Chapter 17, Problem 17.77P

Interpretation Introduction

Interpretation:

The decomposition of Uranyl nitrate is as follows:

  ${\text{UO}}_{\text{2}}{\left({\text{NO}}_{\text{3}}\right)}_{\text{2}\text{(aq)}}\to {\text{UO}}_{\text{3}\text{(s)}}\text{+}\text{2}{\text{NO}}_{\text{2}\text{(g)}}\text{+}\frac{\text{1}}{\text{2}}{\text{O}}_{\text{2}\text{(g)}}$

The rate law of the reaction is first order.  The value of rate constant has to be calculated from the given data.

Concept Introduction:

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

    $\begin{array}{c}\text{rate}\text{of}\text{reaction}\text{=}\text{-}\frac{\text{Δ[A]}}{\text{Δt}}\text{=}\text{k}\text{[A]}\\ \text{ln}\frac{\left[\text{A}\right]}{\left[{\text{A}}_{\text{°}}\right]}\text{=}\text{-kt}\end{array}$

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

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