Question

Equilibrium constant for a reaction is 20. What is the value of \( \Delta G \) at 300 K? (\( R = 8 \times 10^{-3} \, \text{kJ mol}^{-1} \text{K}^{-1} \))

• A. -5.527 kJ mol\(^{-1}\)
• B. -1.663 kJ mol\(^{-1}\)
• C. 16.63 kJ mol\(^{-1}\)
• D. -2.763 kJ mol\(^{-1}\)

Hint:

Remember, \( \Delta G \) is negative when the equilibrium constant \( K \) is greater than 1, indicating that the reaction is spontaneous.

Answer 1

The Correct Option is B

Step 1: Formula for \( \Delta G \).
The formula for calculating the Gibbs free energy change (\( \Delta G \)) is given by: \[ \Delta G = -RT \ln K \] Where: - \( R = 8 \times 10^{-3} \, \text{kJ mol}^{-1} \text{K}^{-1} \) is the gas constant, - \( T = 300 \, \text{K} \) is the temperature, - \( K = 20 \) is the equilibrium constant.

Step 2: Calculation.
Substitute the given values into the equation: \[ \Delta G = - (8 \times 10^{-3} \times 300) \ln(20) = -1.663 \, \text{kJ mol}^{-1} \]
Step 3: Conclusion.
The value of \( \Delta G \) is \(-1.663 \, \text{kJ mol}^{-1}\), so the correct answer is (B) -1.663 kJ mol\(^{-1}\).