The free energy change `DeltaG = 0`, when

Options

A. the system is at equilibrium
B. catalyst is added
C. reactants are initially mixed thoroughly
D. the reactants are completely consumed

Explanation

To determine when the free energy change (ΔG) is equal to zero, we can analyze the conditions under which this occurs. Here’s a step-by-step solution:

### Step 1: Understanding Free Energy Change (ΔG)
Free energy change (ΔG) is a thermodynamic quantity that indicates the spontaneity of a reaction. It is defined as the difference between the free energy of the products and the free energy of the reactants.

### Step 2: Equilibrium Condition
At equilibrium, the rates of the forward and reverse reactions are equal, and there is no net change in the concentrations of reactants and products. Under these conditions, the system has reached a state of balance.

### Step 3: ΔG at Equilibrium
At equilibrium, the change in free energy (ΔG) is equal to zero. This can be expressed mathematically as:
\[ ΔG = ΔG^0 + RT \ln Q \]
Where:
- \( ΔG^0 \) is the standard free energy change,
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin,
- \( Q \) is the reaction quotient.

When the system is at equilibrium, \( Q \) equals the equilibrium constant \( K \), and thus:
\[ ΔG = 0 \]

### Step 4: Analyzing Other Options
1. **Catalyst Addition**: Adding a catalyst speeds up the reaction but does not change the free energy change of the reaction. Therefore, ΔG is not zero just because a catalyst is added.

2. **Reactants Mixed Thoroughly**: Mixing reactants does not guarantee that the system is at equilibrium. Therefore, ΔG is not necessarily zero.

3. **Reactants Completely Consumed**: If reactants are completely consumed, products are formed, and there will still be free energy associated with the products. Hence, ΔG is not zero.

### Conclusion
The only condition under which ΔG is equal to zero is when the system is at equilibrium.

### Final Answer
ΔG = 0 when the system is at equilibrium.

---