When does a reaction become spontaneous as temperature decreases?

For a reaction to become spontaneous at lower temperatures, it is important to consider the relationship between enthalpy change (ΔH), entropy change (ΔS), and temperature in the context of Gibbs free energy (ΔG). The Gibbs free energy is defined by the equation:

ΔG = ΔH - TΔS

A reaction is spontaneous when ΔG is negative. The effect of temperature on spontaneity can be analyzed through the two variables, ΔH and ΔS.

When both ΔH and ΔS are negative, the reaction is exothermic (heat is released) and there is also a decrease in disorder (entropy). In this case, as temperature decreases, the impact of the negative ΔS term (which subtracts from ΔH) becomes less significant. Thus, ΔG remains negative when the temperature is low enough, maintaining the spontaneity of the reaction.

Conversely, if ΔH were positive, or if ΔS were positive, it would complicate spontaneity at lower temperatures. A positive ΔH indicates an endothermic reaction, which typically requires heat; thus, lower temperatures would not favor this reaction. A positive ΔS value indicates an increase in disorder, but if coupled with a negative ΔH, it