Question

consider the following reaction at 25 °c: 5 so₃(g) + 2 nh₃(g) → 2 no(g) + 5 so₂(g) + 3 h₂o(g) if δg° = -125 kj/mol, δh° = 42.4 kj/mol and δs° = 562.3 j/mol•k, is this reaction spontaneous as written under standard conditions? a no, it is not spontaneous because enthalpy and entropy are positive. b no, it is not spontaneous because the free energy is negative. c yes, it is spontaneous because the free energy is negative. d yes, it is spontaneous because the entropy is positive.

Explanation:

To determine if a reaction is spontaneous under standard conditions, we use the Gibbs free energy change ($\Delta G^\circ$). The criterion is: if $\Delta G^\circ < 0$, the reaction is spontaneous; if $\Delta G^\circ > 0$, it is non - spontaneous.

Given that $\Delta G^\circ=- 125\space kJ/mol$, which is less than 0.

• Option A: The fact that enthalpy ($\Delta H^\circ = 42.4\space kJ/mol>0$) and entropy ($\Delta S^\circ=562.3\space J/mol\cdot K > 0$) are positive does not directly determine non - spontaneity. The key factor is $\Delta G^\circ$. So A is incorrect.
• Option B: A negative $\Delta G^\circ$ indicates spontaneity, not non - spontaneity. So B is incorrect.
• Option C: Since $\Delta G^\circ=-125\space kJ/mol < 0$, the reaction is spontaneous because the free energy change is negative. This option is correct.
• Option D: While a positive entropy change can contribute to spontaneity, the ultimate determinant of spontaneity is the sign of $\Delta G^\circ$, not just the sign of $\Delta S^\circ$. So D is incorrect.

Answer:

C. Yes, it is spontaneous because the free energy is negative.