Chapter 14, Problem 125E

Methane (CH₄) is a greenhouse gas emitted by industry, agriculture, and waste systems. It is the second most prevalent greenhouse gas (after carbon dioxide). Methane plays an important role in climate change because it absorbs infrared radiation more efficiently than carbon dioxide. Methane is broken down in the atmosphere by ozone (O₃), making its atmospheric Iifetime shorter than that of carbon dioxide.

${\text{CH}}_{\text{4}}\left(\text{g}\right)+{\text{O}}_{\text{3}}\to \text{products}$

A research group studied the rate of the reaction by which methane reacts with ozone and gets the data shown in the tables shown here. Study the data and answer the questions that follow.
Initial Rate versus Initial Concentrations

[CH4]	[O3]	Initial Rate (M/ s)
0.010	0.010	$\text{3}.\text{94}\times \text{1}{0}^{-\text{7}}$
0.020	0.010	$\text{7}.\text{88}\times \text{1}{0}^{-\text{7}}$
0.020	0.020	$\text{1}.\text{58}\times \text{1}{0}^{-\text{6}}$

Rate Constant versus Temperature

Temperature (K)	K (M-1.s-1)
260	$2.26\times \text{1}{0}^{-5}$
265	$\text{3}.65\times \text{1}{0}^{-5}$
270	$6.76\times \text{1}{0}^{-5}$
275	0.000114
280	0.000187
285	0.000303
290	0.000483

a. Use the data in the first table to determine the order of the reaction with respect to each reactant.
b. Use the data in the second table to determine the activation barrier and pre-exponential factor for the reaction.
c. Atmospheric concentrations of methane and ozone can vary depending on the location and altitude. Calculate the rate of the reaction at 273 K for a methane concentration of 1.8 ppm (by volume) and an ozone concentration of 5.0 ppm (by volume). Note that 1 ppm of CH₄ by volume means 1 L CH₄ /10⁶ L air. Assume STP (standard temperature and pressure) so that 1 mol gas occupies 22.4 L.
d. What is the half-life of methane in the atmosphere in years at 323 K? (Assume that [CH₄] = [O₃] = [A]₀ = $5.0\times \text{1}{0}^{-7}$ M.)