spontaneity of an endothermic reaction?

The spontaneity of an endothermic reaction is determined by the entropy change and the temperature of the system.

In more detail, an endothermic reaction is one where heat is absorbed from the surroundings, resulting in an increase in the internal energy of the system. This is often associated with a positive change in enthalpy (ΔH). However, a positive ΔH alone does not determine whether a reaction is spontaneous or not. The spontaneity of a reaction is determined by the Gibbs free energy change (ΔG), which takes into account both the enthalpy change and the entropy change (ΔS).

The Gibbs free energy change is given by the equation ΔG = ΔH - TΔS, where T is the absolute temperature. For a reaction to be spontaneous, ΔG must be negative. Therefore, even if ΔH is positive (as in an endothermic reaction), the reaction can still be spontaneous if the TΔS term is large enough to make ΔG negative. This means that an endothermic reaction is more likely to be spontaneous at higher temperatures, where the TΔS term is larger.

Entropy is a measure of the disorder or randomness of a system. In general, reactions that result in an increase in entropy (positive ΔS) are more likely to be spontaneous. This is because systems tend to evolve towards states of higher disorder. Therefore, an endothermic reaction that results in a large increase in entropy can be spontaneous, even though it absorbs heat from the surroundings.

In summary, the spontaneity of an endothermic reaction is determined by a combination of the entropy change, the enthalpy change, and the temperature of the system. A positive enthalpy change does not necessarily mean that a reaction is non-spontaneous. Rather, it is the balance between the enthalpy change, the entropy change, and the temperature that determines whether a reaction will occur spontaneously.