Which scenario leads to a reaction being nonspontaneous at all temperatures?

A reaction is considered nonspontaneous at all temperatures when the changes in enthalpy (ΔH) and entropy (ΔS) create an unfavorable condition for reaction spontaneity. According to the Gibbs free energy equation, which predicts the spontaneity of a reaction, the change in free energy (ΔG) is given by:

ΔG = ΔH - TΔS

For a reaction to be nonspontaneous, ΔG must be positive. Analyzing the situation where ΔH is positive and ΔS is negative provides insight into why this leads to nonspontaneity at all temperatures.

When ΔH is positive, the reaction absorbs heat (endothermic), and this contributes to making ΔG positive. Simultaneously, a negative ΔS indicates that the disorder of the system decreases, which also contributes to making ΔG positive, particularly because the TΔS term (where T is absolute temperature) subtracts a negative value, effectively adding to the overall ΔG.

Under any temperature condition, no matter how high the temperature is, the positive ΔH combined with a negative ΔS ensures that the ΔG will remain positive, confirming that the reaction will not happen spontaneously.

In contrast, the