Which of the following relations between the reactions and equilibrium constant for a general reaction `aA+bBhArrc C+dD` is not correct ?

Options

A. (1) `aA+bBhArrcC+dD:K_(c)`
B. (2) `cC+dDhArraA+bB:K_(c)^(')=(1)/(K_(c))`
C. (3) `naA+nbBhArrncC+ndD:K_(c)^('')=K_(c)^(n)`
D. (4) `aA+bBhArrcC+dD:K_(c)=K_(p)`

Explanation

To solve the question, we need to analyze the given options regarding the equilibrium constant \( K_c \) for the general reaction:

\[ aA + bB \rightleftharpoons cC + dD \]

We need to identify which of the provided relations is incorrect.

### Step 1: Understand the Equilibrium Constant \( K_c \)

For the reaction \( aA + bB \rightleftharpoons cC + dD \), the equilibrium constant \( K_c \) is defined as:

\[ K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b} \]

Where \([A]\), \([B]\), \([C]\), and \([D]\) are the molar concentrations of the respective species at equilibrium.

### Step 2: Analyze Each Option

1. **Option A**: \( aA + bB \rightleftharpoons cC + dD \) has an equilibrium constant \( K_c \).
- This is correct as it directly follows from the definition of \( K_c \).

2. **Option B**: \( cC + dD \rightleftharpoons aA + bB \) has an equilibrium constant \( \frac{1}{K_c} \).
- This is also correct. The equilibrium constant for the reverse reaction is the reciprocal of the forward reaction's equilibrium constant.

3. **Option C**: If the reaction is multiplied by \( n \), then \( nA + nB \rightleftharpoons nC + nD \) has an equilibrium constant \( K_c^n \).
- This is correct. When the coefficients of a balanced equation are multiplied by \( n \), the equilibrium constant is raised to the power of \( n \).

4. **Option D**: \( aA + bB \rightleftharpoons cC + dD \) and \( K_p = K_c \).
- This statement is not necessarily correct. The relation between \( K_p \) and \( K_c \) is given by:

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

Where \( \Delta n \) is the change in the number of moles of gas (moles of gaseous products minus moles of gaseous reactants). Without knowing the states of the reactants and products (whether they are gases or not) and the value of \( \Delta n \), we cannot conclude that \( K_p = K_c \).

### Conclusion

The incorrect relation is **Option D**.