Question

Free energy change at equilibrium is

• A. zero
• B. positive
• C. negative
• D. indeterminate

Hint:

Associate the sign of \(\Delta G\) with the "driving force" of a reaction. \(\Delta G \lt 0\) means there is a forward driving force. \(\Delta G \gt 0\) means there is a reverse driving force. \(\Delta G = 0\) means there is no net driving force in either direction – the definition of equilibrium.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The change in Gibbs Free Energy (\(\Delta G\)) is a thermodynamic potential that can be used to determine the spontaneity of a process at constant temperature and pressure. We need to determine its value when a system has reached equilibrium.

Step 2: Key Formula or Approach:
The criteria for spontaneity based on \(\Delta G\) are:

• \(\Delta G \lt 0\): The forward process is spontaneous.

• \(\Delta G \gt 0\): The forward process is non-spontaneous (the reverse process is spontaneous).

• \(\Delta G = 0\): The system is at equilibrium.

Step 3: Detailed Explanation:
A system is said to be at equilibrium when there is no net change in its macroscopic properties over time. For a chemical reaction, this means the rate of the forward reaction is equal to the rate of the reverse reaction. There is no net tendency for the reaction to proceed in either direction.
The Gibbs Free Energy (\(G\)) of a system at constant T and P seeks a minimum value. When a reaction proceeds, the free energy of the system changes as reactants are converted to products.

• If the reaction is proceeding spontaneously towards products, it means the free energy is decreasing, so \(\Delta G\) is negative.

• If the reaction is proceeding spontaneously towards reactants, the \(\Delta G\) for the forward reaction is positive.
Equilibrium is the point where the free energy of the system is at its minimum. At this minimum, any infinitesimal change in the extent of the reaction (either forward or backward) does not change the free energy. Mathematically, the derivative of G with respect to the extent of reaction is zero. This corresponds to the condition \(\Delta G = 0\). At this point, the system has no further potential to do work, and no spontaneous change occurs.

Step 4: Final Answer:
By definition, a system at equilibrium under constant temperature and pressure has reached a minimum in its Gibbs Free Energy. At this point, the net free energy change for the process is zero.