The relationship between `K_p and K_c` is correctly shown as

Options

A. `K_c =K_p (RT)^(Deltan)`
B. `K_p=K_c(RT)^(-Deltan)`
C. `K_p=K_c (RT)^(Deltan)`
D. `K_c=K_p(RT)^(-Deltan)`

Answer

To derive the relationship between \( K_p \) and \( K_c \), we will start with a general chemical reaction and then apply the definitions of these equilibrium constants.

### Step-by-Step Solution

1. **Write the General Reaction**:
Consider a general reaction:
\[ aA + bB \rightleftharpoons cC + dD \]

2. **Define \( K_c \)**:
The equilibrium constant \( K_c \) is defined in terms of the concentrations of the products and reactants:
\[ K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b} \]

3. **Define \( K_p \)**:
The equilibrium constant \( K_p \) is defined in terms of the partial pressures of the products and reactants:
\[ K_p = \frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b} \]

4. **Relate Concentration and Pressure**:
The relationship between concentration and partial pressure can be expressed using the ideal gas law:
\[ P = CRT \]
where \( C \) is the concentration, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.

5. **Substituting for Partial Pressures**:
Substitute the expressions for partial pressures in terms of concentrations into the equation for \( K_p \):
\[ K_p = \frac{(C_C RT)^c (C_D RT)^d}{(C_A RT)^a (C_B RT)^b} \]

6. **Simplifying the Equation**:
This can be simplified to:
\[ K_p = \frac{[C]^c[D]^d (RT)^{c+d}}{[A]^a[B]^b (RT)^{a+b}} \]
Rearranging gives:
\[ K_p = K_c (RT)^{\Delta n} \]
where \( \Delta n = (c + d) - (a + b) \) is the change in the number of moles of gas.

7. **Final Relationship**:
Thus, the relationship between \( K_p \) and \( K_c \) can be expressed as:
\[ K_p = K_c (RT)^{\Delta n} \]

### Conclusion
The correct relationship between \( K_p \) and \( K_c \) is:
\[ K_p = K_c (RT)^{\Delta n} \]