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

Options

A. First
B. Second
C. Third
D. Fourth

Explanation

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

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

### Step 2: Identify the units of the rate
The unit of rate is given as:
\[ \text{Rate} = \text{mole} \cdot \text{litre}^{-1} \cdot \text{second}^{-1} \]

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

### Step 4: Relate the units of rate to the units of k
From the rate expression, we can express the units of \( k \) in terms of the units of concentration and the order of the reaction:
\[ \text{Units of } k = \frac{\text{Units of Rate}}{[\text{Concentration}]^x} = \frac{\text{mole} \cdot \text{litre}^{-1} \cdot \text{second}^{-1}}{(\text{mole} \cdot \text{litre}^{-1})^x} \]
This simplifies to:
\[ \text{Units of } k = \text{mole}^{1-x} \cdot \text{litre}^{x-1} \cdot \text{sec}^{-1} \]

### Step 5: Set the units of k equal to the given units
Now we can set the units of \( k \) equal to the given units:
\[ \text{mole}^{1-x} \cdot \text{litre}^{x-1} \cdot \text{sec}^{-1} = \text{mole}^{-2} \cdot \text{litre}^2 \cdot \text{sec}^{-1} \]

### Step 6: Compare the powers of mole and litre
From the equation above, we can compare the powers of mole and litre:
1. For mole:
\[ 1 - x = -2 \implies x = 3 \]
2. For litre:
\[ x - 1 = 2 \implies x = 3 \]

### Step 7: Conclusion
Since both comparisons give us \( x = 3 \), we conclude that the order of the reaction is:
\[ \text{Order of reaction} = 3 \]