Question

Show that the units of rate constant for a first order reaction do not depend upon the units of concentration.

Answer 1

For a first-order reaction, the rate law is:

Rate = k[A]

Rate is the change in concentration per unit time, so its units are:

mol L⁻¹ s⁻¹ (or any concentration/time unit)

From the rate law

\[\ce{k = \frac{Rate}{[A]}}\]

= \[\ce{\frac{mol L^{-1} s^{-1}}{mol L^{-1}}}\]

= s⁻¹

The units of the rate constant (k) for a first-order reaction are s⁻¹.

These units do not depend on the units of concentration because concentration cancels out in the expression. Hence, for a first-order reaction, k is always expressed in time⁻¹ (e.g., s⁻¹, min⁻¹).