The rate constant for a chemical reaction has unit litre `mol^(-1) sec^(-1)`. Find the order of the reaction.

Options

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

Explanation

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

### Step 1: Understand the units of the rate constant
The unit of the rate constant (k) is given as \( \text{litre mol}^{-1} \text{sec}^{-1} \).

### Step 2: Recall the formula for the units of the rate constant
The unit of the rate constant for a reaction of order \( n \) is given by:
\[ k = \text{concentration}^{(1-n)} \cdot \text{time}^{-1} \]
In terms of molarity (moles per litre), this can be expressed as:
\[ k = \left( \text{mol} \cdot \text{L}^{-1} \right)^{(1-n)} \cdot \text{sec}^{-1} \]

### Step 3: Substitute the units into the formula
Substituting the units into the formula, we get:
\[ k = \left( \text{mol} \cdot \text{L}^{-1} \right)^{(1-n)} \cdot \text{sec}^{-1} = \text{mol}^{(1-n)} \cdot \text{L}^{-(1-n)} \cdot \text{sec}^{-1} \]

### Step 4: Compare with the given unit
We know that the given unit of the rate constant is \( \text{L} \cdot \text{mol}^{-1} \cdot \text{sec}^{-1} \).

### Step 5: Set up the equation
From the comparison, we can set up the following equations for the exponents:
1. For moles: \( 1 - n = -1 \)
2. For seconds: The exponent for time is already \( -1 \).

### Step 6: Solve for \( n \)
From the first equation:
\[ 1 - n = -1 \implies n = 2 \]

### Conclusion
The order of the reaction is \( n = 2 \), which indicates that it is a second-order reaction.

### Summary of the solution:
The order of the reaction is 2, as the unit of the rate constant \( \text{L} \cdot \text{mol}^{-1} \cdot \text{sec}^{-1} \) corresponds to a second-order reaction.

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