For the reaction `A(g) + B(s) hArr C (g) + D (g), K_(c) = 49 mol dm^(-3)` at `127^(@)C`. Calculate `K_(p)`.

Explanation

To calculate \( K_p \) from \( K_c \) for the reaction \( A(g) + B(s) \rightleftharpoons C(g) + D(g) \), we can follow these steps:

### Step 1: Identify the given values
- The equilibrium constant \( K_c = 49 \, \text{mol dm}^{-3} \)
- The temperature \( T = 127^\circ C \)

### Step 2: Convert the temperature to Kelvin
To convert Celsius to Kelvin, use the formula:
\[ T(K) = T(°C) + 273 \]
So,
\[ T = 127 + 273 = 400 \, K \]

### Step 3: Determine the change in the number of moles of gas (\( \Delta n_g \))
For the reaction:
- Products: \( C(g) + D(g) \) contribute 2 moles of gas.
- Reactants: \( A(g) \) contributes 1 mole of gas, and \( B(s) \) is a solid and does not contribute to the gas phase.

Thus,
\[ \Delta n_g = \text{moles of products} - \text{moles of reactants} = 2 - 1 = 1 \]

### Step 4: Use the relationship between \( K_p \) and \( K_c \)
The relationship is given by:
\[ K_p = K_c \cdot R^T \cdot (\Delta n_g) \]
Where \( R \) is the universal gas constant, which is approximately \( 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1} \).

### Step 5: Substitute the values into the equation
Substituting the known values:
\[ K_p = 49 \cdot 0.0821 \cdot 400^{1} \]

### Step 6: Calculate \( K_p \)
Calculating \( K_p \):
\[ K_p = 49 \cdot 0.0821 \cdot 400 \]
\[ K_p = 49 \cdot 32.84 \approx 1619.16 \]
Thus, rounding to two decimal places:
\[ K_p \approx 1.61 \times 10^3 \]

### Final Answer
\[ K_p \approx 1.61 \times 10^3 \]

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