Question

The order of a reaction whose rate constant \(k = 0.693\times10^{-6}\,\text{L mol}^{-1}\text{s}^{-1}\) is:

• A. 0
• B. 2
• C. 1
• D. 3

Hint:

The unit \(\text{L mol}^{-1}\text{s}^{-1}\) is the most commonly asked unit for a second-order reaction in competitive examinations.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The order of a reaction can be determined from the units of the rate constant \( k \). For a reaction of order \( n \), the general unit for the rate constant is given by the formula: $$ \text{Unit of } k = (\text{concentration})^{1-n} \times (\text{time})^{-1} $$ Given that concentration is typically in \( \text{mol L}^{-1} \) (or \( M \)), the unit is \( (\text{mol L}^{-1})^{1-n} \text{ s}^{-1} \).

Step 2: Detailed Explanation:
Let's analyze the given units: \( \text{L mol}^{-1} \text{ s}^{-1} \). This can be rewritten as \( (\text{mol L}^{-1})^{-1} \text{ s}^{-1} \). Comparing this to the general unit formula \( (\text{mol L}^{-1})^{1-n} \text{ s}^{-1} \): $$ 1 - n = -1 $$ $$ -n = -1 - 1 $$ $$ -n = -2 $$ $$ n = 2 $$

Step 3: Verifying the Calculation:
For a second-order reaction (\( n=2 \)): Unit = \( (\text{mol L}^{-1})^{1-2} \text{ s}^{-1} = (\text{mol L}^{-1})^{-1} \text{ s}^{-1} = \text{mol}^{-1} \text{ L s}^{-1} \). This matches the unit \( \text{L mol}^{-1} \text{ s}^{-1} \) provided in the question.

Step 4: Final Answer:
The order of the reaction is 2.