If `Delta G^(@)gt 0` for a reaction then :

Options

A. `K_(p) gt 1`
B. `K_(p) lt 1`
C. Products dominate in the equilibrium mixture
D. `K_(p)=2`

Answer

To solve the question, we need to analyze the relationship between the Gibbs free energy change (ΔG°) and the equilibrium constant (K) for a chemical reaction.

### Step-by-Step Solution:

1. **Understanding ΔG°**: The Gibbs free energy change (ΔG°) indicates the spontaneity of a reaction at standard conditions. If ΔG° is greater than 0 (ΔG° > 0), it means that the reaction is non-spontaneous under standard conditions.

2. **Relationship Between ΔG° and K**: The relationship between the Gibbs free energy change and the equilibrium constant is given by the equation:
\[ ΔG° = -RT \ln K \]
where R is the universal gas constant and T is the temperature in Kelvin.

3. **Analyzing the Equation**: Since ΔG° is positive (ΔG° > 0), we can rearrange the equation:
\[ -RT \ln K > 0 \]
This implies that:
\[ \ln K < 0 \]
(because R and T are both positive values).

4. **Interpreting ln K < 0**: If the natural logarithm of K is less than 0, it means that:
\[ K < 1 \]
This indicates that the equilibrium constant is less than 1.

5. **Conclusion About the Reaction**: A value of K less than 1 suggests that at equilibrium, the concentration of reactants is greater than the concentration of products. Therefore, the reactants dominate in the equilibrium mixture.

6. **Final Answer**: Based on the analysis, if ΔG° > 0 for a reaction, then the equilibrium constant K is less than 1, indicating that the reactants dominate in the equilibrium mixture.

### Answer: The equilibrium constant K is less than 1.

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