The standard Gibbs energy change at `300K` for the reaction `2AhArrB+C` is 2494. `2J`. At a given time, the composition of the reaction mixture is `[A]=1/2, [B]=2` and `[C]=1/2`. The reaction proceeds in the
`(R=8.314JK//"mol"e=2.718)`

Options

A. reverse direction because `Q gt K_(c)`
B. forward direction because `Q lt K_(c)`
C. reverse direction because `Q lt K_(c)`
D. forward direction because `Q gt K_(c)`

Answer

To solve the problem, we need to determine the direction in which the reaction proceeds based on the given concentrations of the reactants and products. We will use the concepts of reaction quotient (Q) and equilibrium constant (K).

### Step-by-Step Solution:

1. **Write the Reaction:**
The reaction given is:
\[ 2A \rightleftharpoons B + C \]

2. **Calculate the Equilibrium Constant (K):**
The equilibrium constant \( K \) can be calculated using the formula:
\[ K = \frac{[B][C]}{[A]^2} \]
Given the concentrations:
\[ [A] = \frac{1}{2}, \quad [B] = 2, \quad [C] = \frac{1}{2} \]
Substitute these values into the equation:
\[ K = \frac{(2)(\frac{1}{2})}{(\frac{1}{2})^2} \]
Simplifying this:
\[ K = \frac{1}{\frac{1}{4}} = 4 \]

3. **Calculate the Reaction Quotient (Q):**
The reaction quotient \( Q \) is calculated using the same formula as \( K \):
\[ Q = \frac{[B][C]}{[A]^2} \]
Using the same concentrations:
\[ Q = \frac{(2)(\frac{1}{2})}{(\frac{1}{2})^2} \]
This simplifies to:
\[ Q = \frac{1}{\frac{1}{4}} = 4 \]

4. **Compare Q and K:**
Now we compare \( Q \) and \( K \):
\[ Q = 4, \quad K = 4 \]
Since \( Q = K \), the system is at equilibrium.

5. **Determine the Direction of the Reaction:**
- If \( Q < K \), the reaction proceeds in the forward direction.
- If \( Q > K \), the reaction proceeds in the backward direction.
- If \( Q = K \), the reaction is at equilibrium.

In this case, since \( Q = K \), the reaction is at equilibrium, and there is no net change in the concentrations of reactants and products.

### Conclusion:
Since \( Q = K \), the reaction does not proceed in either direction; it is at equilibrium.