Select the reaction for which the equilibrium constant is written as `[MX_3]^2=K_(eq)[MX_2]^2[X_2]`

Options

A. `MX_(3)hArrMX_(2)+(1)/(2)X_(2)`
B. `2MX_(3)hArr2MX_(2)+X_(2)`
C. `2MX_(2+X_(2))hArr2MX_(3)`
D. `MX_(2)+(1)/(2)X_(2)hArrMX_(3)`.

Answer

To solve the problem, we need to identify the reaction for which the equilibrium constant is represented by the equation:

\[ [MX_3]^2 = K_{eq} [MX_2]^2 [X_2] \]

### Step-by-Step Solution:

1. **Understanding the Equilibrium Constant Expression**:
The general form of the equilibrium constant \( K_{eq} \) for a reaction can be expressed as:
\[ K_{eq} = \frac{[Products]^{coefficients}}{[Reactants]^{coefficients}} \]
where the concentrations of the products are raised to the power of their coefficients in the balanced chemical equation, and the same applies to the reactants.

2. **Rearranging the Given Equation**:
From the given equation, we can rearrange it to express \( K_{eq} \):
\[ K_{eq} = \frac{[MX_3]^2}{[MX_2]^2 [X_2]} \]

3. **Identifying the Reaction**:
To find the corresponding reaction, we need to consider a reaction that would yield this expression for \( K_{eq} \). The expression suggests that for every 2 moles of \( MX_3 \) produced, we consume 2 moles of \( MX_2 \) and 1 mole of \( X_2 \).

Thus, the balanced reaction can be written as:
\[ 2 MX_2 + X_2 \rightleftharpoons 2 MX_3 \]

4. **Verifying with the Options**:
Now, we need to check the provided options to see which one corresponds to this reaction.

- **Option A**: Does not match.
- **Option B**: Does not match.
- **Option C**: Matches \( 2 MX_2 + X_2 \rightleftharpoons 2 MX_3 \).
- **Option D**: Does not match.

5. **Conclusion**:
Therefore, the correct reaction for which the equilibrium constant is written as \([MX_3]^2 = K_{eq}[MX_2]^2[X_2]\) is option C.

### Final Answer:
The correct answer is **Option C: \( 2 MX_2 + X_2 \rightleftharpoons 2 MX_3 \)**.