Question

A process is spontaneous if :
A. $(\Delta G_{\text{system}})_{T, P} = 0$
B. $\Delta S_{\text{system}} + \Delta S_{\text{surrounding}} > 0$
C. $\Delta S_{\text{system}} + \Delta S_{\text{surrounding}} < 0$
D. $(\Delta G_{\text{system}})_{T, P} < 0$
E. $(\Delta G_{\text{system}})_{T, P} > 0$
Choose the correct answer from the options given below :

• A. A, B, D only
• B. A, C, E only
• C. B, E only
• D. B, D only

Hint:

Remember the signs: Spontaneous means the universe gets messier ($\Delta S_{univ} > 0$) and the system loses free energy ($\Delta G < 0$). Equilibrium is when everything is perfectly balanced ($\Delta S_{univ} = 0$, $\Delta G = 0$).

Answer 1

The Correct Option is D

Step 1: Concept:
The question asks to identify the correct thermodynamic conditions that definitively indicate a process is spontaneous.

Step 2: Key Formula or Approach:
1. The Second Law of Thermodynamics: A process is spontaneous in a given direction if it results in an overall increase in the entropy of the universe.
\[ \Delta S_{\text{universe}} = \Delta S_{\text{system}} + \Delta S_{\text{surrounding}} > 0 \]
2. Gibbs Free Energy: For processes occurring at constant Temperature (T) and Pressure (P), the entropy of the universe criterion is mathematically translated into the Gibbs free energy change of the system. A process is spontaneous if the free energy of the system decreases.
\[ (\Delta G_{\text{system}})_{T, P} < 0 \]

Step 3: Step-by-step Explanation:
Let's review each statement:

• A. $(\Delta G_{\text{system}})_{T, P = 0$:} This condition indicates that the system is at chemical equilibrium, not that a spontaneous change is occurring in a specific direction.

• B. $\Delta S_{\text{system + \Delta S_{\text{surrounding}} > 0$:} This means $\Delta S_{\text{universe}} > 0$. According to the Second Law of Thermodynamics, this is the fundamental definition of a spontaneous process. (True)

• C. $\Delta S_{\text{system + \Delta S_{\text{surrounding}} < 0$:} This indicates a decrease in universal entropy, meaning the process is thermodynamically forbidden (non-spontaneous) in the forward direction.

• D. $(\Delta G_{\text{system}})_{T, P < 0$:} A negative change in Gibbs free energy at constant T and P means the system can do useful work and the process is spontaneous. (True)

• E. $(\Delta G_{\text{system}})_{T, P > 0$:} A positive Gibbs free energy change indicates a non-spontaneous process (it would be spontaneous in the reverse direction).
The only correct criteria for spontaneity are B and D.

Step 4: Final Answer:
The correct statements are B and D, which corresponds to option (D).