carbonate buffer & equilibria

Here's the short-form rundown on the carbonate buffer system, and the
reactions that make it up.

The major reactions involved are:

CO2(aq) <=> CO2 (gas) [i.e. little fizzy bubbles and the atmosphere]
CO2(aq) + H20 <=> H2CO3
H2CO3 <=> H+ + HCO3-   [or you can pretend the H+ turns into H3O+ if you like]
HCO3- <=> H+ + CO3--
XCO3 <=> X++ + CO3--  [e.g., CaCO3; this is why limestone affects pH]
XHCO3 <=> X+ + CO3-   [e.g., NaHCO3]
H20 <=> H+ + OH-  [though this is usually just taken for granted, of course]

The major thing to keep in mind is that all of these run in both directions
constantly.  All other things being constant (a big if, but there you are),
the reaction rates are proportional to the product(s) of the concentrations
of reactants.  (You'll note that this may be constant in the case of things
like CaCO3 sitting in a lump on the floor of the aquarium, or CO2 floating
around at constant pressure in the atmosphere above the aquarium.)

A classic buffer is a combination of a weak acid and its conjugate salt,
for instance carbonic acid H2CO3 and sodium bicarbonate NaHCO3, or even
sodium bicarbonate and calcium carbonate (though this is of little interest
in freshwater).  What happens when you titrate this combination with the
(strong) acid of your choice?  Well, in any buffer system, the boost in
[H+] increases the reaction rate H+ + salt -> weak acid, and takes some H+
out of circulation.
Of course, as it does so, it increases weak acid concentration, so the
reverse reaction rate starts to increase, until you get a new equilibrium.
Similarly, titration with a strong base decreases the H+ + salt -> weak
acid rate, and so (since the weak acid dissociation is still happening),
the weak acid -> H+ + salt adds some H+ to the solution.  Thus the pH
changes less than it would if you titrated pure water--it's buffered.

If the weak acid and conjugate salt are the only things in solution, the pH
is determined by the ratio of acid to salt (this is the source of those
nice tables relating KH, [CO2] and pH).  You can get significant buffering
out to about a 100:1 ratio, so most buffer systems will work over a total
range of about 4 pH units; they work best, of course, near the middle of
their range.  Thus, for the carbonate system we're worried about here, if
you want to keep the same pH but halve or double the KH, you would expect
to halve or double [CO2] to keep the same ratio, and the same equilibrium

In the case of the carbonate buffer, there's a complication:  the
equilibria between carbonic acid, carbon dioxide, and the atmosphere.  Any
increase in [H2CO3] will eventually release CO2 to the atmosphere; this is
a slow process, especially at the concentrations we're talking about here
(consider how long it takes a bottle of soda water to go "completely"
flat).  Of course you don't need to drop blood into your beer to catalyse
the reaction; as I'm sure everyone here has seen, almost anything (e.g.:
salt, an olive, splashing the stuff about while pouring) will increase the
reaction rate.  Thus some fraction of any increase in [H2CO3] eventually
disappears; how much and how soon is a function of this reaction rate.

There are other complications, too:  plants and animals are busy doing
their ion-exchange things, and the mad-scientist aquatic gardeners :-) are
bubbling yeast exhaust through the water, and maybe dumping Arm & Hammer
into the solution.

So all you need to do to predict the response of pH (and all the other
ionic concentrations) to any change in conditions is look up all the
proportionality constants in your CRC Handbook, plug them in, and solve the
resulting system of nonlinear equations.  This is feasible, actually, if
all you need is a numeric result; in the case of the Henderson-Hasselbach
version (which you get for the simplest buffer system) it's just a simple
quadratic equation, and even when you add multiple buffer systems to the
pot you still get a nice system very amenable to Newton-Raphson solutions
(for instance).

Incidentally, your blood combines phosphate and carbonate buffering (sort
of like seawater, what a coincidence), so you too have carbonate,
bicarbonate, and carbonic acid floating around inside you, keeping your
internal chemistry happy and stable.  In fact, an automated CO2 system
(especially one that automates both CO2 and bicarbonate injection) is like
a toy version of the active management your body uses.

So, what do submersed plants (and algae) use for photosynthesis?  What
crosses which membranes where?  Anybody know?

  --Martin Harriman
    martin-h at mail_utexas.edu
    (512) 471-5742