Question

For a first-order reaction, the unit of rate constant is:

• A. \( \text{mol L}^{-1}\text{s}^{-1} \)
• B. \( \text{s}^{-1} \)
• C. \( \text{L mol}^{-1}\text{s}^{-1} \)
• D. \( \text{mol}^{-2}\text{L}^2\text{s}^{-1} \)

Hint:

For an \(n^{th}\)-order reaction: \[ [k]=(\text{concentration})^{1-n}\text{time}^{-1} \] First-order reactions always have unit: \[ \text{s}^{-1} \]

Answer 1

The Correct Option is B

Concept:
The unit of rate constant depends on the order of reaction. For a first-order reaction: \[ \text{Rate} = k[A] \] where:
• Rate has unit \( \text{mol L}^{-1}\text{s}^{-1} \)
• Concentration has unit \( \text{mol L}^{-1} \)

Step 1: Write the rate law.
\[ \text{Rate}=k[A] \]

Step 2: Substitute units.
\[ \text{mol L}^{-1}\text{s}^{-1}=k\times \text{mol L}^{-1} \] \[ k=\frac{\text{mol L}^{-1}\text{s}^{-1}}{\text{mol L}^{-1}} \] \[ k=\text{s}^{-1} \]

Step 3: Conclusion.
Therefore, the unit of first-order rate constant is: \[ \boxed{\text{s}^{-1}} \]