If the equilibrium for a reaction is 4.0 what will be the equilibrium constant for the reverse reaction.

Explanation

To determine the equilibrium constant for the reverse reaction, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Equilibrium Constant (Kc)**:
The equilibrium constant (Kc) for a reaction at equilibrium is a ratio of the concentrations of products to reactants, each raised to the power of their coefficients in the balanced equation.

2. **Given Information**:
We know that the equilibrium constant for the forward reaction is given as Kc = 4. This means that for the reaction:
\[ aA + bB \rightleftharpoons cC + dD \]
the equilibrium constant is expressed as:
\[ K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b} = 4 \]

3. **Writing the Reverse Reaction**:
The reverse reaction would be:
\[ cC + dD \rightleftharpoons aA + bB \]
The equilibrium constant for the reverse reaction (let's call it Kc') can be expressed as:
\[ K_c' = \frac{[A]^a [B]^b}{[C]^c [D]^d} \]

4. **Relating Kc and Kc'**:
The relationship between the equilibrium constants of the forward and reverse reactions is given by:
\[ K_c' = \frac{1}{K_c} \]
Therefore, substituting the value of Kc:
\[ K_c' = \frac{1}{4} \]

5. **Final Answer**:
Thus, the equilibrium constant for the reverse reaction is:
\[ K_c' = 0.25 \]