Question

Derive the units of rate constant for the reactions of various orders.

Answer 1

The power to which the concentration term of a particular reactant in the rate law is raised is called the order of reaction with respect to that reactant, and the sum of all the powers to which all the concentration terms in the rate law are raised to express the observed rate of reaction is called the overall order of reaction.

Rate = k[A]ⁿ

Where

Rate has units of mol L⁻¹ s⁻¹

k is the rate constant

[A] is the concentration in mol L⁻¹

n is the order of the reaction

General formula for units of k:

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

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

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

For a zero-order reaction (n = 0):

Rate = k[A]⁰ = k

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

For a first-order reaction (n = 1):

Rate = k[A]

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

[k] = s⁻¹

For a second-order reaction (n = 2):

Rate = k[A]³

\[\ce{[k] = \frac{mol L^{-1} s^{-1}}{(mol L^{-1})^3}}\]

[k] = mol⁻² L² s⁻¹