The rate constant of reaction is `5xx10^(-2) "litre " ^(3) "mole"^(-3) "min"^(-1)` the order of reaction is

Options

A. `1`
B. `2`
C. `3`
D. `4`

Explanation

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

### Step-by-Step Solution:

1. **Identify the given rate constant (K)**:
The rate constant \( K \) is given as \( 5 \times 10^{-2} \, \text{litre}^3 \, \text{mole}^{-3} \, \text{min}^{-1} \).

2. **Understand the units of the rate constant**:
The units of the rate constant \( K \) can help us determine the order of the reaction. The general form for the rate of a reaction is:
\[ \text{Rate} = K [A]^n \]
where \( n \) is the order of the reaction and \( [A] \) is the concentration of the reactant.

3. **Write the units of rate**:
The rate of a reaction is typically expressed in terms of concentration change over time. For example, the rate can be expressed in units of:
\[ \text{Rate} = \frac{\text{mole}}{\text{litre} \cdot \text{min}} = \text{mol L}^{-1} \text{min}^{-1} \]

4. **Express the units of K**:
Rearranging the rate equation gives:
\[ K = \frac{\text{Rate}}{[A]^n} \]
The units of \( K \) can be expressed as:
\[ K = \frac{\text{mol L}^{-1} \text{min}^{-1}}{(\text{mol L}^{-1})^n} = \frac{\text{mol L}^{-1} \text{min}^{-1}}{\text{mol}^n \text{L}^{-n}} = \text{mol}^{1-n} \text{L}^{-1-n} \text{min}^{-1} \]

5. **Set the units of K equal to the given units**:
The given units of \( K \) are:
\[ \text{litre}^3 \, \text{mole}^{-3} \, \text{min}^{-1} \]
We can rewrite this as:
\[ K = \text{mol}^{-3} \text{L}^3 \text{min}^{-1} \]

6. **Equate the units**:
From the expression for \( K \):
\[ \text{mol}^{1-n} \text{L}^{-1-n} \text{min}^{-1} = \text{mol}^{-3} \text{L}^{3} \text{min}^{-1} \]
By comparing the powers of each unit, we can set up the following equations:
- For moles: \( 1 - n = -3 \)
- For litres: \( -1 - n = 3 \)

7. **Solve for n**:
From the first equation:
\[ 1 - n = -3 \implies n = 4 \]
From the second equation:
\[ -1 - n = 3 \implies n = -4 \quad \text{(not applicable since n must be consistent)} \]

8. **Conclusion**:
The order of the reaction is \( n = 4 \).

### Final Answer:
The order of the reaction is **4**.