What is the required condition for a reaction with a positive change in enthalpy to be spontaneous?

For a reaction to be spontaneous, even when it has a positive change in enthalpy (which indicates that the reaction absorbs heat), it is essential to consider the relationship between enthalpy, entropy, and temperature, described by Gibbs free energy (ΔG). The Gibbs free energy equation is given by:

ΔG = ΔH - TΔS

where ΔG is the change in Gibbs free energy, ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy.

When ΔH is positive, it indicates that the reaction is endothermic. For such a reaction to still be spontaneous (meaning ΔG must be negative), the entropy change ΔS must be sufficiently positive. A large positive value for ΔS can offset the positive ΔH, particularly when the temperature (T) is also high enough.

Conducting the reaction at a higher temperature increases the TΔS term and can make the overall ΔG negative, thus allowing the reaction to occur spontaneously despite its positive enthalpy. This is why a higher temperature is a necessary condition for spontaneity in this scenario.

Therefore, the condition that allows a reaction with a positive change in enthalpy to