# Re: KH, CO2 ...yet again

```> Date: Thu, 9 Sep 1999 23:13:52 -0400
> From: "wayne jones" <waj at mnsi_net>
> Subject: CO2, KH ....yet again.
>
>  >NO.  This has come up many times.  The
> _change_ in pH, for a given
> >change in CO2 concentration, is the
> same whatever the KH. The actual pH will
> >be higher for a higher KH.
>
>  >Double the CO2 concentration, reduce
> pH by 0.3 (log(2)).
>  >Double the KH, increase pH by 0.3.
>
>  >Look at the archives or the KH/pH/CO2
> tables.
>
> Does this mean that if the pH drops
> the concentration of CO2 will always be
> about 15 mg/liter regardless of the the
> initial kH/pH?

No, it means that the "addition of CO2" resulted in the CO2
concentration increasing by a factor of 10^0.4 from what it was before.
That is, a factor of about 2.5.

> Does it also mean that using baking soda
> to prevent pH swings is pointless as the
> pH fluctuation will always be the same
> regardless of how much baking soda is

Provided there is _some_ KH there, the size of the swing caused
by CO2 fluctuations will be the same, whatever the KH.  The thing that
large amounts of KH does protect against is swings caused by the addition
of strong acids, e.g., nitric from oxidation of ammonia. As the nitric
acid is added, the KH will fall as the bicarbonate ions are replaced
by nitrate.  When it (KH) becomes very small (near-zero), the pH will crash.
(What is log(0)?).

> Sorry to ask such silly questions
> but for some reason I have a hard time
> wrapping my mind around this.

Maybe this will help:

The equilibrium that interests us is:

"H2CO3"  <->  H+   +   HCO3-

There is an equilibrium constant for this:

[H+][HCO3-]/["H2CO3"]   =  4.16 x 10^-7   (concentrations in
g-moles per litre)  The "H2CO3" is in quotes because we are actually talking
about total CO2, although only a small part of it is really H2CO3.
See Cotton and Wilkinson, Advanced Inorganic Chemistry, under "Carbonic Acids"
(their quotes).

Take logs of both sides:

log([H+])  +  log([HCO3-]) - log(["H2CO3"])  =  constant

(I'm only going to be looking at changes, so the actual constant doesn't
matter, and neither do the units for HCO3- and "H2CO3".  Changes of units
just change the constant.)

-pH  +  log([HCO3-])  -  log(["H2CO3"])  =  constant
(definition of pH)

This equation is the basis of the pH/KH/CO2 table.

Now, if you double the KH (HCO3- concentration), the log of that
will increase by log(2), so the pH must also increase by log(2).  Similarly,
if you double the CO2 concentration, the second log term will decrease by
log(2), and the pH must decrease by that amount.

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