The equilibrium constant `(K)` for the reaction. `A+2BhArr2C+D` is:

Options

A. `([C]^(2)[D])/([A][2B])`,
B. `([2C][D])/([A][2B])`
C. `([C][D])/([A][B])`
D. `([C]^(2)[D])/([A][B]^(2))`

Answer

To find the equilibrium constant \( K \) for the reaction \( A + 2B \rightleftharpoons 2C + D \), we will follow these steps:

### Step 1: Write the expression for the equilibrium constant \( K \)

The equilibrium constant \( K \) is defined as the ratio of the concentrations of the products to the concentrations of the reactants, each raised to the power of their respective coefficients in the balanced equation.

### Step 2: Identify the products and reactants

From the reaction \( A + 2B \rightleftharpoons 2C + D \):
- **Products**: \( 2C \) and \( D \)
- **Reactants**: \( A \) and \( 2B \)

### Step 3: Write the expression for \( K \)

Using the general formula for the equilibrium constant:

\[ K = \frac{[\text{Products}]^{\text{coefficients}}}{[\text{Reactants}]^{\text{coefficients}}} \]

For our reaction, we can express \( K \) as:

\[ K = \frac{[C]^2[D]}{[A][B]^2} \]

### Step 4: Final expression for \( K \)

Thus, the equilibrium constant \( K \) for the reaction \( A + 2B \rightleftharpoons 2C + D \) is:

\[ K = \frac{[C]^2[D]}{[A][B]^2} \]