Question

The unit of rate constant for a first-order reaction is

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

Hint:

Remember that the order of the reaction determines the units of the rate constant. For a zero-order reaction, the units are the same as those of the rate, while for a first-order reaction, the units are inverse time (s$^{-1}$).

Answer 1

The Correct Option is A

Step 1: Recall the rate law.
For a first order reaction the rate depends on one concentration. The rate law is $\text{Rate} = k[A]$. We must find the units of $k$.
Step 2: Write units of rate.
Rate is a change of concentration with time. Its units are $\text{mol L}^{-1}\ \text{s}^{-1}$.
Step 3: Write units of concentration.
Concentration $[A]$ has units $\text{mol L}^{-1}$.
Step 4: Make k the subject.
From the rate law, $k = \dfrac{\text{Rate}}{[A]}$. So we divide the units.
Step 5: Divide the units.
\[ k = \frac{\text{mol L}^{-1}\ \text{s}^{-1}}{\text{mol L}^{-1}} = \text{s}^{-1} \]The concentration units cancel and only the time unit is left.
Step 6: Final choice.
So the rate constant of a first order reaction has units $\text{s}^{-1}$.\[ \boxed{\text{s}^{-1}} \]