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Re: CO2 myths, buffers

> From: "Cathy Hartland" <hartland at nfis_com>
> Subject: Re: CO2 myths
> 
> Paul,  I am so glad you wrote that post.  There had been a raging 
> controversy on a message board concerning the relationship 
> between CO2, KH and pH.  I don't think any of us really understood 
> it.  I know I contributed my share of confusion.  

	The important equilibrium is:

	"H2CO3"   <->  H+  +  HCO3-

	It has an equilibrium constant:

	[H+][HCO3-]/["H2CO3"]  =  4.16 x 10^-7   (Temperature dependent)

The square brackets mean that we are talking about molar concentrations,
but the relationship can be rewritten for other units, and this equation
is the basis of the CO2/pH/KH tables.   They were derived from it.
I wrote "H2CO3" because most of the CO2 in the water is there as CO2,
only a small fration (a more or less constant one) being really H2CO3,
but lumping the two together is acceptable, since that fraction _is_ 
constant.  In the pH/KH/CO2 tables, the KH is HCO3-, and the pH is minus
the log of [H+]. 

	This is a classic buffering equation, but there is an important
wrinkle:  The CO2 is free to come and go.

	In the more usual situation, the materials involved are _not_
free to come and go.  One can make an excellent buffer system using
H2PO4- and HPO4--.  If you put equimolar amounts of those two ions
into an aqueous solution, the pH will be 7.1, because of the equilibrium

	H2PO4-   <->   H+  +  HPO4--

which has its own equilibrium constant.  Note that a buffer involves _two_
species, and the equilibrium between them.  The pH will be "buffered",
because adding a small amount of acid (say) will change the ratio of
the two species a bit, but the pH doesn't move much.  If we add acid
equivalent to 10% of the HPO4--, then (roughly) 10% of it will be
converted to H2PO4-, and the pH will shift by: -log(1.1/0.9), or about
-0.09.

	Back to CO2/HCO3-.  In this case, the CO2 can come and go.
There is another equilibrium:

	CO2(gas)  <->  "H2CO3" (in water)  which will have its own
equilibrium constant, dependent on the CO2 system (if any), the
temperature, the amount of water disturbance, the plants and the fish.	
An equilibrium CO2 concentration will be set up, which will change if
you alter things, but the KH is irrelevant to the equilibrium value.

	The "buffering" one usually talks about in aquaria is the resistance
to pH shifts caused by addition of other acids.  If nitric acid is added
(in effect) by bacterial action on ammonia, then the pH would crash if there
were no HCO3- around.  As it is, the acid just reacts with HCO3-,
making CO2 (which leaves), leaving some HCO3- (KH).  We now have the same
"H2CO3" as before and lower KH, so the pH is lower, but not by all that
much (halve the KH, cut the pH by 0.3).  _That_ is the buffering effect.
If you add enough acid to destroy _all_ the HCO3-, the pH will crash.
(What is log(0)?)  The pH will no longer be controlled by the 
H2CO3/HCO3- buffering system.
> 
> So you say that KH has no influence on the availability of CO2.  In 
> other words, pH can be reduced by CO2 increase, or increased by 
> KH increase, but KH and CO2 do not influence one another 
> directly.  

	That's it!

> In other words, there is no buffering going on?  Can you 
> elaborate?  What happened to the buffering concept?

	I hope it's clear now.

>  What am I 
> missing? (And thank you so much for allowing us to blame the 
> textbooks rather than ourselves!)

	No-one can be expected to get it right if provided _only_ with
error-ridden textbooks.  A good basic understanding of chemistry and
access to equilibrium constants for the reactions makes it easy to
work it all out.

> Cathy Hartland, living in the state of Confusion

	Less so now, I hope.
> 
> > From: Paul Sears <psears at nrn1_NRCan.gc.ca>
> > Subject: Re: CO2 having no effect
> > 
> > 	A couple of replies to the original posting on this stated that
> > having a high KH can stop the CO2 from reducing the pH.
> > 
> > 	This has come up before, and it is not true.
> > 
> > 	A higher KH will cause the pH to be higher for a given CO2 
> > concentration, but the pH _change_ is the same for a given CO2 change,
> > whatever the KH is.  Look at the tables, or, better, the equations discussed
> > recently.  The relationships are logarithmic, so by "change", I mean the
> > factor involved, not the number of ppm CO2 increase (or KH increase).
> > 
> > 	An increase of a factor of 10 in the CO2 concentration will
> > decrease the pH by 1.  An increase of a factor of 10 in the KH (bicarbonate)
> > will increase the pH by 1.  
> > 
> > 	If the CO2 is increased by a factor of "x", the pH will drop by log(x).
> > 
> > 	Also, the higher KH will not stop the CO2 being available to plants.
> > The CO2 concentration in the water depends on the CO2 system and the rest
> > of the tank setup - the KH has no influence on it.  The misconception can
> > be blamed on a number of aquarium textbooks.
> > 
-- 
Paul Sears        Ottawa, Canada