For a reaction: `nA rarr` Product, if the rate constant and the rate of reactant are equal what is the order of the reaction?

Options

A. `0`
B. `1`
C. `2`
D. `3`

Explanation

To determine the order of the reaction given that the rate constant (k) and the rate of the reactant (R) are equal, we can follow these steps:

### Step 1: Write the rate expression
For the reaction \( nA \rightarrow \text{Products} \), the rate expression can be written as:
\[ R = k[A]^n \]
where \( R \) is the rate of the reaction, \( k \) is the rate constant, \( [A] \) is the concentration of reactant A, and \( n \) is the order of the reaction.

### Step 2: Set the condition given in the problem
According to the problem, we have the condition that the rate of the reactant is equal to the rate constant:
\[ R = k \]

### Step 3: Substitute the condition into the rate expression
Substituting \( R = k \) into the rate expression gives:
\[ k = k[A]^n \]

### Step 4: Simplify the equation
We can divide both sides of the equation by \( k \) (assuming \( k \neq 0 \)):
\[ 1 = [A]^n \]

### Step 5: Analyze the equation
The equation \( [A]^n = 1 \) implies that the concentration \( [A] \) must equal 1 (in appropriate units). This is true for any value of \( n \) as long as \( [A] \) is not zero. However, we can also consider specific cases for \( n \).

### Step 6: Consider \( n = 0 \)
If we set \( n = 0 \):
\[ [A]^0 = 1 \]
This is true for any concentration of \( A \). Therefore, if \( n = 0 \), we have:
\[ R = k \cdot 1 = k \]
This satisfies the condition \( R = k \).

### Conclusion
Thus, the order of the reaction is:
\[ \text{Order of the reaction} = 0 \]

### Final Answer
The order of the reaction is **0**.

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