If `K_(p)` for a reaction is 0.1 at `27^(@)C` the `K_(c )` of the reaction will be

Options

A. can not be calculate as `Delta n_(g) ` is not given
B. `(K_(p))/( RT)`
C. `K_(p) RT`
D. `(K_(p))/( ( RT)^(2))`

Answer

To solve the problem of finding \( K_c \) from the given \( K_p \) value, we need to use the relationship between \( K_p \) and \( K_c \). The equation that relates these two constants is:

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

Where:
- \( K_p \) is the equilibrium constant in terms of partial pressures.
- \( K_c \) is the equilibrium constant in terms of concentrations.
- \( R \) is the universal gas constant (0.0821 L·atm/(K·mol)).
- \( T \) is the temperature in Kelvin.
- \( \Delta N \) is the change in the number of moles of gas (moles of gaseous products - moles of gaseous reactants).

### Step-by-step Solution:

1. **Convert Temperature to Kelvin**:
\[ T = 27^\circ C + 273.15 = 300.15 \, K \]

2. **Identify Given Values**:
- \( K_p = 0.1 \)
- \( R = 0.0821 \, L·atm/(K·mol) \)
- \( T = 300.15 \, K \)

3. **Determine \( \Delta N \)**:
Since \( \Delta N \) is not provided in the question, we cannot calculate \( K_c \) directly. However, we can express \( K_c \) in terms of \( K_p \) and \( \Delta N \):
\[ K_c = \frac{K_p}{(RT)^{\Delta N}} \]

4. **Conclusion**:
Without the value of \( \Delta N \), we cannot determine a specific value for \( K_c \). Therefore, the problem cannot be solved completely with the information given.

### Final Answer:
Since \( \Delta N \) is not provided, we cannot determine \( K_c \).

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