What happens when ΔH is positive and ΔS is negative?

When the enthalpy change (ΔH) is positive, it indicates that the reaction is endothermic, meaning it absorbs heat from the surroundings. A positive ΔS suggests that the entropy of the system decreases, which is generally associated with a more ordered state and indicates that the randomness and disorder of the system is decreasing.

In thermodynamics, the spontaneity of a reaction can be determined using the Gibbs free energy change (ΔG), which is given by the equation:

ΔG = ΔH - TΔS

For a reaction to be spontaneous, ΔG must be negative. When ΔH is positive and ΔS is negative, the term -TΔS becomes more negative as temperature increases, but since ΔH is positive, it is more likely to outweigh this term, resulting in a positive ΔG. Therefore, as both ΔH is positive and ΔS is negative, the total effect is that ΔG remains positive, indicating the reaction is nonspontaneous at all temperatures.

This leads to the conclusion that the reaction will not occur spontaneously under any conditions, validating the assertion that it is nonspontaneous at all temperatures.