`NH_(4)COONH_(4)(s) hArr 2NH_(3)(g)+CO_(2)(g)`. for the
above reaction, `K_(p)` is 4, `K_c` will be

Answer

To solve the problem, we need to find the value of \( K_c \) given the reaction:

\[ NH_4COONH_4(s) \rightleftharpoons 2NH_3(g) + CO_2(g) \]

and the equilibrium constant \( K_p = 4 \).

### Step-by-Step Solution:

1. **Identify the Reaction**:
We have the equilibrium reaction where solid ammonium carbamate decomposes into gaseous ammonia and carbon dioxide.

2. **Write the Relationship Between \( K_p \) and \( K_c \)**:
The relationship between \( K_p \) and \( K_c \) is given by the formula:
\[ K_p = K_c (RT)^{\Delta N_g} \]
where \( R \) is the universal gas constant, \( T \) is the temperature in Kelvin, and \( \Delta N_g \) is the change in the number of moles of gas.

3. **Calculate \( \Delta N_g \)**:
- Count the moles of gaseous products:
- From the products, we have \( 2 \) moles of \( NH_3 \) and \( 1 \) mole of \( CO_2 \), giving a total of \( 2 + 1 = 3 \) moles.
- Count the moles of gaseous reactants:
- The reactant \( NH_4COONH_4 \) is a solid, which does not contribute to \( \Delta N_g \).
- Therefore, \( \Delta N_g = \text{moles of products} - \text{moles of reactants} = 3 - 0 = 3 \).

4. **Substitute Values into the Equation**:
Now we can substitute \( K_p \) and \( \Delta N_g \) into the equation:
\[ K_p = K_c (RT)^{\Delta N_g} \]
Rearranging gives:
\[ K_c = \frac{K_p}{(RT)^{\Delta N_g}} \]

5. **Plug in the Known Values**:
Substitute \( K_p = 4 \) and \( \Delta N_g = 3 \):
\[ K_c = \frac{4}{(RT)^3} \]

6. **Final Expression**:
Since we do not have the values for \( R \) and \( T \), we leave the answer in terms of \( R \) and \( T \):
\[ K_c = \frac{4}{(RT)^3} \]

### Final Answer:
\[ K_c = \frac{4}{(RT)^3} \]