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This question bugs me for years since I started learning the oxygen, carbon dioxide and hydrogen tests. I know you can make a glowing splinter burn when doing the oxygen test due to enough oxygen. But why won't it burn in ordinary air?

So, my question is what factor differentiate a glowing splinter and a burning splinter

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    $\begingroup$ I'm guessing you are defining a burning splinter as having visible smoke, while a glowing splinter does not. Is this correct? If so then both splinters are burning. The burning in the glowing splinter is complete. $\endgroup$ – Agriculturist Jan 24 '16 at 20:22
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Ordinary air is made up of only approximately $21~\%~\ce{O2}$, the primary component being nitrogen. According to the partial pressure rule, at standard laboratory temperature and pressure, this is a partial pressure $p(\ce{O2}) = 21~\mathrm{kPa}$. In a test tube filled with pure oxygen, e.g. from water electrolysis, the partial pressure of oxygen is $p(\ce{O2}) = 100~\mathrm{kPa}$ — five times as much.

According to the rate law, the combustion of wood ($\ce{C_{$n$}H_{$m$}O_{$l$}}$) with oxygen will be dependent of oxygen’s partial pressure somewhat. Thus, we can assume at least a five-fold increase in reaction rate. A five-fold rate increase also means a five-fold increase of enthalpy per time-frame which means five times the heat is liberated which means that the glowing splinter will get hotter much more quickly and finally ignite.

Technically of course, glowing is just a weaker form of burning and oftentimes only requires more oxygen to reignite. Hence why sometimes a fire can be reignited by blowing onto the embers.

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A splinter can undergo multiple types of thermal reactions depending on both the maximum temperature and amount of oxygen present. The answer to the question seems to be in the difference between total and partial inceneration.

In total inceneration, which is very likely in the total oxygen atmosphere at high temperatures, all of the organic carbon is converted to carbon dioxide. Carbon dioxide is colorless so the emission of electrons, i.e. the glowing, is observable.

In partial inceneration, which occurs when oxygen is present but deficient, the organic carbon is converted into both carbon dioxide and a variety of volatile compounds observable as smoke. Smoke forms at lower temperatures than thermal emissions. Smoke can also obscure thermal emissions.

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