`Delta G^(@)` of reversible reaction at its equilbrium is

Options

A. Positive
B. Negative
C. Always zero
D. May be(1) or (2)

Answer

To determine the value of ΔG° (Gibbs free energy change) for a reversible reaction at equilibrium, we can follow these steps:

### Step 1: Understand the concept of Gibbs Free Energy (ΔG)
Gibbs free energy (G) is a thermodynamic potential that measures the maximum reversible work that can be performed by a thermodynamic system at constant temperature and pressure. The change in Gibbs free energy (ΔG) during a reaction indicates whether the reaction is spontaneous or not.

### Step 2: Define equilibrium in a chemical reaction
At equilibrium, the rates of the forward and reverse reactions are equal, and the concentrations of reactants and products remain constant over time. This state indicates that the system is in a balanced condition.

### Step 3: Relate ΔG to equilibrium
The change in Gibbs free energy (ΔG) can be expressed in terms of the standard Gibbs free energy change (ΔG°) and the reaction quotient (Q):
\[ \Delta G = \Delta G° + RT \ln Q \]
Where:
- R is the universal gas constant,
- T is the temperature in Kelvin,
- Q is the reaction quotient at any point in the reaction.

### Step 4: Analyze the condition at equilibrium
At equilibrium, the reaction quotient (Q) becomes equal to the equilibrium constant (K). Therefore, we can rewrite the equation as:
\[ \Delta G_{eq} = \Delta G° + RT \ln K \]
At equilibrium, the change in Gibbs free energy (ΔG) is zero:
\[ 0 = \Delta G° + RT \ln K \]

### Step 5: Solve for ΔG°
Rearranging the equation gives us:
\[ \Delta G° = -RT \ln K \]
This indicates that at equilibrium, the standard Gibbs free energy change (ΔG°) is related to the equilibrium constant (K) of the reaction.

### Conclusion
At equilibrium, the value of ΔG° for a reversible reaction is zero:
\[ \Delta G° = 0 \]

### Final Answer
The value of ΔG° of a reversible reaction at its equilibrium is **0**.

---