If a reaction is exothermic and its entropy change is positive, which statement is true? If a reaction is exothermic and its entropy change is positive, which statement is true? a. The reaction is spontaneous only at higher temperatures. b. The reaction is nonspontaneous at all temperatures. c. The reaction is spontaneous at all temperatures. d. The reaction is spontaneous only at lower temperatures.

c. The reaction is spontaneous at all temperatures.

Explanation:

The spontaneity of a reaction can be determined by the thermodynamic property named Gibb's free energy or simply free energy (G).

The change in the free energy of a system is defined as the difference between the increase in enthalpy (ΔH) and the product of the temperature (T) times the increase in entropy (ΔS):

ΔG = ΔH - T ΔS

The sign of ΔG tells if a reaction is spontaneous according to this:

ΔG <0, the reaction is spontaneous.Δ the reaction is in equilibrium.ΔG> 0, the reaction is not spontaneous.

The question states that a reaction is exothermic, and its entropy change is positive. That means:

Exhotermic: ΔH <0Positive entropy change: ΔS> 0

Remember that the temperature is stated in absolute scale, so T is always positive.

Hence, ΔG = ΔH - T ΔS = (negative) - T (positive) = (negative) + (negative) = negative.

Conclusion: since ΔG is negative, regardless the temperature, you conclude that the reaction is spontaneous at all temperatures, which is the option c.