Chapter 16: Q16.22 P (page 729)

Although the depletion of stratospheric ozone threatens life on Earth today, its accumulation was one of the crucial processes that allowed life to develop in prehistoric times:
$3 O_{2 (g)} \to 2 O_{3 (g)}$
(a) Express the reaction rate in terms $[O_{2}]$ and $[O_{3}]$
(b) At a given instant, the reaction rate in terms of is 2.17105 mol/L s. What is it in terms of $[O_{3}]$ ?

Short Answer

Expert verified

a. The reaction rate of is, $Reactionrate = - \frac{1}{3} \frac{Δ [O_{2}]}{Δ t}$

The reaction rate ofis, $Reactionrate = \frac{1}{2} \frac{Δ [O_{3}]}{Δ t}$

b. The reaction rate in terms of data-custom-editor="chemistry" $[O_{3}]$ is $1.45 \times 10^{- 5} m o l / L . s$

Step by step solution

(a) Calculate the rate of reaction in terms of [O2]and [O3]

The rate of reaction can be measured in terms of reactant disappearance or product appearance. Calculate the reaction rate of as follows:

$Reactionrate = - \frac{1}{3} \frac{Δ [O_{2}]}{Δ t}$

In terms of data-custom-editor="chemistry" $[O_{3}]$ , express the reactionrate as follows:

$Reactionrate = \frac{1}{2} \frac{Δ [O_{3}]}{Δ t}$

The inverse of the fraction yields the molecules' stoichiometric coefficients. The negative sign indicates that the reactant concentration is decreasing.

(b) The reaction rate in terms of [O2] is 2.17105 mol/L s at any given time. In terms of [O3], what is it?

Calculate the reaction rate in terms of $[O_{2}]$ :

$\begin{array}{rcl} - \frac{1}{3} \frac{Δ [O_{2}]}{Δ t} & = & \frac{1}{2} \frac{Δ [O_{3}]}{Δ t} \\ \frac{Δ [O_{3}]}{Δ t} & = & \frac{2}{3} \times (- \frac{Δ [O_{2}]}{Δ t}) \\ = & \frac{2}{3} \times (2.17 \times 10^{- 5} m o l / L . s) \\ = & 1.45 \times 10^{- 5} m o l / L s^{- 1} \end{array}$

As a result, the reaction rate in terms of $[O_{3}]$ is $1.45 \times 10^{- 5} m o l / L s^{- 1}$

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Short Answer

Step by step solution

(a) Calculate the rate of reaction in terms of [O2]and [O3]

(b) The reaction rate in terms of [O2] is 2.17105 mol/L s at any given time. In terms of [O3], what is it?

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