A reaction that contributes to the depletion of ozone in the...

A reaction that contributes to the depletion of ozone in the stratosphere is the direct reaction of oxygen atoms with ozone: $$\mathrm{O}(\mathrm{g})+\mathrm{O}_{3}(g) \longrightarrow 2 \mathrm{O}_{2}(g)$$ At $298 \mathrm{~K}$ the rate constant for this reaction is $4.8 \times 10^{5} \mathrm{M}^{-1} \mathrm{~s}^{-1}$. (a) Based on the units of the rate constant, write the likely rate law for this reaction. (b) Would you expect this reaction to occur via a single elementary process? Explain why or why not. (c) From the magnitude of the rate constant, would you expect the activation energy of this reaction to be large or small? Explain. (d) Use $\Delta H_{f}^{\circ}$ values from Appendix $C$ to estimate the enthalpy change for this reaction. Would this reaction raise or lower the temperature of the stratosphere?

A reaction that contributes to the depletion of ozone in the stratosphere is the direct reaction of oxygen atoms with ozone:
$$\mathrm{O}(\mathrm{g})+\mathrm{O}_{3}(g) \longrightarrow 2 \mathrm{O}_{2}(g)$$
At $298 \mathrm{~K}$ the rate constant for this reaction is $4.8 \times 10^{5} \mathrm{M}^{-1} \mathrm{~s}^{-1}$. (a) Based on the units of the rate constant, write the likely rate law for this reaction. (b) Would you expect this reaction to occur via a single elementary process? Explain why or why not. (c) From the magnitude of the rate constant, would you expect the activation energy of this reaction to be large or small? Explain.
(d) Use $\Delta H_{f}^{\circ}$ values from Appendix $C$ to estimate the enthalpy change for this reaction. Would this reaction raise or lower the temperature of the stratosphere?

Key Concepts

Rate Laws and Reaction Order

When analyzing a reaction, the units of the rate constant provide insight into the overall order of the reaction. For example, a rate constant with units of M?¹s?¹ typically indicates a second?order reaction, which, in an elementary process, suggests the rate is proportional to the product of the concentrations of two reactants (first order in each).

Elementary Reaction Mechanism

An elementary reaction occurs in a single, concerted step where the rate law can be directly deduced from the stoichiometry. However, if the mechanism involves several steps (a complex mechanism), the overall rate law may not simply reflect the stoichiometry of the overall reaction, which must be considered when determining if a reaction proceeds by a single elementary step.

Activation Energy and Rate Constant Relationship

The activation energy is the energy barrier that must be overcome for a reaction to occur. A relatively large rate constant at a given temperature implies that the activation energy is low, thus allowing the reaction to proceed more readily. This concept is often analyzed using the Arrhenius equation, which links the rate constant to activation energy.

Reaction Enthalpy and Thermochemistry

Reaction enthalpy is a measure of the heat absorbed or released during a reaction, calculated using the standard enthalpies of formation of the reactants and products. A negative reaction enthalpy indicates an exothermic reaction, meaning that heat is released into the surroundings. In an atmospheric context, such a release of heat could affect the temperature profile of the environment.

Transcript

00:01 Quite a bit of writing on this, but not too hard.

00:04 A reaction that contributes to the depletion of ozone in the stratosphere is the direct reaction of oxygen atoms plus ozone.

00:13 And here's our product.

00:16 At 298 kelvin, the rate constant for this reaction is 4 .8 times 10 to the 5th.

00:43 Based on the units for the rate constant, we're asked to write the likely rate law.

01:13 And there are four parts to this.

01:16 So the rate constant, m to the minus 1, s to the minus 1, indicates that this is second overall.

01:30 So i would probably think that this would be 0 .03k equals rate.

01:46 That's what i would guess it would probably be.

01:48 It could also be the rate equals k times o squared or o3 squared.

02:06 It could be either one of those.

02:10 But i don't know if two of them like this, i would just guess it was the other one.

02:16 B.

02:19 What does b ask us? let's do each one of these on a separate page.

02:26 Would you expect this reaction to occur via a single elementary process? yes or no? and explain why.

03:03 We came up with yes here.

03:06 Most atmospheric processes are initiated by collision.

03:37 So we could imagine an activated complex of four o atoms collapsing to form two, 02 molecules.

04:19 Also our rate constant is pretty large and that is less likely for multi -step.

04:50 And based on information in the test this text, this react reaction is similar to to the destruction of 03 by chlorine atoms.

05:15 And your text this is 18 .7.

05:18 Equation 18 .7.

05:20 And this is also second order and has a large rate constant...

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