For the reaction `N_(2(g))+O_(2(g))rArrNO_((g))`, the value of `K_(c)` at `800^(@)` C is 0.1 . What is the value of `K_(p)` at this temperature ?

Options

A. 0.5
B. 0.01
C. 0.05
D. 0.1

Explanation

To find the value of \( K_p \) for the reaction \( N_2(g) + O_2(g) \rightleftharpoons 2NO(g) \) at 800°C, given that \( K_c = 0.1 \), we can use the relationship between \( K_c \) and \( K_p \):

### Step-by-Step Solution:

1. **Write the Reaction**:
The balanced chemical equation is:
\[ N_2(g) + O_2(g) \rightleftharpoons 2NO(g) \]

2. **Identify the Change in Moles (\( \Delta n \))**:
\( \Delta n \) is calculated as the difference between the number of moles of gaseous products and the number of moles of gaseous reactants.
- Products: \( 2 \) moles of \( NO \)
- Reactants: \( 1 \) mole of \( N_2 \) + \( 1 \) mole of \( O_2 \) = \( 2 \) moles

Therefore,
\[ \Delta n = \text{moles of products} - \text{moles of reactants} = 2 - 2 = 0 \]

3. **Use the Relationship between \( K_c \) and \( K_p \)**:
The relationship is given by:
\[ K_p = K_c \cdot R^T \cdot ( \Delta n ) \]
where:
- \( R \) is the ideal gas constant (0.0821 L·atm/(K·mol))
- \( T \) is the temperature in Kelvin

4. **Convert Temperature to Kelvin**:
\[ T = 800°C + 273.15 = 1073.15 \, K \]

5. **Substitute Values into the Equation**:
Since \( \Delta n = 0 \):
\[ K_p = K_c \cdot R^{1073.15} \cdot (0) \]
This simplifies to:
\[ K_p = K_c \cdot 1 = K_c \]

6. **Final Calculation**:
Given \( K_c = 0.1 \):
\[ K_p = 0.1 \]

### Conclusion:
The value of \( K_p \) at 800°C is \( 0.1 \).