# Ozone-oxygen cycle

Ozone-oxygen cycle in the ozone layer .

The ozone-oxygen cycle , also known as Chapman's cycle , is the process by which ozone is continually renewed in the ozone layer , with ultraviolet radiation being converted into thermal energy . In 1930 the chemical relationships involved were clarified by Sydney Chapman .

## Formation of ozone

Atomic oxygen is a prerequisite for the formation of ozone. This can occur when ultraviolet sunlight ( wavelength less than 240 nm ) splits an oxygen molecule (O 2 ). These atoms often react with other oxygen molecules to form ozone.

${\ displaystyle \ mathrm {O_ {2} + (radiation <240nm) \ longrightarrow 2O}}$
${\ displaystyle \ mathrm {2 \ (O_ {2} + O + M) \ longrightarrow 2 \ (O_ {3} + M)}}$

M is a so-called “third collision partner”, a molecule (usually nitrogen or oxygen) that transports away the excess energy of the reaction. Ozone is created slowly because sunlight is not very intense at wavelengths below 240 nm.

## What function ozone fulfills

When ozone comes into contact with ultraviolet light in the upper atmosphere , a chemical reaction occurs rapidly . The triatomic ozone molecule becomes diatomic molecular oxygen plus a free oxygen atom:

${\ displaystyle \ mathrm {O_ {3} + radiation \ longrightarrow O_ {2} + O}}$

Free atomic oxygen reacts quickly with other oxygen molecules and in turn forms ozone:

${\ displaystyle \ mathrm {O_ {2} + O + M \ longrightarrow O_ {3} + M}}$

The chemical energy that is released when O and O 2 combine is converted into kinetic energy of molecular movement. The overall effect is to convert penetrating ultraviolet light into harmless heat. This cycle keeps the ozone layer in a stable equilibrium, while at the same time protecting the lower atmosphere from UV radiation, which is harmful to most living things. It is also one of the two most important sources of heat in the stratosphere (the other is based on the kinetic energy that is released when O 2 is photolyzed to form O atoms ).

## How ozone breaks down

When an oxygen atom and an ozone molecule meet, they recombine to form two oxygen molecules:

${\ displaystyle \ mathrm {O_ {3} + O \ longrightarrow 2 \ O_ {2}}}$

The total amount of ozone in the stratosphere is determined by a balance between production from solar radiation and decay from recombination.

Free radicals , the most important of which are hydroxyl (OH), nitroxyl (NO) and chlorine (Cl) and bromine (Br) atoms, catalyze the recombination. This reduces the amount of ozone in the stratosphere.

Most of the hydroxyl and nitroxyl radicals are naturally present in the stratosphere, but human influences, especially the decomposition products of chlorofluorocarbons ( CFCs and halons ), have greatly increased the concentrations of chlorine and bromine atoms, which has contributed to the creation of the ozone hole . Each Cl or Br atom can catalyze tens of thousands of decay events before it is removed from the stratosphere.

## Mathematical consideration

The ozone-oxygen cycle can be described by the following differential equation:

${\ displaystyle {\ frac {dc_ {1}} {dt}} = {\ frac {c_ {2}} {\ tau _ {2}}} - {\ frac {c_ {1}} {\ tau _ { 1}}}}$

Here c 1 is the concentration of ozone and c 2 is the concentration of oxygen. The equation reflects that the production rate of ozone is proportional to the concentration of oxygen, and the decay rate (-) is proportional to the concentration of the ozone itself. The proportionality constants have the dimension of a time. They depend on the known influencing factors of the reactions involved and can therefore change if these boundary conditions vary. ${\ displaystyle \ tau _ {1}, \ tau _ {2}}$

The lifespan of ozone depends in particular on the energy flux density of the ozone-destroying UV radiation, on the probability that ozone is destroyed in collision processes (thus on temperature and pressure), and on the concentration of destructive radicals. Under normal conditions, i.e. H. in the absence of competing decay processes caused by light or radicals, the service life is given as about 20 min . With the aforementioned influences, the service life will be correspondingly shorter. ${\ displaystyle \ tau _ {1}}$${\ displaystyle \ tau _ {1} \ approx 10 ^ {3} s}$

The time also depends on the energy flow density of the ozone-generating UV radiation. ${\ displaystyle \ tau _ {2}}$

The solution of the above differential equation is greatly simplified by the fact that the concentration of diatomic oxygen can be viewed as constant. This means that no corresponding differential equation has to be solved for oxygen. The time constants and the corresponding boundary conditions are also initially viewed as constant. The general solution of the differential equation, as is easily verified by plugging in, is:

${\ displaystyle c_ {1} (t) = {\ frac {\ tau _ {1}} {\ tau _ {2}}} c_ {2} -A \ cdot e ^ {- t / \ tau _ {1 }}.}$

The additional constant A only defines the initial concentration of ozone. The following conclusion can be drawn from the result. First of all, it should be noted that the exponential factor tends towards zero for times that are much longer than the decay time of the ozone. The fictitious final state represents the equilibrium concentration of the ozone. The time for the establishment of equilibrium is therefore equal to the chemical life of the ozone, i.e. less than 20 minutes . For the state of equilibrium, a simple form of the law of mass action also applies according to the above equation${\ displaystyle \ tau _ {1}}$

${\ displaystyle {\ frac {c_ {1GG}} {c_ {2}}} = {\ frac {\ tau _ {1}} {\ tau _ {2}}}.}$

From this it can be seen in principle that the equilibrium concentration of ozone is lower, the shorter its lifespan. The equilibrium concentration of ozone in the stratosphere is given as around 10 ppm. So it is and with it ${\ displaystyle c_ {1GG} \ approx 10 ^ {- 5} c_ {2}}$

${\ displaystyle \ tau _ {2} \ approx 100000 \ tau _ {1}.}$

However, this period of time, which is on the order of years, should not be confused with the time until equilibrium is reached. Conversely, it rather represents approximately the time that would be required in the fictitious absence of decay processes to convert all of the oxygen into ozone.

With the same concentrations of ozone and oxygen, the production of ozone would take place much more slowly than the destruction of ozone, which is the direct explanation of the low ozone concentrations in the stratosphere.

According to the standard of the natural decay time of ozone (in the dark), the equilibrium reacts sensitively to additional decay processes caused by free radicals and UV radiation. As a first approximation, the additional decay processes are linearly included in the decay law and thus the inverse lifetime:

${\ displaystyle {\ frac {1} {\ tau _ {1}}} = {\ frac {1} {\ tau _ {push}}} + {\ frac {1} {\ tau _ {radical}}} + {\ frac {1} {\ tau _ {radiation}}}}$

This in turn depends on the concentration of free radicals and, accordingly, on the intensity of the destructive radiation. The more free radicals or the more UV radiation there is, the shorter the corresponding service life. ${\ displaystyle \ tau _ {radical}}$${\ displaystyle \ tau _ {radiation}}$

Even if z. If, for example, the destruction of ozone by radicals would take 25 times as long as their natural disintegration by impacts and radiation, this would nevertheless result in a 4% shift in the equilibrium, i.e. a 4% reduction in the ozone content. The more free radicals there are in the stratosphere, the lower the ozone content, which is in equilibrium.