In terms of rate constants for forward and backward reactions `(k_(f) and k_(b))` , equilibrium constant of a reaction is equal to `…………. .`

Answer

To find the equilibrium constant \( K \) in terms of the rate constants for the forward and backward reactions (\( k_f \) and \( k_b \)), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Reaction**:
Consider a general reaction at equilibrium:
\[ A + B \rightleftharpoons C \]
Here, \( A \) and \( B \) are reactants, and \( C \) is the product.

2. **Define Rate Constants**:
- Let \( k_f \) be the rate constant for the forward reaction (where \( A \) and \( B \) form \( C \)).
- Let \( k_b \) be the rate constant for the backward reaction (where \( C \) decomposes back into \( A \) and \( B \)).

3. **Write Rate Expressions**:
- The rate of the forward reaction can be expressed as:
\[ \text{Rate}_{\text{forward}} = k_f [A][B] \]
- The rate of the backward reaction can be expressed as:
\[ \text{Rate}_{\text{backward}} = k_b [C] \]

4. **Establish Equilibrium Condition**:
At equilibrium, the rate of the forward reaction equals the rate of the backward reaction:
\[ k_f [A][B] = k_b [C] \]

5. **Rearranging for Equilibrium Constant**:
Rearranging the above equation gives:
\[ \frac{[C]}{[A][B]} = \frac{k_f}{k_b} \]

6. **Define the Equilibrium Constant**:
The equilibrium constant \( K \) (or \( K_c \) for concentrations) is defined as:
\[ K = \frac{[C]}{[A][B]} \]

7. **Final Expression**:
Therefore, we can express the equilibrium constant in terms of the rate constants:
\[ K = \frac{k_f}{k_b} \]

### Final Answer:
The equilibrium constant of a reaction is equal to:
\[ K = \frac{k_f}{k_b} \]