Question

What is the correct unit for the rate constant in a first-order reaction?

• A. Moles per litre per second
• B. Per second
• C. Litre per mole per second
• D. Moles squared per litre squared per second

Hint:

For first-order reactions, the unit of the rate constant \( k \) is always \(\text{s}^{-1}\).

Answer 1

The Correct Option is B

Step 1: Understanding the rate law.
For a first-order reaction, the rate law is \( r = k[A] \), where \( k \) is the rate constant, and \([A]\) represents the concentration of reactant \( A \). The unit of the rate \( r \) is concentration/time (e.g., mol/L·s).
Step 2: Unit analysis.
To find the units of \( k \), we can solve for \( k \) from the rate law equation: \[ k = \frac{r}{[A]} \] Since the rate \( r \) has units of mol/L·s and \([A]\) has units of mol/L, the unit of \( k \) will be: \[ \frac{\text{mol/L·s}}{\text{mol/L}} = \text{s}^{-1} \] Step 3: Conclusion.
Therefore, the correct unit for the rate constant \( k \) in a first-order reaction is \(\text{s}^{-1}\), which corresponds to option (B).