`K_p` is how many times equal to `K_c` for the given reaction ?
`N_2(g) +3H_2 (g) hArr 2NH_3(g)`

Options

A. `1/(R^2T^2)`
B. `R^2T^2`
C. `R/T`
D. `RT`

Answer

To find out how many times \( K_p \) is equal to \( K_c \) for the reaction:

\[ N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) \]

we can use the relationship between \( K_p \) and \( K_c \):

\[ K_p = K_c \cdot (RT)^{\Delta n} \]

### Step 1: Identify the reaction and coefficients
The reaction is:
- Reactants: \( N_2(g) \) and \( 3H_2(g) \)
- Products: \( 2NH_3(g) \)

### Step 2: Calculate \( \Delta n \)
\( \Delta n \) is defined as the difference between the sum of the stoichiometric coefficients of the products and the reactants in the gaseous phase.

\[ \Delta n = n_p - n_r \]

Where:
- \( n_p \) = sum of stoichiometric coefficients of products in gaseous phase
- \( n_r \) = sum of stoichiometric coefficients of reactants in gaseous phase

For our reaction:
- \( n_p = 2 \) (from \( 2NH_3 \))
- \( n_r = 1 + 3 = 4 \) (from \( N_2 \) and \( 3H_2 \))

Thus,

\[ \Delta n = 2 - 4 = -2 \]

### Step 3: Substitute \( \Delta n \) into the equation
Now, substituting \( \Delta n \) into the equation for \( K_p \):

\[ K_p = K_c \cdot (RT)^{-2} \]

### Step 4: Rearranging the equation
To find the ratio \( \frac{K_p}{K_c} \):

\[ \frac{K_p}{K_c} = (RT)^{-2} \]

This can also be expressed as:

\[ K_p = \frac{K_c}{(RT)^2} \]

### Step 5: Conclusion
Thus, \( K_p \) is equal to \( \frac{1}{(RT)^2} \) times \( K_c \). Therefore, we can conclude that:

\[ K_p = \frac{K_c}{(RT)^2} \]

### Final Answer
\( K_p \) is equal to \( \frac{1}{(RT)^2} \) times \( K_c \).

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