Rate constant of a reaction (k) is `4 xx 10^(-2) "litre"^(2) "mol"^(-2)sec^(-1)`. What is the order of reaction ?

Options

A. `2^(nd)`
B. `1^(st)`
C. `4^(th)`
D. `3^(rd)`

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 the reaction
The rate of a reaction can be expressed as:
\[ \text{Rate} = k [A]^x \]
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 typically expressed as:
\[ \text{Rate} = \text{mole} \cdot \text{liter}^{-1} \cdot \text{second}^{-1} \]

### Step 3: Identify the units of the rate constant \( k \)
The given unit of the rate constant \( k \) is:
\[ k = 4 \times 10^{-2} \, \text{litre}^2 \cdot \text{mol}^{-2} \cdot \text{s}^{-1} \]

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

### 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:
\[ \text{mole}^{1-x} \cdot \text{liter}^{-1+x} \cdot \text{second}^{-1} = \text{mole}^{-2} \cdot \text{liter}^2 \cdot \text{second}^{-1} \]

### Step 6: Compare the exponents for each unit
By comparing the exponents for each unit, we get two equations:
1. For mole: \( 1 - x = -2 \)
2. For liter: \( -1 + x = 2 \)

### Step 7: Solve the equations
From the first equation:
\[ 1 - x = -2 \implies x = 3 \]
From the second equation:
\[ -1 + x = 2 \implies x = 3 \]

### Conclusion
Both equations confirm that the order of the reaction \( x \) is 3. Therefore, the order of the reaction is:
\[ \text{Order of Reaction} = 3 \]