Question

The hydroxyl radical (OH)is an important oxidizing agent in the atmosphere. At 298 K the rate constant for the reaction of (OH)with benzene is$\mathbf{1}\mathbf{.}\mathbf{24}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{12}}\mathbf{}{\mathbf{molecules}}^{\mathbf{-}\mathbf{1}}$. Calculate the value of the rate constant in${\mathbf{Lmol}}^{\mathbf{-}\mathbf{1}}{\mathbf{s}}^{\mathbf{-}\mathbf{1}}$.

Short answer

The value of the rate constant is $7.47\times {10}^8{\mathrm{Lmol}}^{-1}{\mathrm{s}}^{-1}$.

Step-by-step solution

Definition of the rate laws.

The rate of reaction a reaction depend on concentrations is the differential rate law. While the concentrations of species in the reaction depend on time is the integrated rate law.

Determine the value of the rate constant.

We have, $1{\mathrm{cm}}^3={10}^{-3}{\mathrm{dm}}^3$and the Avogadro unit ${\mathrm{N}}_{\mathrm{A}}=6.02214076{\mathrm{mol}}^{-1}$

So, the rate constant is,

$\begin{array}{rcl}\mathrm{k}& =& 1.24\times {10}^{-12}{\mathrm{cm}}^3{\mathrm{molecules}}^{-1}{\mathrm{s}}^{-1}\times 6.02214076{\mathrm{mol}}^{-1}\times {10}^{-3}{\mathrm{dm}}^3\\ & =& 7.47\times {10}^8{\mathrm{Lmol}}^{-1}{\mathrm{s}}^{-1}\end{array}$