Calculate `K_(P)` for the reaction `A(g) iff B(s)+2C(g), K_(C)=0.2` at 305 K.

Answer

To calculate \( K_P \) for the reaction \( A(g) \iff B(s) + 2C(g) \) given that \( K_C = 0.2 \) at 305 K, we will use the relationship between \( K_P \) and \( K_C \).

### Step-by-Step Solution:

1. **Identify the Reaction and Given Values**:
- The reaction is \( A(g) \iff B(s) + 2C(g) \).
- We are given \( K_C = 0.2 \) and the temperature \( T = 305 \, K \).

2. **Use the Relationship Between \( K_P \) and \( K_C \)**:
- The relationship is given by the formula:
\[ K_P = K_C \times R T^{\Delta N_G} \]
- Where:
- \( R \) is the universal gas constant (0.0821 L·atm/(K·mol)).
- \( T \) is the temperature in Kelvin.
- \( \Delta N_G \) is the change in the number of moles of gas.

3. **Calculate \( \Delta N_G \)**:
- In the reaction, we have:
- Moles of gaseous products = 2 (from \( 2C(g) \))
- Moles of gaseous reactants = 1 (from \( A(g) \))
- Thus, \( \Delta N_G = \text{moles of products} - \text{moles of reactants} = 2 - 1 = 1 \).

4. **Substitute Values into the Equation**:
- Now, substitute \( K_C \), \( R \), \( T \), and \( \Delta N_G \) into the equation:
\[ K_P = 0.2 \times 0.0821 \times 305^{1} \]

5. **Calculate \( K_P \)**:
- First, calculate \( 0.0821 \times 305 \):
\[ 0.0821 \times 305 = 25.1 \]
- Now, calculate \( K_P \):
\[ K_P = 0.2 \times 25.1 = 5.02 \]

6. **Final Result**:
- Therefore, the value of \( K_P \) is approximately \( 5.02 \).

### Summary:
The equilibrium constant \( K_P \) for the reaction \( A(g) \iff B(s) + 2C(g) \) at 305 K is approximately \( 5.02 \).