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# 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:

base
pH = pK + log ----
acid

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)

"pH=8.0"
line from 1,0.30 to 10,3.01

"pH=7.9"
line from 1,0.38 to 10,3.79

"pH=7.8"
line from 1,0.48 to 10,4.77

"pH=7.7"
line from 1,0.60 to 10,6.01

"pH=7.6"
line from 1,0.76 to 10,7.56

"pH=7.5"
line from 1,0.95 to 10,9.52

"pH=7.4"
line from 1,1.20 to 10,11.98

"pH=7.3"
line from 1,1.50 to 10,14.99

"pH=7.2"
line from 1,1.90 to 10,19.00

"pH=7.1"
line from 1,2.39 to 10,23.92

"pH=7.0"
line from 1,3.04 to 10,30.11

"pH=6.9"
line from 1,3.79 to 10,37.89

"pH=6.8"
line from 1,4.78 to 10,47.75

"pH=6.7"
line from 1,6.00 to 8.34,50

"pH=6.6"
line from 1,7.56 to 6.62,50

"pH=6.5"
line from 1,9.52 to 5.26,50

"pH=6.4"
line from 1,12.01 to 4.17,50

"pH=6.3"
line from 1,15.10 to 3.32,50

"pH=6.2"
line from 1,19.01 to 2.63,50

"pH=6.1"
line from 1,23.93 to 2.09,50

"pH=6.0"
line from 1,30.09 to 1.66,50

Have fun.

George

```