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The Three-way KH-pH-CO2 Relationship

Contents:

  1. KH/pH buffer interaction
    by cineaste-at-uclink.berkeley.edu (Eric Yun-Sung Fang) (8 Feb 1994)
  2. KH/pH buffer interaction
    by cineaste-at-uclink.berkeley.edu (Eric Yun-Sung Fang) (8 Feb 1994)
  3. KH/pH buffer interaction
    by booth-at-lvld.hp.com () (8 Feb 1994)
  4. Kh, Ph, Buffering, and Baking Soda.
    by "Birdy" <birdy/aa.net> (Mon, 17 Apr 2000)

KH/pH buffer interaction

by cineaste-at-uclink.berkeley.edu (Eric Yun-Sung Fang)
Date: 8 Feb 1994


A while ago, George Booth asked me to consider the behavior 
of a mixture of hardness buffer and phosphate pH buffer.

The hardness buffer is based on the carbonic acid-
bicarbonate ion equilibrium, while the phosphate pH buffer 
is based on the second acid ionization of phosphoric acid, 
the H2PO4- <-> HPO4-2 orthophosphate equilibrium.

Explicitly, these equations are:
                                                Ka              pKa
1) H2CO3        <-->            H+      +       HCO3-   4.30e-7 6.37
2) H2PO4-       <-->            H+      +       HPO4-2  6.23e-8 7.21

Inverting the second equation,

H2CO3           <-->    H+      +       HCO3-   4.30e-7 6.37
HPO4-2  +       H+      <-->            H2PO4-          1.6e7   n/a

Which sums to:
H2CO3   +       HPO4-2  <-->    HCO3-   +   H2PO4-
        with Ka= 6.9

This equation describes the interaction between the two 
buffers. Basically, this equation favors the bicarbonate and 
dihydrogen phosphate ions over the carbonic acid and 
biphosphate ions, but what actually happens when you mix two 
solutions will depend on the starting concentrations. This 
equation says nothing about pH, but it turns out that pH 
will affect the concentrations of the ions. See below:

If we go back to equations 1&2 and sum them, we get:

H2CO3  +  H2PO4-  <-->  2H+  +  HCO3-  +  HPO4-2
        with a Keq of 2.7e-14

This equation does depend on the pH.

Now George also asked me to consider the effects of 
nitriication as well. Organisms produce ammonia as waste, 
which in water solution forms ammonium ion, NH4+. NH4+ is 
oxidized by biological processes in this overall reaction:

NH4+  +  2 O2  <-->  NO3-  +  H2O  +  2 H+

I think it’s most reasonable to look at this process 
separately and to think of it as increasing the presence of 
H+ ions in the water, or generally acidifying things, which 
does affect our previous equations by changing the 
equilibrium concentrations of the various other ions.

The interaction of the two buffers doesn’t normally affect 
the buffering power of either, though it may reduce or 
increase the buffering capacity of either somewhat. The pH 
of the resulting solution ranges betweeen 6.37 and 7.21, 
depending again on the actual concentrations of the four 
ions in the buffers.

An analysis of the two equations we derived here indicates 
that  we can express the concentration of hydrogen ions as 
the following:

        [H+]= 6.3e-8 x  [H2PO4-]/[HPO4-2]

from which we can easily calculate pH. This can also be 
expressed in terms of the other buffer, via the equilibrium 
expression of the first equation. The mixture of buffers is 
less tolerant of change in the ratio between acid and 
conjugate base, but we must remember that since it is a 
mixture of two buffers, these ratios will be slower to 
change as well.

Eric Fang
cineaste-at-uclink.berkeley.edu



KH/pH buffer interaction

by cineaste-at-uclink.berkeley.edu (Eric Yun-Sung Fang)
Date: 8 Feb 1994

        I think my parent post got screwed up when I uploaded it. Anyway, in
the first four equilibrium equations, there are two numbers after each. The
first is the Ka, or acid ionization constant, and the second is the pKa (Ka's
negative log). I had the labels on the line above, but they appear to be 
shifted over to the left.

Eric


KH/pH buffer interaction

by booth-at-lvld.hp.com ()
Date: 8 Feb 1994

Eric Yun-Sung Fang (cineaste-at-uclink.berkeley.edu) wrote:

> A while ago, George Booth asked me to consider the behavior 
> of a mixture of hardness buffer and phosphate pH buffer.

Very nicely done, Eric.  At least as far as I know :-)  Perhaps Craig
Bingman could also critique this.  But, anyway, this all started out
as a challenge to the notion that the pH/KH/CO2 tables were valid only
if carbonate was the only buffer present.  *I think* what you found 
out was that this is true - if phosphate or another buffer is present,
they augment the buffering action of the carbonate or bicarbonate and
alter the pH/KH/CO2 ratios.  

=============================================================================
George L. Booth                   Founding Member, The Colorado Aquarium, Inc
booth-at-hplvec.lvld.hp.com           __          Aquatic Gardener's Association
Software Development Engineer     /  \  /\          Colorado Aquarium Society
Manufacturing Test Division    /\/    \/  \           Rainbowfish Study Group
Hewlett-Packard Company       /  \/\  /    \/\             Modern Aquascaping
Loveland, Colorado  _________/    \ \/      \ \___x__________________________
=============================================================================



Kh, Ph, Buffering, and Baking Soda.

by "Birdy" <birdy/aa.net>
Date: Mon, 17 Apr 2000

In order learn something about the relationship between Ph, Kh, and
buffering, I conducted the following experiment.

Using a 5-gallon bucket of water that I removed from my aquarium in the
course of a normal water change, I began adding Baking Soda in 1/4
tablespoon doses, resulting in the following results.

Dose    Ph      Kh (dH)

0           6.5      4
1           6.6      5
2           6.7      6
3           6.8      9
4           7.0      11


In doing the Ph tests, I actually have 5 test tubes, so I can lay them side
by side on white paper, and see straight progression of color from 6.5 to
7.0.

So, I want to ask anyone who knows... Previous to doing this test, I had
understood that the term Ph Buffering refers to using a substance that adds
alkalinity, (the ability to absorb acids), without actually changing Ph.
But in this test, the Ph changed along with the Kh.

So, in adding baking soda, I increased both the Ph, and the Kh.  Is this
what Ph Buffering looks like?

I am following the advise of those who say, "don't start adding CO2 to your
aquarium until you understand Ph buffering and the relationship between Kh,
and Ph."

So, if I added CO2 to the water described above, would there be a
precipitous, unmanageable, Ph drop?

Thanks.


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