Identifying the Incorrect Statement

This question requires identifying the false statement concerning chemical equilibrium and Gibbs free energy ($\Delta G$). Let's evaluate each statement:

1. Chemical Potential at Equilibrium

A system is at equilibrium when the chemical potential ($\mu$) of a species is the same in all accessible phases. This statement is correct.

2. Gibbs Free Energy Change at Equilibrium

At equilibrium, the Gibbs free energy ($G$) of the system is minimized. Consequently, the change in Gibbs free energy ($\Delta G$) for any process occurring at equilibrium is zero. This statement is correct.

Condition: $\Delta G = 0$

3. Spontaneity and Positive $\Delta G$

The criterion for a spontaneous process is a negative Gibbs free energy change ($\Delta G$). A positive $\Delta G$ indicates that the process is non-spontaneous under the given conditions.

• Spontaneous: $\Delta G < 0$
• Equilibrium: $\Delta G = 0$
• Non-spontaneous: $\Delta G > 0$

Therefore, the statement 'Gibb's free energy change is positive for reaction to occur spontaneously' is incorrect.

4. Temperature Dependence of $\Delta G$

The relationship is $\Delta G = \Delta H - T \Delta S$. The change in $\Delta G$ with temperature ($T$) depends on the sign of the entropy change ($\Delta S$). If $\Delta S > 0$, $\Delta G$ becomes more negative with increasing $T$. If $\Delta S < 0$, $\Delta G$ becomes less negative (or more positive). This statement is not universally true and depends on $\Delta S$. However, statement 3 is definitionally incorrect.

The definitively incorrect statement is number 3.