`NH_4COONH_2 (s) hArr 2NH_3(g)+CO_(2)(g)`
If equilibrium pressure is 8 atm for the above reaction, `K_p` will be :(volume and temperature are constant)

Options

A. 64
B. 80
C. 28
D. 22

Explanation

To solve the problem, we need to find the equilibrium constant \( K_p \) for the reaction:

\[ NH_4COONH_2 (s) \rightleftharpoons 2NH_3(g) + CO_2(g) \]

Given that the equilibrium pressure is 8 atm, we can follow these steps:

### Step 1: Understand the Reaction and the Gases Involved
The reaction involves one solid reactant and two gaseous products. At equilibrium, the solid does not affect the equilibrium constant, which depends only on the gases.

### Step 2: Define the Partial Pressures
Let:
- \( P \) be the partial pressure of \( NH_3 \)
- \( P \) be the partial pressure of \( CO_2 \)

From the stoichiometry of the reaction:
- For every mole of \( NH_4COONH_2 \) that decomposes, 2 moles of \( NH_3 \) and 1 mole of \( CO_2 \) are produced.

### Step 3: Express Total Pressure in Terms of Partial Pressures
The total pressure at equilibrium is given as 8 atm. The total pressure can be expressed as:
\[ P_{total} = P_{NH_3} + P_{CO_2} = 2P + P = 3P \]
Given that \( P_{total} = 8 \, \text{atm} \):
\[ 3P = 8 \implies P = \frac{8}{3} \, \text{atm} \]

### Step 4: Calculate the Partial Pressures
Now we can find the partial pressures:
- \( P_{NH_3} = 2P = 2 \times \frac{8}{3} = \frac{16}{3} \, \text{atm} \)
- \( P_{CO_2} = P = \frac{8}{3} \, \text{atm} \)

### Step 5: Write the Expression for \( K_p \)
The expression for \( K_p \) is given by:
\[ K_p = \frac{(P_{NH_3})^2 \cdot P_{CO_2}}{P_{NH_4COONH_2}} \]
Since \( NH_4COONH_2 \) is a solid, it does not appear in the expression. Thus:
\[ K_p = (P_{NH_3})^2 \cdot P_{CO_2} \]

### Step 6: Substitute the Values
Substituting the values we calculated:
\[ K_p = \left(\frac{16}{3}\right)^2 \cdot \left(\frac{8}{3}\right) \]
Calculating this:
\[ K_p = \frac{256}{9} \cdot \frac{8}{3} = \frac{2048}{27} \]

### Step 7: Final Calculation
Now, we can simplify:
\[ K_p \approx 28.4 \]

Thus, the final answer for \( K_p \) is approximately 28.