Question

The unit of rate constant of first-order reaction is _________

Answer 1

The unit of the rate constant of a first-order reaction is ${\mathrm{s}}^{-1}$

Step 1: Write differential rate law:

• According to the differential rate law
• For the reaction $\mathrm{A}\to \mathrm{B}$
• Rate = $-\frac{d\mathrm{A}}{d\mathrm{t}}$

Step 2: Write the rate law:

• According to rate law
• For the reaction $\mathrm{A}\to \mathrm{B}$
• Rate$\propto {\left[\mathrm{A}\right]}^{\mathrm{x}}$ where $\mathrm{x}$ is the order of reactant $\mathrm{A}$
• Rate $=\mathrm{K}{\left[\mathrm{A}\right]}^x$where $\mathrm{K}$ is the rate constant of reaction and$\left[\mathrm{A}\right]$is the concentration of reactant

Step 3: Finding the unit for rate of the reacton:

A reaction in which the rate depends on the concentration of only one reactant is called a first-order reaction.

• Therefore rate of reaction $=-\frac{\mathrm{dA}}{\mathrm{dt}}=\mathrm{K}{\left[\mathrm{A}\right]}^{\mathrm{x}}$${\left[\mathrm{A}\right]}^x$
• Unit or rate of reaction $=\mathrm{mol}{\mathrm{L}}^{-1}{\mathrm{s}}^{-1}$
• For a first-order reaction:-
• Rate = $-\frac{d\mathrm{A}}{d\mathrm{t}}=\mathrm{K}{\left[\mathrm{A}\right]}^1$
• Unit of the rate of reaction = $=\mathrm{mol}{\mathrm{L}}^{-1}{\mathrm{s}}^{-1}$
• Unit of concentration $=\mathrm{mol}{\mathrm{L}}^{-1}$
• $$\begin{gathered} \mathrm{K}=\frac{\mathrm{Rate}}{{\left[\mathrm{A}\right]}^1} \\ =\frac{\mathrm{mol}{\mathrm{L}}^{-1}{\mathrm{s}}^{-1}}{\mathrm{mol}{\mathrm{L}}^{-1}} \\ \mathrm{K}={\mathrm{s}}^{-1} \end{gathered}$$
• Therefore unit of the rate constant of a first-order reaction is ${\mathrm{s}}^{-1}$.