Which of the following can help to predict the rate of reaction if the standard Gibb's free energy of reaction `(Delta_rG^@)` is known ?

Options

A. Equilibrium constant
B. `Delta_rH^@`
C. `Delta_rU^@`
D. Heat liberated during the course of reaction in calorimeter

Answer

To solve the question regarding which factor can help predict the rate of reaction if the standard Gibbs free energy of reaction (Δ_rG^@) is known, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Gibbs Free Energy (Δ_rG^@)**:
- The standard Gibbs free energy change (Δ_rG^@) is a thermodynamic quantity that indicates the spontaneity of a reaction at standard conditions. A negative Δ_rG^@ suggests that the reaction is spontaneous, while a positive value indicates non-spontaneity.

2. **Relation Between Δ_rG^@ and Equilibrium Constant (K)**:
- The relationship between the standard Gibbs free energy change and the equilibrium constant is given by the equation:
\[ \Delta_rG^@ = -RT \ln K \]
where R is the universal gas constant and T is the temperature in Kelvin. This equation shows that if we know Δ_rG^@, we can calculate the equilibrium constant (K).

3. **Predicting Reaction Rate**:
- The equilibrium constant (K) is a measure of the extent of a reaction at equilibrium. While Δ_rG^@ provides information about spontaneity, K gives insight into the concentrations of reactants and products at equilibrium.
- A larger K value indicates a reaction that favors products, which can correlate with a faster reaction rate under certain conditions.

4. **Conclusion**:
- Therefore, knowing the standard Gibbs free energy change (Δ_rG^@) allows us to determine the equilibrium constant (K), which can help predict the rate of reaction.

### Final Answer:
The correct option is **equilibrium constant (K)**.

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