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If ozone is a gas, and gases have the highest entropy, then how does the ozone gas stay within a few layers of the atmosphere, even though they span for kilometers?

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    $\begingroup$ Entropy and ozone at the top of the atmosphere are two unconnected things. Harmful UV rays from the Sun are unable to penetrate deep into the atmosphere because they encounter oxygen molecules. They absorb the UV and form ozone on the top. If ozone reached us, nobody could survive. It is a harmful thing. Read more about the en.wikipedia.org/wiki/Ozone%E2%80%93oxygen_cycle $\endgroup$ – M. Farooq May 3 at 14:39
  • $\begingroup$ @M.Farooq - For clarification - there's plenty of ground level ozone around. It's not good for us, but it's not so bad at low concentrations that we don't survive. I suspect most people are familiar with the smell of ozone, even if they don't know what they're smelling. $\endgroup$ – Andrew May 3 at 15:47
  • $\begingroup$ Right, Andrew, ozone at part per million levels it is not that great! It immediately hurts the throat if you are sensitive. If you recall the smell of older photocopy machines, the smell is not that pleasant but fresh rain is of wonderful but that must be parts per billion conc. $\endgroup$ – M. Farooq May 3 at 15:58
  • $\begingroup$ Plus some rare highly reactive agens like peroxyacetylnitrate can be created, what reportedly acted in past during some Los Angeles smog situations as plant defoliant. Additionally, ozone is the starter of immission damage to conifer trees by SO2. $\endgroup$ – Poutnik May 3 at 16:07
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It does not have much to do with entropy, rather with the way and place of ozone creation.

Stratospheric ozone is produced typically at altitude 20-30 km by UVC radiation with $\lambda \lt \pu{280 nm}$:

$$\ce{O2 + \nu -> 2 O}$$ $$\ce{O + O2 -> O3}$$

See ozone cycle as courtesy of @M. Farooq.

Ozone in lower troposphere troposphere is created by UVB (280-320 nm) (+UVA >320 nm ??) mostly due catalytic effects of nitrogen oxides that come typically of the oxidative smog of the Los Angeles type:

$$\ce{NO2 + \nu -> NO2^{*}}$$ $$\ce{NO2^{*} + O2 -> NO + O3}$$ $$\ce{2 NO + O2 -> 2 NO2}$$

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Technically, the concentration and positioning of ozone in the atmosphere likely relates directly to both ozone formation, stabilization and a destruction cycle.

While formation creation cycles has already been outlined, I would like to add more detail on the chemistry based on this source:

Creation:

$\ce{O2 + ℎν → 2 O• }$

$\ce{O• + O2 → O3 }$

which is followed by the 'ozone–oxygen cycle' where the ozone molecules formed by the reaction above absorbs radiation in wavelengths between UV-C and UV-B.

$\ce{O3 + ℎν(240–310 nm) → O2 + O }$

forming atomic oxygen which can further react with dioxygen:

$\ce{O + O2 → O3 + kinetic energy }$

The cited net effect of the ozone–oxygen cycle is the conversion of penetrating UV-B light into heat, with no net loss of O3. This cycle reputedly keeps the ozone layer stable and results in the protection of the lower atmosphere from harmful UV radiation.

Removal of Ozone:

$\ce{O3 + O· → 2 O2}$

$\ce{2 O· → O2 }$

Also, per a source, on the net effect of the two reactions, to quote:

$\ce{2 O3 → 3 O2 }$

This reaction proceeds more rapidly with increasing temperature.

So, higher colder altitudes are more conducive to the preservation of created ozone.

On its destruction cycles, to quote a source:

Ozone is a highly reactive molecule that easily reduces to the more stable oxygen form with the assistance of a catalyst. Cl and Br atoms destroy ozone molecules through a variety of catalytic cycles. In the simplest example of such a cycle,[11] a chlorine atom reacts with an ozone molecule (O3), taking an oxygen atom to form chlorine monoxide (ClO) and leaving an oxygen molecule (O2). The ClO can react with a second molecule of ozone, releasing the chlorine atom and yielding two molecules of oxygen. The chemical shorthand for these gas-phase reactions is:

$\ce{Cl· + O3 → ClO + O2}$

A chlorine atom removes an oxygen atom from an ozone molecule to make a ClO molecule

$\ce{ClO + O3 → Cl· + 2 O2}$

This ClO can also remove an oxygen atom from another ozone molecule; the chlorine is free to repeat this two-step cycle.

Now, pollutants in the atmosphere include chloro-(and bromo-) organics, which can, under UV photolysis, liberate a chlorine (or bromine) radical.

So, as one gets closer to the surface of the earth, radiation-induced ozone formation is abated, warmer temperatures are unfavorable and any diffused ozone entering the lower layers, could be further subject to attack by increasing concentration of photosensitized pollutants engaging in catalytic destruction cycles.

And, that is why the ozone layer resides at a high altitude, maintains itself and is not found closer to the surface of the earth.

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