Question

question 27 of 30
at what temperatures is a reaction that has a positive change in entropy spontaneous?

a. at lower temperatures for endothermic reactions
b. at all temperatures for exothermic reactions
c. at all temperatures for endothermic reactions
d. at no temperatures for exothermic reactions

Explanation:

To determine when a reaction with positive entropy change (\(\Delta S>0\)) is spontaneous, we use the Gibbs free energy equation \(\Delta G=\Delta H - T\Delta S\). A reaction is spontaneous when \(\Delta G < 0\).

• For option A: Endothermic reactions have \(\Delta H>0\). At lower temperatures, \(T\Delta S\) is small (since \(T\) is small). So \(\Delta G=\Delta H - T\Delta S\) would be positive (non - spontaneous), so A is wrong.
• For option B: Exothermic reactions have \(\Delta H < 0\). Given \(\Delta S>0\), then \(-T\Delta S\) is negative (because \(T>0\) and \(\Delta S>0\)). So \(\Delta G=\Delta H - T\Delta S\) will be \(\text{negative}-\text{positive}\) (more negative overall). Since \(\Delta H < 0\) and \(\Delta S>0\), for any positive temperature \(T\), \(\Delta G=\Delta H - T\Delta S<0\) (because both \(\Delta H\) is negative and \(T\Delta S\) is positive, so subtracting a positive from a negative makes it more negative). So exothermic reactions with \(\Delta S > 0\) are spontaneous at all temperatures.
• For option C: Endothermic reactions have \(\Delta H>0\). Even with \(\Delta S>0\), at low temperatures, \(T\Delta S\) may be smaller than \(\Delta H\), so \(\Delta G=\Delta H - T\Delta S>0\) (non - spontaneous). So they are not spontaneous at all temperatures, C is wrong.
• For option D: Exothermic reactions with \(\Delta S>0\) are spontaneous at all temperatures (as shown in option B analysis), so D is wrong.

Answer:

B. At all temperatures for exothermic reactions