If `DeltaG^(@)` is zero for a reaction, then

Options

A. `DeltaH^(@) = 0`
B. `DeltaS^(@) = 0`
C. K (equilibrium constant) = 0
D. K(equilibrium constant) = 1

Answer

To solve the problem, we need to analyze the implications of the Gibbs free energy change (ΔG°) being zero for a reaction.

### Step-by-Step Solution:

1. **Understanding ΔG°**: The Gibbs free energy change at standard conditions (ΔG°) indicates the spontaneity of a reaction. If ΔG° is negative, the reaction is spontaneous; if positive, it is non-spontaneous; and if zero, the system is at equilibrium.

2. **Using the Gibbs Free Energy Equation**: The relationship between ΔG° and the equilibrium constant (K) is given by the equation:
\[ \Delta G° = -2.303 RT \log K \]
where R is the universal gas constant and T is the temperature in Kelvin.

3. **Setting ΔG° to Zero**: If we set ΔG° to zero, we have:
\[ 0 = -2.303 RT \log K \]

4. **Solving for K**: Since R and T are both positive quantities, the only way for the equation to hold true is if:
\[ \log K = 0 \]
This implies that:
\[ K = 10^0 = 1 \]

5. **Conclusion**: Therefore, if ΔG° is zero for a reaction, the equilibrium constant (K) for that reaction is equal to 1.

### Final Answer:
If ΔG° is zero for a reaction, then the equilibrium constant K is equal to 1.

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