The rate constant of a reaction is equal to the rate of reaction when

Options

A. Concentration of all reactants are unity
B. Concentration of all reactants and products are equal
C. Concentration of reactants and products do not change with time
D. The reaction takes infinite time for completion

Answer

To solve the question "The rate constant of a reaction is equal to the rate of reaction when," we need to analyze the relationship between the rate constant (k) and the rate of reaction (r) in the context of reaction order.

### Step-by-Step Solution:

1. **Understand the Rate Equation**:
The rate of a reaction can be expressed using the rate law:
\[ r = k[A]^n \]
where \( r \) is the rate of reaction, \( k \) is the rate constant, \( [A] \) is the concentration of the reactant, and \( n \) is the order of the reaction.

2. **Set the Rate Equal to the Rate Constant**:
We want to find the condition under which the rate of reaction equals the rate constant:
\[ r = k \]
Substituting the rate equation into this:
\[ k[A]^n = k \]

3. **Simplify the Equation**:
To simplify, we can divide both sides by \( k \) (assuming \( k \neq 0 \)):
\[ [A]^n = 1 \]

4. **Determine the Value of n**:
The equation \( [A]^n = 1 \) implies that the concentration of the reactant \( [A] \) must be equal to 1 (since any number raised to the power of 0 is 1). Therefore, for the equation to hold true for any concentration:
\[ n = 0 \]

5. **Conclusion**:
When \( n = 0 \), the reaction is a zero-order reaction. In a zero-order reaction, the rate of reaction is constant and does not depend on the concentration of the reactants. Thus, the rate constant \( k \) is equal to the rate of reaction \( r \) when the reaction is zero-order.

### Final Answer:
The rate constant of a reaction is equal to the rate of reaction when the reaction is a **zero-order reaction**.