Which of the following is consistent with a spontaneous process in the forward direction? A) ∆Suniv >0, ∆G<0, T∆Suniv >0.
B) ∆Suniv <0, ∆G>0, T∆Suniv <0.
C) ∆Suniv >0, ∆G<0, T∆Suniv <0.
D) ∆Suniv <0, ∆G<0, T∆Suniv <0.
E) ∆Suniv >0, ∆G>0, T∆Suniv >0.

A) ∆Suniv >0, ∆G<0, T∆Suniv >0.

Explanation:

The connection between entropy and the spontaneity of a reaction is expressed by the second law of thermodynamics: The entropy of the universe increases in a spontaneous process and remains unchanged in an equilibrium process.

Mathematically, we can express the second law of thermodynamics as follows:

For a spontaneous process: ΔSuniv = ΔSsys + ΔSsurr > 0

Therefore, the second law of thermodynamics tells us that a spontaneous reaction increases the entropy of the universe; that is, ΔSuniv > 0.

If we want spontaneity expressed only in terms  of the properties of the system (ΔHsys and ΔSsys), we use the following equation:

-TΔSuniv = ΔHsys - TΔSsys < 0

That means that T∆Suniv >0.

This equation says that for a process carried out at constant pressure and temperature  T, if the changes in enthalpy and entropy of the system are such that ΔHsys - TΔSsys  is less than zero, the process must be spontaneous.

Finally, if the change in free energy is less than zero (ΔG<0), the reaction is spontaneous in the forward direction.

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