Question

The rate law for the decomposition of hydrogen iodide is - = d[HI]/dt = k[HI]2. The units of rate constant k are: 

• A. L mol^-1 s^-1
• B. L^-1 mol s^-1
• C. L² mol^-2 s^-1
• D. L^1/2 mol^1/2 s^-1

Answer 1

The Correct Option is A

To solve the problem, we need to determine the units of the rate constant \(k\) for the given rate law:

Given:
Rate law: \( \frac{-d[HI]}{dt} = k[HI]^2 \)
This is a second-order reaction because the exponent on the concentration term is 2.

1. General Unit Formula for Rate Constant:
For a reaction of order \(n\), the units of the rate constant \(k\) are:
\[ \text{Units of } k = \frac{\text{mol L}^{-1} \cdot \text{s}^{-1}}{(\text{mol L}^{-1})^n} = \text{mol}^{1-n} \cdot \text{L}^{n-1} \cdot \text{s}^{-1} \]

2. Apply for Second-Order Reaction:
Here, \(n = 2\):
\[ \text{Units of } k = \text{mol}^{1-2} \cdot \text{L}^{2-1} \cdot \text{s}^{-1} = \text{mol}^{-1} \cdot \text{L} \cdot \text{s}^{-1} \]

Final Answer:
The correct units of \(k\) are L mol⁻¹ s⁻¹.