re: KH, pH, CO2 table ...

> From: "Matthew Paul Rhoten" <mrhoten at surly_org>
> Date: Wed, 18 Dec 1996 18:55:55 -0800
> Does anyone know the original source of those tables on the Krib? Were
> they derived empirically, or from the equations governing equilibria?
> I am tempted to dust off my high school chemistry knowledge and a CRC
> handbook and figure this out for myself, but I remember these weird
> multiple-equilibrium systems being taxing.

You can derive the tables using the Henderson-Hasselbach equation:

  pH = pK + log ----

In the bicarbonate and carbonate buffering cases, this is:

                  HCO3-                            CO3--
  pH = 6.37 + log -----    and    pH = 10.25 + log -----
                  H2CO3                            HCO3-

Karla (my biochemist wife) worked this out some time ago, but I've
lost the method that she used to determine HCO3- and H2CO3
concentrations based on KH and dissolved CO2 levels.  Karla doesn't
seem interested in doing this anymore, so perhaps other chemists
amongst us could fill in the missing bits. 

I still have the results of the calculations and have the data for a
chart that is much easier to use than the tables.  In the chart, CO2
concentration is the vertical scale (0 to 50 mg/l) and dKH is the
horizontal scale (1 to 10 dKH).  Both the scales are linear.  Lines of
constant pH are then drawn; the pH lines are straight but "fan out"
from a CO2/KH point of 0, 0 (not on the chart).  Here are the
coordinates of various pH lines:
#------- lines of constant pH (coordinates are KH,CO2)

line from 1,0.30 to 10,3.01

line from 1,0.38 to 10,3.79

line from 1,0.48 to 10,4.77

line from 1,0.60 to 10,6.01

line from 1,0.76 to 10,7.56

line from 1,0.95 to 10,9.52

line from 1,1.20 to 10,11.98

line from 1,1.50 to 10,14.99

line from 1,1.90 to 10,19.00

line from 1,2.39 to 10,23.92

line from 1,3.04 to 10,30.11

line from 1,3.79 to 10,37.89

line from 1,4.78 to 10,47.75

line from 1,6.00 to 8.34,50

line from 1,7.56 to 6.62,50

line from 1,9.52 to 5.26,50

line from 1,12.01 to 4.17,50

line from 1,15.10 to 3.32,50

line from 1,19.01 to 2.63,50

line from 1,23.93 to 2.09,50

line from 1,30.09 to 1.66,50

Have fun.