Chapter 17, Problem 17.44P

Interpretation Introduction

Interpretation:

A graph of time versus $\text{1/[HBr]}$ has to be drawn to prove the second order reaction.  Also, the value of rate constant of the reaction has to be determined.

Concept Introduction:

For the second-order decomposition of a single reactant A, the rate expression is

    $\begin{array}{l}\text{rate}\text{of}\text{reaction}\text{=}\text{-}\frac{\text{Δ[A]}}{\text{Δt}}\text{=}\text{k}{\text{[A]}}^{\text{2}}\\ \\ \text{By using elementary calculus, the concentration}\\ \text{of A at any time}\text{. The result is}\\ \\ \frac{\text{1}}{\text{[A]}}\text{=}\frac{\text{1}}{{\text{[A]}}_{\text{o}}}\text{+}\text{kt}\end{array}$

By comparing the above equation to the equation $\text{y=mx+b}$, it is clear that a plot of

$\text{1/}\left[\text{A}\right]$ versus time, t, is a straight line whose slope is the rate constant, k.