Question

a reaction will be spontaneous at all temperatures if ______

Explanation:

To determine when a reaction is spontaneous at all temperatures, we use the Gibbs free energy equation: $\Delta G = \Delta H - T\Delta S$. A reaction is spontaneous when $\Delta G < 0$.

• If $\Delta H < 0$ (exothermic) and $\Delta S > 0$ (increase in disorder), then:
• The $\Delta H$ term is negative (favorable for spontaneity).
• The $-T\Delta S$ term: since $\Delta S > 0$, $T\Delta S$ is positive, so $-T\Delta S$ is negative (also favorable for spontaneity).
• For any temperature $T$ (in Kelvin, so $T>0$), the sum $\Delta H - T\Delta S$ will always be negative because both terms are negative. Thus, $\Delta G < 0$ for all temperatures.

Answer:

$\boldsymbol{\Delta H < 0}$ (enthalpy change is negative, exothermic) and $\boldsymbol{\Delta S > 0}$ (entropy change is positive, increase in disorder)