Question

The hypothetical elementary reaction $\mathbf{2}\mathbf{A}\mathbf{\to }\mathbf{B}\mathbf{+}\mathbf{C}$has a rate constant of ${\mathbf{10}}^{\mathbf{‐}\mathbf{6}}{\mathbf{M}}^{\mathbf{‐}\mathbf{1}}{\mathbf{s}}^{\mathbf{‐}\mathbf{1}}$. What is the reaction velocity when the concentration of $\mathbf{A}$ is $\mathbf{10}\mathbf{mM}$?

Short answer

The reaction velocity for the hypothetical elementary reaction $2\mathrm{A}\to \mathrm{B}+\mathrm{C}$ is 10^-10Ms^-1.

Step-by-step solution

Introduction

The pace of an elementary reaction is proportional to the frequency with which the reacting molecules come in contact with each other at a constant temperature. Thus, the rate constant of an elementary reaction can be used to calculate the reaction velocity.

Formula to calculate reaction velocity

For a bimolecular reaction, the reaction velocity is calculated as

v=k[A]²

Where

vis reaction velocity.

Kis reaction constant.

$\left[\mathrm{A}\right]$is the concentration of $\mathrm{A}$.

Calculation

It is given

Concentration of A=10mM (0.01M)

Rate constant=10^-6M^-1s^-1

On substituting the values,

v=k[A]²

=10^-6 x (0.010M)²

=10^-10Ms^-1

Thus, for the hypothetical elementary reaction, the reaction velocity is 10^-10Ms^-1.