5.27: Photochemical Kinetics

Introduction

When light is absorbed by molecules it deposits energy in the molecules. This energy can be reemitted as photons in the form of phosphorescence and fluorescence, dissipated as thermal energy or provide the energy for a chemical process. The kinetics of these processes thus impact the intensity and decay rate of fluorescence (which might be used for analytical detection of species) and the kinetics of photochemical reactions. Photochemical reactions are key contributors to the maintenance of the protective stratospheric ozone layer and smog. In this section we will discuss the concept of quantum yield and some of the photochemistry of stratospheric ozone and smog. 

Quantum yield

Quantum yield can be defined as the fraction of the absorbed photons that result in the outcome of interest, be it release of a fluorescent photon or the production of a particular chemical species. We will consider the case of fluorescence photon yield. Our kinetic model is as follows where F is the fluorofore, F* is the excited species, \(h\nu_a\) is the photon of the correct energy to be absorbed, \(h\nu_f\) is an emitted (fluorescent) photon, and Q is another species that can carry the energy away and thus quench the fluorescence:

\[\ce{F + h\nu_a \overset{k_a}{->}F\text{*}}\nonumber\]

\[\ce{F\text{*} \overset{k_f}{->}F + h\nu_f}\nonumber\]

\[\ce{F\text{*} + Q \overset{k_q}{->}F +Q}\nonumber\]

\[\ce{F\text{*} \overset{k_{rel}}{->}F }.\nonumber\]

The last reaction represents relaxation of the energy through additional paths to generate heat and a species that cannot fluoresce (e.g. vibrational relaxation, intersystem crossing, etc...). This mechanism yields the rate law:

\[\frac{d[F*]}{dt} = k_a[h\nu_a][F] - k_f[F\text{*}] - k_q[Q][F\text{*}] - k_{rel}[F\text{*}],\label{rateF*}\]

where \([h\nu]\), the photon concentration is proportional to the light intensity. In the case of fluorescence detection as might be done for quantitative analysis the exciting light source is on continuously during the measurement. Thus, a steady-state should be achieved where creation and destruction of F* balance out. Setting the rate of change in [F*] to zero and solving for [F*]_ss yields:

\[[F\text{*}]_{ss} = \frac{k_a[h\nu_a][F]_o}{k_a[h\nu_a] + k_f + k_q[Q] + k_{rel}},\label{F*ss}\]

where [F]_o is the concentration before excitation. The intensity of the fluorescence is just proportional to the rate of the emission reaction and the rate photons are absorbed is just proportional to the first photon absorption reaction rate. The quantum yield is the ratio of these:

\[\phi = \frac{k_f[F\text{*}]_{ss}}{k_a[h\nu_a][F]} = \frac{k_f k_a }{k_a[h\nu_a]([F]_o - [F\text{*}]_{ss})} = \frac{k_f}{k_f + k_q[Q] + k_{rel}}.\label{quantum_yield}\]

Thus if the rates of quenching and other relaxation processes were zero the quantum yield would be 1. As the concentration of quenchers increases or as the rate of other relaxation processes increases the quantum yield drops towards zero.

We can also consider how fast the fluorescence turns off (decays) after the excitation light source shuts off. Without an excitation source rate law \(\ref{rateF*}\) becomes:

\[\frac{d[F*]}{dt} =  - k_f[F\text{*}] - k_q[Q][F\text{*}] - k_{rel}[F\text{*}] =- (k_f + k_q[Q] + k_{rel})[F\text{*}] .\label{F*}\]

This is just a first order rate law. The the time dependence of the fluorescence which is proportional to [F*] is thus:

\[[F\text{*}] = [F\text{*}] _o e^{- (k_f + k_q[Q] + k_{rel})t}.\label{F*decay}\]

Therefore, the more quencher or the faster other relaxation and the fluorescence processes are the more rapidly the fluorescence shuts off after the excitation source is removed. The inverse of the sum in parentheses in equation \(\ref{F*decay}\) is the fluorescence lifetime and can be monitored with fast photodetectors.

Atmospheric ozone

Ozone, O₃, at ground level is a pollutant. It is extremely reactive and can cause damage to lungs at low concentrations (current exposure recommendations can be found at the US EPA website). Because ozone absorbs light in the 210 to 300 nm range (UVB radiation) significant concentrations of ozone in the stratosphere help to protect organisms on the surface from exposure to these damaging UV photons. Photochemistry is integral to the formation of this "ozone layer" and processes that destroy it.

Chapman mechanism

The Chapman cycle describes the reactions involving ozone and other oxygen species that provide UVB protection:

\[\ce{O2 + h\nu_1 \overset{k_1}{->} 2O} \quad\text{185 to 220 nm photons}\nonumber\]

\[\ce{O + O2 \overset{k_2}{->} O3\text{*}}\nonumber\]

\[\ce{O3\text{*} \overset{k_{-2}}{->}O + O2 }\nonumber\]

\[\ce{O3\text{*}+ M \overset{k_3}{->}O3 + M} \nonumber\]

\[\ce{O3 + h\nu_2 \overset{k_4}{->}O2 + O} \quad\text{210 to 300 nm photons}\nonumber\]

\[\ce{O3 + O \overset{k_5}{->}2O2}\nonumber\]

The second (k₂) third (k_-2) and fourth (k₃) reactions are often combined into a single trimolecular reaction for simplicity. This was not done here to emphasize the fact that simultaneous collisions of three gas phase species are rarely seen to contribute to reaction mechanisms. This mechanism ignores other reactions that involve these oxygen species, but provides a simple model for an initial understanding.

Consider a particular time of day. The sunlight intensity and thus the concentration of the photons involved will be constant. Additionally, molecular oxygen being about 20% of the atmosphere will have a constant concentration that is significantly larger than the ozone and other species. So, we will consider the O₂ concentration constant as well. As there are competing processes creating and destroying ozone, this will lead to steady-state concentrations of all the oxygen species in this mechanism. Without doing the steady state analysis we can still develop some conclusions about how the ozone concentration in the stratosphere will behave. The rate of the second reaction will depend on [O], which is created in the first reaction. As we go to lower altitude more of the light in the 185 to 220 nm range will have been absorbed by higher altitude oxygen molecules. This favors decreasing ozone concentration with decreasing altitude. However, at the high altitudes with lower pressure the third reaction (excited ozone falling apart) will dominate the fourth reacation where the energy is carried away before ozone can fall apart. The competition between the decrease in photoproduction of O atoms with decreasing altitude and the increase in pressure increasing the rate of collisional stabilization of ozone suggests that there will be an intermediate altitude where the ozone concentration reaches a maximum. This is what is observed as shown in the figure below.

Figure \(\PageIndex{1}\): Ozone partial pressure versus altitude. This shows an altitude where the concentration reaches a maximum when the production of O atoms by photodissociation is still high enough to produce ozone and the collisional stabilization is rapid enough because of the increased pressure to prevent all the energized ozone created from falling apart again. Source: Twenty Questions and Answers About the Ozone Layer: 2014 Update, World Meteorological Organization. https://library.wmo.int/idurl/4/54606.

Other reactions that destroy ozone

HO_x reactions

Below 30 km HO catalytically destroys ozone.

\[\ce{OH + O3 -> HO2 + O2}\nonumber\]

\[\underline{\ce{HO2  + O3 -> OH + 2O2}}\nonumber\]

\[\text{sum:}\quad\ce{2O3 -> 3O2}\nonumber\]

Above 40 km OH mostly reacts with free oxygen atoms and is not involved with destruction of ozone. Stratospheric OH can be produced by photodissociation of the limited amount of water vapor in the stratosphere.

NO_x reactions

NO can also catalytically destroy ozone.

\[\ce{NO + O3 -> NO2 + O2}\nonumber\]

\[\underline{\ce{NO2  + O -> NO + O2}}\nonumber\]

\[\text{sum:}\quad\ce{O3 + O -> 2O2}\nonumber\]

In addition NO₂ can react with OH to form HNO₃, which can then dissolve in water and be rained out.

\[\ce{NO2 + OH  + M -> HNO3 + M}.\nonumber\]

A major source of NO_x compounds are human made combustion reactions, that expose high temperature metal surfaces to atmospheric N₂ and O₂.

ClO_x reactions

Chlorine species also catalytically destroy ozone.

\[\ce{Cl + O3 -> ClO + O2}\nonumber\]

\[\underline{\ce{ClO  + O -> Cl + O2}}\nonumber\]

\[\text{sum:}\quad\ce{O3 + O -> 2O2}\nonumber\]

Chlorine leaves the atmosphere through formation of the water soluble HCl which rains out:

\[\ce{Cl + RH -> HCl + R}.\nonumber\]

The majority of Cl species in the atmosphere come from man made organic compounds that contain chlorine and fluorine (chlorofluorocarbons, CFCs). These molecules are stable in the troposphere so over time migrate to the stratosphere where UV light photodissociates the C-Cl bonds creating the reactive chlorine species. For example:

\[\ce{CClF3 + h\nu -> CF3 + Cl}.\nonumber\]

These CFCs were used as refrigerants and propellants due to their incredible stability near the Earth’s surface. However, the decomposition in the upper atmosphere to form Cl radicals is responsible for the catalytic decomposition of ozone. The world community addressed this issue by drafting the Montreal Protocol, which focused on the emission of ozone-destroying compounds. The result of this action has been a decrease in CFC emissions and an apparent stabilization and expected future increase in stratospheric ozone. This is one example of science-guided political, industrial, and economic policies leading to positive changes for our environment.

It is noteworthy that one reason for the success of this was many commercial enterprises saw a big market for products to replace the chlorine containing CFC products that were the source of the stratospheric chlorine. Thus, they may not have fought as strongly against the regulations phasing out CFCs.

Antarctic and Artic ozone holes

Both the Antarctic and Artic exhibit seasonal (during their hemisphere's Springs) drops in stratospheric ozone concentrations. These areas over the poles of very low ozone concentration are referred to as ozone holes. How they form is a good illustration of the impact of conditions and heterogenous chemistry on the kinetics of reactions.

If you look at satellite data showing amount of ozone in a vertical column of air looking down at the planet each spring (March or September) you will observe low ozone concentrations over the Poles (especially the South Pole) compared to the surrounding atmosphere. This is shown in the montages below.

Figure \(\PageIndex{2}\): Spring atmospheric column total ozone measurements. Left: Northern hemisphere in March. Right: Southern hemisphere in September. Blue is the lowest amount of ozone and red is the highest. Notice that a "hole" only forms occasionally in the Arctic (Northern hemisphere), but appears every year over the Antarctic. In the 1980s before significant amounts of chlorofluorocarbons had migrated to the stratosphere the Antarctic hole was less pronounced. More up-to-date data may be found at the NASA website from which thes images were taken: Northern hemisphere at https://ozonewatch.gsfc.nasa.gov/mon...ogy_03_NH.html and Southern hemisphere at https://ozonewatch.gsfc.nasa.gov/mon...ogy_09_SH.html.

The key to the difference between the South Pole and the North Pole is that the atmosphere around the South Pole has a stronger polar vortex (the winds that circulate clockwise around the poles when looking down at them). The stronger vortex effectively isolates the atmosphere above the South Pole from the rest of the atmosphere for a large fraction of its winter. The isolation combined with the lack of sunlight during the winter allows the atmosphere to get extremely cold. Small ice crystals form into clouds in the polar stratosphere (polar stratospheric clouds). On the surface of these ice crystals reactions occur that produce Cl₂ and HOCl from HCl and ClONO₂. The Cl₂ and HOCl build up during the polar winter. When the sun comes up in the spring they are photolyzed into Cl and ClO which catalyze the destruction of ozone. Because of the polar vortex the high concentrations of these catalysts are trapped until the atmosphere warms enough for the vortex to collapse. The high concentrations of the ozone destroying species leads to a much lower steady-state ozone concentration.

If you squint at the image of the Antarctic ozone hole, you may be able to convince yourself that it has improved somewhat in recent years because of the reduced CFC emissions dictated by the Montreal Protocol. It is projected that it will be at least 2050 before it returns to behaving more like it did prior to the 1980s.

Photochemical smog

Smog is what we call the noxious haze that often develops in cities. The word originally referred to the combination of coal smoke and fog that was common in London, England when lots of coal was burned for heat. Here we consider what is called photochemical smog, which forms on sunny days when there is lots of exhaust emission from internal combustion engines.

In order for photochemical smog to form there must be adequately high concentrations of NO_x (any oxide of N), hydrocarbons, O₂ and sunlight. Thus photochemical smog is most likely to form in places like Los Angeles, California or Mexico City where the air is trapped over the city by the surrounding mountains with the prevailing wind from the west.

Photochemical smog is mainly composed of ozone and nitrogen dioxide. During the formation of ozone, nitrogen dioxide from vehicle exhaust is photolyzed by incoming solar radiation to produce nitrogen oxide and an unpaired oxygen atom. The lone oxygen atom then combines with an oxygen molecule to produce ozone. Under normal conditions, the majority of ozone molecules oxidize nitrogen oxide back into nitrogen dioxide, creating a cycle that leads to only a very slight build up of ozone near ground level. However, when volatile organic compounds (VOCs) are present in the atmosphere, the equation changes entirely. Highly reactive VOCs oxidize nitrogen oxide into nitrogen dioxide without breaking down any ozone molecules in the process. This leads to a proliferation of ozone near ground level and dense smog formation.

Reactions and composition of smog

As would be expected for a process dependent on photochemistry the composition depends on the time of day as shown in the figure below. When pollutants are produced adds additional complexity to the kinetics.

Figure \(\PageIndex{3}\): Cartoon illustrating the typical time behavior of the concentration of smog components in photochemical smog. Based on figure 4.2 in G. W. vanLoon and S. J. Duffy, Environmental Chemistry 2 ed. (Oxford University Press, New York, 2005). 

There are hundreds of chemical reactions involved in the formation of photochemical smog, but the key features can be understood in terms of only a few.

The first important reaction is the formation of NO catalyzed by hot metal surfaces in engines.

\[\ce{ N2(g) + O2(g)\overset{\text{on hot metal}}{->}2 NO(g)}\nonumber\]

In figure \(\PageIndex{3}\) you can see the typical rise of NO concentrations because of morning rush hour traffic. Under ambient conditions the NO reacts spontaneously (\(\Delta G^o_{rxn} = -69.8 kJ\)) to form NO₂:

\[\ce{2NO(g) + O2(g) -> 2NO2(g)}\nonumber\]

Notice that the concentration of NO₂ rises rapidly with only a little lag from the rise in NO concentration indicating that the reaction is not only spontaneous but also quite rapid.  NO₂ is brown-yellow in color and one of the main reasons smog has a color.

Simultaneous with the growth of NOx there is an increase in the concentration of hydrocarbons. In Los Angeles the hydrocarbons come from partially burned fossil fuel emissions and the plants growing in the region.

The Nitrogen Dioxide (\(NO_2\)) is the beginning of the photochemical chain. Ultraviolet (UV) radiation (\(h\nu\)) from the sun and decomposes the \(NO_2\) into Nitrogen Oxide (\(NO\)) and an oxygen radical:

\[NO_2 + h\nu \rightarrow NO + O^. \label{1} \]

The oxygen radical then reacts with an atmospheric oxygen molecule to create ozone, O₃:

\[O^. + O_2 \rightarrow O_3 \label{2} \]

O₃ reacts readily with NO, to reverse the process, producing NO₂ and an oxygen molecule:

\[O_3 + NO \rightarrow O_2 + NO_2 \label{3} \]

If this were all that is happening only to a temporary increase in net ozone production would be observed. To create photochemical smog on the scale observed in Los Angeles, the process must include Volatile organic compounds (VOC's).

VOC's react with hydroxide in the atmosphere to create water and a reactive VOC molecule:

\[RH + OH^. \rightarrow R^. + H_2O \label{4} \]

The reactive VOC can then bind with an oxygen molecule to create an oxidized VOC:

\[R^. + O_2 \rightarrow RO_2 \label{5} \]

The oxidized VOC can now bond with the nitrogen oxide produced in the earlier set of equations to form nitrogen dioxide and a reactive VOC molecule:

\[RO_2+ NO \rightarrow RO-. + NO_2 \label{6} \]

In the second set of equations, it is apparent that nitrogen oxide, produced in reaction \(\ref{1}\), is oxidized in reaction \(\ref{6}\) without the destruction of any ozone. This means that in the presence of VOCs, reaction \(\ref{3}\) is essentially eliminated, leading to a large and rapid build up in the of the ozone typical of photochemical smog in the lower atmosphere.

So why does the NO₂ concentration drop off? Reaction \(\ref{6}\) appears to recreate it from NO. The key is that NO and NO₂ can react with many of the VOCs to form additional compounds. These VOCs react with O₃ and NO₂ in many different ways to produce irritating molecules that contain O, N, C and H. They often contain functional groups like ketones, aldehydes and nitrate groups (-NO₂). One of the worst molecules produced is called peroxyacetyl nitrate (PAN, figure \(\PageIndex{4}\)). PAN is a strong lachrymator, meaning that it causes tearing. PAN can also cause breathing problems for some. So once we create high O₃ concentrations with the help of sunlight we deplete the hydrocarbons and the NO_x molecules. The O₃ buildup is so high that in the evenings NO_x is used up as fast as it is produced by reactions that involve NO₂, O₃ and hydrocarbons.

Figure \(\PageIndex{4}\): The Lewis structure of PAN a strong lachrymator commonly found in photochemical smog.

In summary, as shown in figure \(\PageIndex{3}\): In the morning, NO and VOC concentrations are high, as people fill their cars with gas and drive to work. By midmorning , VOC's begin to oxidize NO into NO₂, thus reducing their respective concentrations. At midday, NO₂ concentrations peak just before solar radiation becomes intense enough to photolyze the NO₂ bond, releasing an oxygen atom that quickly gets converted into O₃. By late afternoon, peak concentrations of photochemical smog are present.

Controlling Photochemical Smog

Every new vehicle sold in the United States must include a catalytic converter to reduce photochemical emissions. Catalytic converters force CO and incompletely combusted hydrocarbons to react with a metal catalyst, typically platinum, to produce CO₂ and H₂O. Additionally, catalytic converters reduce nitrogen oxides from exhaust gases into O₂ and N₂, eliminating the cycle of ozone formation. Many scientists have suggested that pumping gas at night could reduce photochemical ozone formation by limiting the amount of exposure VOCs have with sunlight.

Contributors

• Jonathan Gutow (UW Oshkosh)

References

1. Cooksy Physical Chemistry: Thermodynamics (Pearson Education, Inc. Columbus, OH, 2014) Chapter 14.

2. Twenty Questions and Answers About the Ozone Layer: 2014 Update, World Meteorological Organization. https://library.wmo.int/idurl/4/54606.