Rate constant of a reaction (k) is `3 xx 10^(-2) "litre"^(-1) molsec^(-1)`. What is the order of reaction ?

Options

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

Explanation

To determine the order of the reaction based on the given rate constant (k), we can follow these steps:

### Step 1: Write the rate law expression
The rate law for a reaction can be expressed as:
\[ \text{Rate} = k \cdot [A]^x \]
where:
- \( k \) is the rate constant,
- \( [A] \) is the concentration of the reactant,
- \( x \) is the order of the reaction.

### Step 2: Identify the units of the rate constant
The given rate constant \( k \) has the units:
\[ k = 3 \times 10^{-2} \, \text{litre}^{-1} \, \text{mol}^{-1} \, \text{sec}^{-1} \]

### Step 3: Write the units for the rate of reaction
The rate of a reaction is typically expressed in terms of concentration change over time, which has the units:
\[ \text{Rate} = \text{mol} \, \text{litre}^{-1} \, \text{sec}^{-1} \]

### Step 4: Relate the units of the rate constant to the order of the reaction
From the rate law, we can express the units of \( k \) as:
\[ k = \frac{\text{Rate}}{[A]^x} \]
Substituting the units:
\[ \text{Units of } k = \frac{\text{mol} \, \text{litre}^{-1} \, \text{sec}^{-1}}{(\text{mol} \, \text{litre}^{-1})^x} \]

This simplifies to:
\[ k = \text{mol}^{1-x} \, \text{litre}^{x-1} \, \text{sec}^{-1} \]

### Step 5: Set up the equation for the units
Now we can equate the units of \( k \) we derived from the rate law to the units given:
\[ \text{mol}^{1-x} \, \text{litre}^{x-1} \, \text{sec}^{-1} = \text{mol}^{-1} \, \text{litre}^{-1} \, \text{sec}^{-1} \]

### Step 6: Compare the exponents of the units
From the equation, we can compare the exponents of the units:
1. For moles:
\[ 1 - x = -1 \]
Solving this gives:
\[ x = 2 \]

2. For litres:
\[ x - 1 = -1 \]
Solving this gives:
\[ x = 0 \]

### Step 7: Conclusion
Since both conditions must hold true, we find that the order of the reaction \( x \) is:
\[ x = 0 \]

Thus, the order of the reaction is **0**.