Carbonation and Henry's law
Claude Jolicoeur
started playing with Henry's law and to program it into my
spreadsheet.
There is one thing that bugs me a bit...
On Feb. 16 2011, Andrew wrote:
> Also you need to subtract 1 bar for normal atmospheric
> pressure at the end, because what you actually measure in a soft drink
> is the pressure over 1 bar - i.e. gauge pressure not absolute
When I prime my cider then bottle it, there is some air on top of the
cider, under the hermetic closure. This air is at 1 atm (or 1 bar) -
and will stay there.
As the priming sugar ferments, CO2 will be released and will build a
partial pressure of CO2. But I don't see the point in substracting 1
bar since we will still have 1 bar of partial pressure from the air.
Hence, the partial pressure of CO2 calculated from Henry's law should
be equal to the actual gage pressure in the bottle.
Does this makes sense?
Claude
Andrew Lea
>
> There is one thing that bugs me a bit...
> On Feb. 16 2011, Andrew wrote:
>> Also you need to subtract 1 bar for normal atmospheric
>> pressure at the end, because what you actually measure in a soft drink
>> is the pressure over 1 bar - i.e. gauge pressure not absolute
>
> When I prime my cider then bottle it, there is some air on top of the
> cider, under the hermetic closure. This air is at 1 atm (or 1 bar) -
> and will stay there.
> As the priming sugar ferments, CO2 will be released and will build a
> partial pressure of CO2. But I don't see the point in substracting 1
> bar since we will still have 1 bar of partial pressure from the air.
> Hence, the partial pressure of CO2 calculated from Henry's law should
> be equal to the actual gage pressure in the bottle.
> Does this makes sense?
No, not to me :-) The presence of air inside the bottle isn't awfully
relevant. Nor are 'partial pressures' in the headspace. Air (mostly
nitrogen) isn't very soluble compared to CO2 (I think about 50 times
less) and the headspace volume is small compared to the total volume. So
CO2 is by far the dominant partner in the system (by about 98%).
The 1 atmosphere offset consideration is that Henry's Law deals in
absolutes. Hence you must saturate your cider with CO2 to get up to the
1 atm of normal atmospheric pressure that we all live under. Only after
that will there be 'carbonation'. The gauge pressure is the bottle
pressure in excess of the 1 atmosphere required for saturation that
takes place without carbonation being apparent.
My Henry's Law spreadsheet is at
http://www.cider.org.uk/carbonation_table.xls (not very elegant but it
does the job). All cells should be locked except the blue input cell at
F29. If you check it against all the published tables you'll find it
only agrees if the "1 bar offset" is applied. That is another reason for
doing so!!
[BTW don't put too much faith in the higher temperature figures. They
are extrapolations which were only included to answer the original
question we had here about what happens to the pressure at
pasteurisation temperatures]
Andrew
--
Wittenham Hill Cider Pages
www.cider.org.uk
Cornelius Traas
That is a very useful spreadsheet. However, it still prompts a question for
me when considering the effect of pasteurisation. If I fill a beer bottle of
water to the brim and the put on a crown cap, and stick it in a hot water
bath, the expansion of the water will break the bottle. On the other hand,
if I leave a little airspace, perhaps 5 to 10 cm3, then the bottle will not
break, as the airspace can accommodate the increasing volume of the liquid
as it is being heated. Clearly pressure in the headspace is increasing as
the volume decreases in this latter example.
My question is, in the spreadsheet, is this increase in pressure included in
the calculation, or just the pressure due to CO2?
Con Traas
The Apple Farm,
Moorstown, Cahir, Co. Tipperary.
Andrew Lea
>
> My question is, in the spreadsheet, is this increase in pressure
> included in the calculation, or just the pressure due to CO2?
> Con Traas
No the spreadsheet does not allow for volume expansion of the liquid nor
for compression of the headspace vacuity. It is simply Henry's Law
relating solubility to pressure above the liquid. The industry standard
'vacuity' in a carbonated drinks bottle is in the region of 3 - 5
percent of the total volume. It may seem a bit counter-intuitive but in
fact variations in the volume of the headspace between 1 and 5% have
relatively little effect on the overall pressure inside the bottle. That
is because most of the CO2 is actually stored in the liquid and more
dissolves back in there as the pressure rises, so the normal gas law
PV=nRT does not apply to the headspace. (And paradoxically, there is
more kinetic energy stored in the headspace of a half-full bottle of
carbonated drink that there is in a full one, simply because there is a
bigger volume of gas under pressure).
It gets a bit mind-boggling at times ;-)
Andrew
--
Wittenham Hill Cider Page
Ray Blockley
> It gets a bit mind-boggling at times ;-)
Yes it sure does :-)
I'm afraid all this is way over my head, but fascinating all the less! Just
wish I'd listened harder in Maths and Physics classes at school. :-)
Cheers,
Ray.
Cornelius Traas
>
> Yes it sure does :-)
What a brilliant bit of logic though. I think I get it, but so
counter-intuitive.
Many thanks Andrew.
Con Traas
Claude Jolicoeur
> If you check it against all the published tables you'll find it
> only agrees if the "1 bar offset" is applied. That is another reason for
> doing so!!
purged, so then there would be no air at all, hence the partial
pressure of CO2 would be equal to the absolute pressure in the bottle
- then the substraction of 1 atm (or 1 bar) makes sense. And actually
it agrees with tabulated data.
My reasoning was that when I do my bottling that air doesn't get
purged, and the partial pressure of CO2 computed by Henry's law would
add to this 1 atm of partial pressure from the air. So I thought that
for the same carbonation, the actual pressure in the bottle would have
to be 1 atm more than if the air is purged.
However, if I continue my reasoning, then this air would also dissolve
in the cider according to Henry's law. So I did the calculation,
assuming 2 ml of air, 750 ml of cider, assuming air is 21% O2 and 79%
N2, and doing the calculation for a temperature of 25C to skip the
temperature dependance equations, I obtained partial pressures of
0.022 and 0.156 respectively for O2 and N2, for a total of 0.18 atm of
partial pressure from the air on top of the cider.
So, would it make more sense to say:
- if there is no air in the bottle, gage pressure in the bottle would
be pressure computed from Henry's law minus 1 atm
- if there is air, then we would substract only about 0.8 atm from the
Henry's law computed pressure.
Andrew also wrote:
>[BTW don't put too much faith in the higher temperature figures. They
>are extrapolations which were only included to answer the original
>question we had here about what happens to the pressure at
>pasteurisation temperatures]
temperature dependance correction. From what I can see, these are
derived from the van 't Hoff equation.
http://en.wikipedia.org/wiki/Van_%27t_Hoff_equation
However, there is nothing on the validity range of these equations. If
it was limited to something like 30 or 50C, I would assume it would be
written...
Claude
Dick Dunn
> ...However, it still prompts a question for
> water to the brim and the put on a crown cap, and stick it in a hot water
> bath, the expansion of the water will break the bottle. On the other hand,
Realize that the expansion percentage of the liquid is very small in this
case. It's just that with no headspace the situation is hydraulic. Where
pressure and volume are inversely related for a gas at a particular
temperature, the tendency for a fluid to expand with heat won't be denied.
--
Dick Dunn rc...@talisman.com Hygiene, Colorado USA
Andrew Lea
> So, would it make more sense to say:
> - if there is no air in the bottle, gage pressure in the bottle would
> be pressure computed from Henry's law minus 1 atm
> - if there is air, then we would substract only about 0.8 atm from the
> Henry's law computed pressure.
>
>
Yes I believe you are right Claude. I was in danger of trying to
oversimplify earlier! In fact the adverse effect of air on 'force
carbonation' is well known to drinks technologists and they usually
de-aerate the drinks before carbonation to ensure minimal air content.
This is partly to minimise the long term effect of chemical oxidation in
the drink (the solubility of O2 is about double that of N2), but also
because empirically it is known that dissolved air causes 'fobbing' of
CO2 both during filling and on opening (this was put to good use some
years ago in the canned Guinness 'widget' which was pressurised with
nitrogen in order to create a deliberate head of foam when the pressure
was suddenly released. Not sure if it ever made it out to Qu�bec!).
Hence most semi-manual carbonation / filling rigs include a 'snifting'
(gas releasing) stage to try and purge any remaining air from the bottle
headspace and ensure it is filled only with CO2 before it is sealed. It
is also (picking up on your calculation) an issue when you come to
measure CO2 in a bottle by means of an 'aphrometer'see
http://www.vigoltd.com/in-bottle-co2-pressure-tester.php If any air is
in the headspace it will interfere and give a false reading of the true
pressure due solely to the CO2 (and which is what we are trying to
measure). The 50-fold solubility issue works against us here because a
small amount of dissolved air will make a much larger contribution /
error to the headspace pressure than a similar amount of CO2. So, the
standard procedure with an aphrometer is to shake vigorously, then to
'snift' to release any air, re-seal, shake again and only then to take
an equilibrium pressure reading.
All this has made me realise for the first time that one of the
fundamental differences between force-carbonation and 'conditioned'
carbonation must be the small amount of dissolved and/or headspace air
in the latter. Some of it may be taken out metabolically by the yeast
but probably more remains than in the case of a force carbonation rig
(if operated with de-aeration and snifting). One impact that this could
have is a greater tendency to 'fob' than with force carbonation,
although the presence of solids (yeast / colloids) to act as nuclei
probably makes at least as large a contribution.
It does also mean that any calculation of total internal pressure
achievable from sugar addition probably needs to take into account the
effect of headspace air which you describe, rather than just a straight
Henry's Law calculation based on the in-bottle yield of CO2.
Interesting .......!!
sparkybloke99
I have noticed that my own bottled cider has a much finer or smaller
sized bubble/ foam when opened and poured than the supermarket stuff.
Is this because of forced carbonation vs natural co2 generated ?
I usually leave at least 30 mm or so of air in the top of 500 ml
bottle and after a few months in the shed its usually got a 'light
fizz' at room temperature.
(I have to drink the supermarket cider as its my only source of
bottles since my wife has forbidden me from 'collecting' other
peoples!)
Andrew Lea
> presume 'fobbing' is formation of bubbles ?
The implication of 'fobbing' or 'gushing' is a rapid and uncontrollable
release of gas and foam. The sort of thing that shoots all up your arm.
Or what crass sportsmen do to celebrate when they shake up bottles of
champagne and spray it everywhere ;-)
> I have noticed that my own bottled cider has a much finer or smaller
> sized bubble/ foam when opened and poured than the supermarket stuff.
> Is this because of forced carbonation vs natural co2 generated ?
>
Almost certainly that is the difference. Natural conditioning tends to
produce a much finer 'mousse' with smaller longer lasting bubbles than
forced carbonation. This is usually ascribed to yeast derived colloids /
proteins / fatty acids etc acting as 'micro nucleation sites' where the
CO2 bubbles are formed and released. This has been studied quite a lot
by the French champagne and the Spanish cider industry, who have
published several learned scientific papers on the topic.
'Fobbing' in force carbonated beers has also been studied and attributed
to a multitude of causes, even down to the presence of mould spores on
the barley AFAIR.
Claude Jolicoeur
> Yes I believe you are right Claude. I was in danger of trying to
> oversimplify earlier! In fact the adverse effect of air on 'force
> carbonation' is well known to drinks technologists and they usually
> de-aerate the drinks before carbonation to ensure minimal air content.
> achievable from sugar addition probably needs to take into account the
> effect of headspace air which you describe, rather than just a straight
> Henry's Law calculation based on the in-bottle yield of CO2.
I redid my calculation however, since my first assumption of 2 ml of
air is too small and I had done a small logic error.
I did a test, and the amount of headspace air in a 750 ml Champagne
bottle is more like 10 or 12 ml. And since the solubility or O2 and N2
is much less than CO2, this causes a greater increase of pressure than
I first calculated.
Here are the results that I get:
I write Po the pressure obtained from Henry's law minus 1 atm, i.e.
with all air purged.
if 2 ml of air, pressure would be Po + 0.15 atm
if 5 ml of air, Po + 0.31 atm
if 10 ml, Po + 0.47 atm
if 15 ml, Po + 0.57 atm
if 20 ml, Po + 0.64 atm
if 100 ml, Po + 0.90 atm
if 325 ml (i.e. falf full), Po + 0.97 atm
and the graph would show an asymptot at Po + 1 atm when the bottle is
all air.
So, for all practical purposes, it seems that an increase of pressure
of 0.5 atm due to headspace air would be a correct avereage value
considering a headspace in the 10-12 ml range.
And this would fit pretty well with common wisdom that says 20 ml of
priming sugar should be maximum dosage for a heavy Champagne bottle
that resists a pressure of 90 psi (6 atm or bars).
If we calculate, 20 g/l of sugar would ferment into 9.3 g/l of CO2
(from Pasteur, 46.6% of the sugar becomes CO2). This would give 4.7
volumes of carbonation, and from Henry's law, at 25C, the pressure
would be 6.2 atm. Let us remove 1 atm from this to convert to gage
pressure, and add 0.5 atm from the headspace air, and we get to 5.7
atm, or 84 psi.
Claude