The `K_c` for given reaction will be `A_2 (g) +2B (g) hArr C(g) +2D(s)`

Options

A. `K=([C][D]^2)/([A_2][B]^2)`
B. `K=([C])/([A_2][B]^2)`
C. `K=([A_2][B]^2)/([C][D]^2)`
D. `K=([A_2][B]^2)/([C])`

Answer

To find the equilibrium constant \( K_c \) for the reaction \( A_2 (g) + 2B (g) \rightleftharpoons C(g) + 2D(s) \), we can follow these steps:

### Step 1: Understand the Reaction
We have the following reaction:
\[ A_2 (g) + 2B (g) \rightleftharpoons C(g) + 2D(s) \]

### Step 2: Identify the Components
In this reaction:
- \( A_2 \) and \( B \) are gaseous reactants.
- \( C \) is a gaseous product.
- \( D \) is a solid product.

### Step 3: Define the Equilibrium Constant \( K_c \)
The equilibrium constant \( K_c \) is defined in terms of the concentrations of the products and reactants at equilibrium:
\[ K_c = \frac{[\text{Products}]}{[\text{Reactants}]} \]

### Step 4: Write the Expression for \( K_c \)
For the given reaction, we only consider the gaseous components because the concentration of solids does not appear in the equilibrium expression. Therefore, the expression for \( K_c \) will be:
\[ K_c = \frac{[C]}{[A_2][B]^2} \]
Here, we take the concentration of \( C \) in the numerator and the concentrations of \( A_2 \) and \( B \) in the denominator. Note that the coefficient of \( B \) is 2, so we raise its concentration to the power of 2.

### Step 5: Final Expression
Thus, the final expression for \( K_c \) for the reaction is:
\[ K_c = \frac{[C]}{[A_2][B]^2} \]

### Step 6: Conclusion
Since \( D \) is a solid, it does not contribute to the equilibrium constant expression. Therefore, the correct expression for \( K_c \) is as derived above.