Questions: Consider the reaction below which has a ΔG=+0.5 kJ/mol: A+B ⇌ C+D 10 M A, 10 M B, 1 M C and 1 M D are added to a container at room temperature. Which of the following statements is TRUE? To reach equilibrium, the reaction will proceed in the forward direction. To reach equilibrium, the reaction will proceed alternating between forward and reverse direction. To reach equilibrium, the reaction will proceed in the reverse direction. To reach equilibrium, the reaction will NOT proceed in either direction.

Solution Steps

The reaction given is: \[ A + B \rightleftharpoons C + D \] with a Gibbs free energy change, \(\Delta G = +0.5 \, \text{kJ/mol}\).

The initial concentrations are:

• \( [A] = 10 \, \text{M} \)
• \( [B] = 10 \, \text{M} \)
• \( [C] = 1 \, \text{M} \)
• \( [D] = 1 \, \text{M} \)

To determine the direction in which the reaction will proceed to reach equilibrium, we need to compare the reaction quotient \( Q \) with the equilibrium constant \( K \).

The reaction quotient \( Q \) is given by: \[ Q = \frac{[C][D]}{[A][B]} \]

Substituting the given concentrations: \[ Q = \frac{(1)(1)}{(10)(10)} = \frac{1}{100} = 0.01 \]

The relationship between \(\Delta G\) and the equilibrium constant \( K \) is given by: \[ \Delta G = -RT \ln K \]

Given that \(\Delta G = +0.5 \, \text{kJ/mol} = 500 \, \text{J/mol}\) and assuming room temperature \( T = 298 \, \text{K} \), we can solve for \( K \): \[ 500 = - (8.314 \, \text{J/mol·K})(298 \, \text{K}) \ln K \] \[ \ln K = -\frac{500}{(8.314)(298)} \] \[ \ln K \approx -0.202 \] \[ K \approx e^{-0.202} \approx 0.8171 \]

We have: \[ Q = 0.01 \] \[ K \approx 0.8171 \]

Since \( Q < K \), the reaction will proceed in the forward direction to reach equilibrium.

Final Answer