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

Options

A. `MX_3hArr MX_2+1/2X_2`
B. `2MX_3 hArr 2MX_2+X_2`
C. `2MX_2+X_2 hArr 2MX_3`
D. `MX_2+1/2X_2hArr MX_3`

Answer

To determine the reaction for which the equilibrium constant is expressed as \([MX_3]^2 = K_{eq}[MX_2]^2[X_2]\), we can follow these steps:

### Step 1: Understand the Equilibrium Constant Expression
The equilibrium constant \(K_{eq}\) for a reaction is given by the ratio of the concentrations of the products raised to the power of their coefficients to the concentrations of the reactants raised to the power of their coefficients.

### Step 2: Analyze the Given Expression
The expression provided is:
\[ [MX_3]^2 = K_{eq}[MX_2]^2[X_2] \]
This can be rearranged to:
\[ K_{eq} = \frac{[MX_3]^2}{[MX_2]^2[X_2]} \]
This indicates that \(MX_3\) is a product and \(MX_2\) and \(X_2\) are reactants.

### Step 3: Write the Balanced Chemical Equation
From the expression, we can infer the balanced chemical equation. Since the concentration of \(MX_3\) is squared, it suggests that there are 2 moles of \(MX_3\) produced. The reactants \(MX_2\) and \(X_2\) must combine to form \(MX_3\).

Thus, we can write the reaction as:
\[ 2MX_2 + X_2 \rightleftharpoons 2MX_3 \]

### Step 4: Confirm the Reaction Matches the Expression
Now, we can confirm that this reaction matches the expression for \(K_{eq}\):
- Products: \(2MX_3\) contributes \([MX_3]^2\)
- Reactants: \(2MX_2\) contributes \([MX_2]^2\) and \(X_2\) contributes \([X_2]\)

Thus, the equilibrium constant expression derived from this reaction is indeed:
\[ K_{eq} = \frac{[MX_3]^2}{[MX_2]^2[X_2]} \]

### Step 5: Identify the Correct Option
Upon reviewing the options provided in the question, the reaction \(2MX_2 + X_2 \rightleftharpoons 2MX_3\) corresponds to option C.

### Final Answer
The correct reaction for which the equilibrium constant is written as \([MX_3]^2 = K_{eq}[MX_2]^2[X_2]\) is:
\[ 2MX_2 + X_2 \rightleftharpoons 2MX_3 \]

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