While there are many factors which can inhibit yeast activity: alcohol
content, lack of nutrients, lack of oxygen, pressure as well as
others, at bottling time in beers, it seems that all but the oxygen
requirment are present. Beers don't generally have adequate alcohol,
there's plenty of nutrients left, and at bottling time, pressure is
essentially ambient. Only oxygen is left.

Well, chemistry tells us that there needs to be an adequate supply of
oxygen for CO2 production. After fermentation, the beer has little
available dissolved oxygen left, and the headspace above the beer in
the fermentor is predominantly CO2 already. Some oxygen is made
avialable from the digestion of the priming sugar itself. Fructose
and glucose for instance have six carbon atoms and six oxygen atoms
Maltose and sucrose each have 12 carbons and only 11 oxygens. The
problem is that carbonation uses oxygen at twice the rate of carbon
(ie cabron DI-oxide) so there has to be at least some residual oxygen
available for use in CO2 production.

As a test, I tried with a recent batch of beer taken from the
secondary and most of it was carbonated as usual. A small portion of
it though, I aerated with an oxygen cylinder and stone to introduce
dissolved oxygen into the beer.(Don't get on me about the addition of
oxygen to the beer at this time, it was a test of a theory) Then I
added priming sugar and filled five bottles to the top. Capping
actually squeezed a little beer out of each bottle so I know they were
full. Within a week and a half, three of the bottles had either
ruptured or blown thier tops and I took the remaining two outside to
pop them before my wife tried to kill me for making the basement smell
like an old frat house. It tasted pretty poor, but the carbonatioin
was excellent (over-carbonated actaully). This leads me to conclude
that an adequate headspace must be left as a reservoir of oxygen for
the yeast to use for carbonation.

Not really a conclusive test, but it satisfied my curiosity and that
of my brewing friend who had asked that same question about why
headspace is required.

VK