🚀 go-pugleaf

My initial question about converting ppm CaCO3 to dKH resulted in an explanation of the qualitative facts about hardness and alkalinity. My request for the quantitative implications did not,however, meet with much success. So I dusted off my old chemistry books, went to the library, did a few experiments, and made some phone calls. The result of this little exercise is a set of notes that may be useful to others who are trying to understand what's going on. 

These notes are still incomplete, but if there is sufficient interest I will continue to post my notes as I go along.  

SUMMARY

There are two main sections here. The first section summarizes the essential quantitative facts needed to understand and visualize some aspects of water chemistry. The second section gives detailed information about test kits, i.e. what they actually measure and how they do it (chemistry!). This information was obtained by calling around to the manufacturers and discussing the chemistry of their kits. Also several people contributed via e-mail. I only have experience with the LaMotte calcium kit so I may h
ave missed some information on the other kits.

LaMotte (and Hach) make test kits that measure total Calcium in solution and test kits that measure both Calcium and total hardness. With the latter kits you can estimate magnesium hardness too, but this is not too useful for aquarists. For people that have Ca hardness test kits I describe a delightful experiment that illustrates how the buffering effect of CaCO3 maintains the level of free Ca++ ions in solution. It demonstrates that that the time scale of the CaCO3 equilibrium reaction is ~5 seconds or le
ss. 

The terms "Carbonate Hardness" and "Carbonate Alkalinity" are identical. They both refer to HCO3- and CO3-- concentrations. Measurements of these quantities are only indirectly related to the amount of calcium in the water through the 
reaction CaCO3 + CO2 + H2O <=> Ca++ + 2[ HCO3-].  

Thiel refers exclusively to dKH in his book (Advanced Reef Keeping). He gives 18.9 as the conversion factor to go from dKH to ppm CaCO3. Two points here. First, Thiel's carbonate hardness test kit actually measures total alkalinity but the difference between total alkalinity and carbonate hardness  is only about 3%, so for us aquarists, there's no point in making an issue of it. 
Second, according to Thiel, you can convert from his dKH figures to total alkalinity in ppm CaCO3 by multiplying the dKH figure by 18.9. I work through a detailed example calculation below. Moe and Thiel don't completely agree on their ppm CaCO3 to dKH conversion factors. Moe gives the conversion factor as 17.9 or 1/0.05 = 20, Thiel says 18.9.  The difference may be related to the ~3% difference between total and alkalinity and carbonate alkalinity, but without further information I can't determine this. I
n any case, neither Moe nor Thiel gives a satisfactory explanation of the "gotcha's" involved in these conversions. 

Also, I'm still looking for more detailed data on the following test kits: Hach, Tetra, others?. If folks would provide me with customer service telephone numbers and as much information about a particular kit as they have, I can try to follow through and get more detailed information on their kits. I might add that, I don't have infinite funds to spend on phone bills, so if anyone else feels motivated to call and get information on a particular test kit, that would help out considerably.


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NOTES
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DEFINITIONS , WEIGHTS AND MEASURES

Concentrations are often stated as milligrams (mg) per liter (l) of fluid so 
the units are (mg/l). One liter of water weighs almost exactly 1 kg = 1000 grams . So concentrations are often given in terms of (mg/kg). Now a milligram is  1/1000000 of a kg or 1 part per million ( 1 ppm). So for our purposes,  we have that...
 
				1 mg/l = 1 mg/kg = 1 ppm.

Concentrations of a chemical species are often given in units of moles per liter. A mole is 6.022x10^23 molecules (a very large number). 

When you see square brackets around the symbol for a chemical species 
(e.g. [HCl] ) it refers to the concentration of that species. Usually moles/liter.
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ATOMIC AND MOLECULAR WEIGHTS

one atom of Hydrogen weighs 1.6725x10^-21 mg (mg = milligrams)

Atomic and molecular weights are given in multiples of the weight of hydrogen 

element 	symbol	atomic weight
hydrogen	H        1
Carbon  	C        12
Oxygen  	O        16
Calcium 	Ca       40    

Molecules           composition(symbol)     molecular weight     

Water               H2O                     18
Carbon Dioxide      CO2                     44
Carbonic Acid	  H2CO3                   62
Calcium Carbonate   CaCO3                   100          
Carbonate           CO3                     60         
Bicarbonate         HCO3                    61          

Example calculation -- How much does a mole of Bicarbonate weight?

From the table we find that a bicarbonate molecule weighs 61 times as much as 
a hydrogen atom. A mole of bicarbonate molecules is 6.022x10^23 molecules. 
and one atom of Hydrogen weighs 1.6725x10^-21 mg, thus a mole of Bicarbonate weighs...

(6.022x10^23) x (61) x (1.6725x10^-21 mg) = 61,437 mg = 61.4 grams

Similarly, we can do a  mole of Calcium carbonate and discover that 1 mole
of CaCO3 weighs 100.7 grams.

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EQUIVALENT WEIGHT

Equivalent weight is a concept that comes up when dealing with acids. 
One "equivalent weight" is the weight of a substance needed to provide ONE
mole of Hydrogen ions.

Examples:

Each ion of Bicarbonate (HCO3-) can only contribute one Hydrogen ion. So
one mole of  Bicarbonate is "equivalent" to one mole of H+. As we saw above,
one mole of Bicarbonate weighs 61.4 grams. So, we say the weight of one 
equivalent of Bicarbonate is 61.4 grams.

What about carbonic acid? Well carbonic acid (H2CO3) contributes two H+ ions
per molecule. So it only takes 1/2 mole of carbonic acid to make a mole of H+
ions. So one weight of one equivalent of Carbonic acid is...

(6.022x10^23) x (62) x (1.6725x10^-21 mg) = 62,445 mg = 62.4 grams

1 equivalent of  H2CO3 = 1/2 * (weight of 1 mole  H2CO3) = 31.2 grams 

We will mostly deal with milli-equivalent weights (meq) which is 1/1000 of
an equivalent weight. So we have

1 meq of HCO3  = 62.4 mg
1 meq of H2CO3 = 31.2  mg

Finally, we are ultimately interested in concentrations which are usually stated as milligrams (mg) per liter (l) of fluid so the units are (mg/l). 

(1 meq of HCO3)/l  = 62.4 mg/l of HCO3 = 62.4 ppm
(1 meq of H2CO3)/l = 31.2  mg/l of H2CO3 = 31.2 ppm


This same idea of equivalent weights gets used when dealing with Carbonate
hardness. In that case the one "equivalent weight" is the weight of CaCO3 needed to provide ONE mole of HCO3- or CO3--. 

The point about CaCO3 equivalent weights is that they are not physical concentrations of CaCO3. Instead it is the amount of CaCO3 you WOULD get IF you combined the physical amount of HCO3- and CO3-- with enough Ca++ to use up all the HCO3- and CO3--.
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ALKALINITY

The following is taken from "Chemical Oceanography, Millerno & Sohn, (1992).

"The total alkalinity of seawater is defined as the concentration of all the 
bases that can accept H+ when a titration is made with HCl to the carbonic acid endpoint."  (p. 283)

note: I assume that the carbonic acid endpoint refers to the point at which all the carbonate and bicarbonate bases in the solution have been bound with H+ to form carbonic acid.
 
DEFINITIONS

Total Alkalinity =  [HCO3-] + 2[CO3--] +	[B(OH)4-] + [SiO(OH)3-]
+ [MgOH+ ] + [ OH- ] + 2[ HPO4- ] + 3[PO4---]

Carbonate Alkalinity = [HCO3-] + 2[CO3--]

COMPOSITION  various bases contributing to total Alkalinity (at 25 degrees C?)  
             in Seawater
 	
 		BASE       percent (by moles/liter )
 		__________________	
 		HCO3-     89.8
 		CO3--	     6.7
 		B(OH)4-    2.9
 		SiO(OH)3-  0.2
 		MgOH+      0.1   
 		OH-        0.1
 		HPO4-      0.1
		PO4         ?

note: As you can see from the table, the difference between carbonate alkalinity and total alkalinity is only about 3%. This difference is probably much less  than the precision of the test kits commonly available to aquarists.

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Illustrative experiment and calculation # 1: 
Free Ca++, bound Ca (CaCO3) and equivalent CaCO3, CaCO3 buffering. 
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From the atomic weight tables we see that 40% of the weight of CaCO3 is in Ca++ and the rest is in CO3--. Thus every 40 mg of Ca++ can form 100 mg of CaCO3. That means that to get the CaCO3 equivalent of X mg of Ca++ you have to multiply X by 2.5.

I bought a bottle of CaCO3 tablets and some distilled water (calcium carbonate tablets available as "calcium supplements" in the vitamin section of the local drugstore, distilled water is usually available in the contact lens or water section). The tablets I bought had 1500mg of CaCO3 each. I dissolved 1 tablet in 0.1 liters of distilled water. I let my solution sit for a few days. Most of the tablet wound up at the bottom of the beaker as a white powder.

I measured the Ca++ concentration using my LaMotte Ca test kit and got 64ppm Ca++ (160ppm CaCO3 equivalent). So the 0.1 liter of water had 6.4 mg of Ca++ or 16 mg CaCO3 equivalent. This drives home the point that the CaCO3 equivalent is not the same as CaCO3 actually added to the solution since I added 1500mg of CaCO3.

Now, lets see the buffering effect of CaCO3 directly! You may want to read the writeup below on the LaMotte Ca test kit. The test kit measures Ca++ directly. In the process of measuring the Ca++ it removes all free Ca++ from the solution by binding it to an indicator (calcon). The calcon turns red when bound to Ca++. Next an EDTA solution is titrated into the solution which in turn strips the Ca++ from the Calcon. The Calcon turns blue when the EDTA has removed all the Ca from it and the titration is over.
  Now think about the following equilibrium equation

                 CaCO3 + CO2 + H2O <=> Ca++ + 2[ HCO3- ]. 

In the process of performing the titration, we have unbalanced the equilibrium since the Ca++ has been removed from the right hand side. Physics demands that some of the 1500mg of CaCO3 disassociate to rebalance the equation. So after five seconds or so, your blue indicator turns red again! (WOW!)

Effectively, the calcon acts like a Ca++ sponge that is red when it is "wet" and blue when it is squeezed "dry." The "sponge" is wrung out when you titrate the EDTA. Each time you sop up all the Ca++ from the solution, the CaCO3 buffer simply replaces it. This replacement takes less than 5 seconds, so it takes about 5 seconds for the "sponge" to turn red after you have "wrung" it out. Try it: keep adding EDTA until the solution turns blue, then wait a few seconds until it turns red again. Add more EDTA unt
il it turns blue, then wait a few seconds until it turns red again, add more...Once you get this going it only takes one drop to perform a blue/red cycle. 

Sea water and aquarium water probably has very little CaCO3 floating around. Most of it is bound up in the rocks, corals and sediment. So it is unlikely that you'll see this effect when you test your aquarium water unless you happen to have stirred up some sediment. 

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Illustrative calculation #2: Alkalinity -- converting from meq/l to ppm to dKH 
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Note: This is in here so you can see how the alkalinity and hardness fits together quantitatively. 

Moe states on p.34 of his Marine Reference that Sea Water has an ALKALINITY of 
2.1 to 2.5 meq/l. He's not specific, but probably he means TOTAL alkalinity of the species given above. We can make a simplifying assumptions to make this calculation easy. If we assume the measurement was taken at a pH=8.2 and at T=24 degrees C, then about 90% of the alkalinity is in the form of HCO3- (see e.g. the composition table above). This means we can expect at most a 10% error in our calculation if we assume that all the alkalinity is in the form of HCO3-. We know that each meq of HCO3 is 1/1000 o
f a mole of HCO3-. So there must be 2.1x10^-3 moles of HCO3- in solution. To calculate the CaCO3 "equivalent" to this much HCO3- we calculate the weight of CaCO3 if all the HCO3- were to bind with Ca++. The reaction is

            CaCO3 + CO2 + H2O <=> Ca++ + 2[ HCO3- ]. 

We see  that each mole of HCO3- will produce half a mole of CaCO3. So we will be left  with 1.05x10^-3 moles of CaCO3. This will weigh

(1.05x10^-3 moles)x(100.7 grams) = 105.7 mg of equivalent CaCO3.

or 105.7 ppm equivalent CaCO3.

Finally,  let's convert this to dKH. The significance of the conversion factor is not clear to me. Furthermore Moe and Theil disagree on the exact conversion factor. Moe (p.36) says it is either 17.9 or ~1/0.05 (p.36) while Thiel (p.101) says is is 18.9 . Lets take 18.9. This produces 105.7 ppm CaCO3/18.9 = 5.6dKH which is in the right ball park. Similarly 2.5 meq/l of HCO3 translates into 6.65 dKH. This is a reasonable answer for sea water.
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Note that the actual physical weight of HCO3- in solution can be calculated from the alkalinity of 2.1 meq/l according to (2.1 meq/l HCO3) x 61.4 ppm/(meq/l) = 128.9 ppm of HCO3-. 

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REFERENCES

Advanced Reef Keeping 1, Albert J. Theil,Aardvark Press, Bridgeport CT,(1989)

The Marine Aquarium Reference, Martin A. Moe, Green Turtle Publications, Plantation FL, (1989)

Chemical Oceanography, Frank J. Millero and Mary L. Sohn, CRC Press, Boca Raton FL, (1992).
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SUMMARY OF TEST KIT INFORMATION
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KIT:       The LaMotte Test kit (Model CA-DR, Code:3609)

MEASURES:  This test kit measures Ca++ directly. 

UNITS:         

The reading is given in units of ppm Ca++ or in ppm (CaCO3 equivalent).

CHEMISTRY:

Reagent #1:  Sodium Hydroxide.
	
This boosts pH to 12-13 so titration will work and also precipitates 
out of solution the Magnesium as magnesium oxide. This leaves only Ca 
in solution (and trace amounts of other metals).

Reagent #2: Calcon

This is an indicator with a strong affinity for calcium. It bonds
to all the Ca++ in the solution. All the calcium (free Ca++ or 
CaCO3) in the sample is eventually bound to the indicator. The
indicator is red when bound to Ca and blue when not bound to Calcium.

Reagent #3: EDTA a chelating agent

The EDTA has an even higher affinity to Ca than the 
indicator. So as the EDTA is added to the solution,
it strips the Ca from the indicator in proportion to the amount
of EDTA added. When no Ca remains bound to the indicator it turns
blue. The amount of EDTA added to the solution up to this
point is proportional to the amount of Ca that was in solution.

REFERENCE: 

LaMotte technical assistance 1-800-344-3100
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KIT:       The LaMotte Test kit (Model <>?, Code:4824)

MEASURES:  This test kit measures Ca and (Mg++, Fe++ etc.) or just Ca++ 

UNITS:     

The reading is given in units of ppm Ca++ or in ppm CaCO3  equivalent.

CHEMISTRY:

With this test kit you can measure either Ca hardness or total 
hardness. Also, since 99% of total hardness in sea water consists of Ca 
and Mg, you can estimate Mg hardness by doing both tests and 
subtracting the Ca hardness from the total hardness)

Besides the reagents found in the Ca hardness kit (code: 3609) this 
kit contains an additional indicator Eriochrome Black T which binds
to all divalent ions. 

The Calcium test has the same chemistry as described above in the 
Ca Hardness test kit. The chemistry for the total hardness test kit is 
as follows:

Reagent #1:  Sodium Hydroxide.
	
This boosts pH to 10. So titration will work.

Reagent #2: Eriochrome Black T

This is an indicator with a strong affinity for all divalent ions( Ca++, 
Mg++, Fe++, etc.)  All the divalent elements are eventually bound to 
the indicator. The indicator is <color>? when bound to divalent ions 
and <color>? when not bound the divalent ions.

Reagent #3: EDTA a chelating agent

The EDTA has an even higher affinity for the divalent ions 
than the indicator. So as the EDTA is added to the solution,
it strips the divalent ions from the indicator in proportion to the 
amount of EDTA added. When no divalent remains bound to the indicator 
it turns <color>?. The amount of EDTA added to the solution up 
to this point is proportional to the total amount of divalent elements 
that were originally in the solution.

REFERENCE: 

LaMotte technical assistance 1-800-344-3100
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KIT: Thiel Aqua-tech (Model: Carbonate Hardness, KH Test, No:1111)

MEASURES:  

Customer service at Thiel claims that the test kit measures
Calcium Alkalinity [HCO3-, CO3--]. Their chemistry, however is a standard HCl
titration, therefore they are actually measuring TOTAL alkalinity. In any case, at normal temperatures (25 C) this amounts to only a 3% error  (see ALKALINITY ).
           
UNITS: dKH  -- after applying a conversion factor that the kit supplies (2.8). 

CHEMISTRY:

Instead of separate reagents the Thiel kit combines two reagents into a single
squeeze bottle.

Reagent #1: 
A pH indicator dissolved in a dilute HCl solution (0.5% ?).
(Theil Aquatek would not reveal the particular reagent nor the exact dilution of the HCl). The reagent is yellow-orange in the squeeze bottle. The indicator is  yellow orange when in an acid and turns blue when the pH increases above some value. I don't know the value but I guess that it is less than pH 6 or 7.

The HCl/indicator reagent is initially orange-yellow. When it is first added to the sea-water solution it turns blue since the sea water is very basic compared to the dilute HCl. As more reagent is added to the solution the HCl disassociates into H+ and Cl-. The H+ binds with the bases until there are no free bases left. At this point the H+ ions remain free, the solution becomes acidic, and the pH drops dramatically. The indicator reverts to its yellow-orange color. The amount of HCl added to the solution
 up to this point is proportional to the total alkalinity.
				

REFERENCE: 

Theil technical assistance 505-526-4000, (Al Bear) 
	
REMARKS FROM A USER (Arch Hughs):

The reagent bottle comes "unpierced".  You have to poke a pin
through it.  It looks like (though I have not measured it) it would
hold about 5 cc of the reagent.  On occasion, the bottle won't
"behave" well and an air bubble forms at the tip while I'm making
drops and it becomes harder to count "good" drops.  Once in a long
while, I'll see a little "spray" (a few very tiny drops) come out
while I'm forming a "real" drop and I have to make a call about whether
to count that spray as a drop or not.  (Each drop only represents a
0.7 dKH step (computed as 2.8/4), so it's not very critical when your
result is in the mid teens.)

It (the test kit) comes with a nice 15 cc translucent plastic test
vial with red imprinted graduations, the single sheet instructions,
and all in a "zip lock" plastic bag.  
My impression is that it doesn't provide anything close to the 50 tests
that the TFP catalog lists it as providing.  I'd say it provides more
like 10 or 15 tests.  Of course, mileage varies depending on your
KH....the higher the KH, the more reagent you use per test, and the
fewer tests you'll end up making per purchase.

"That Fish Place" item 055056, $12.95 each ($10.95 on sale now)
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KIT:       Hach (Model ?, Code:?)

MEASURES:  Ca and total Hardness

UNITS:     ppm CaCO3, ppm Ca++

CHEMISTRY:


Reagents

REMARKS FROM A USER (K. Rogers)
It gives results as mg/l of CaCO3.  I only use the calcium part of the kit as
that's what I care about.  I did measure the total hardness of my tap
water when I first got it just to see what it was.  Total hardness is
meaningless to saltwater keepers.

REMARKS FROM A USER (Brian Hunter)
I bought the hach kit after 'talking' to someone who had tried the 
lamotte kit.  The Hach end point is much easier to determine.`
Interestingly when choosing a nitrate kit La Motte is generally
considered better.

REFERENCE: 

Hach technical assistance 1-800-227-4224

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KIT:       Tetra (Model ?, Code:?)

MEASURES:  

UNITS:     

CHEMISTRY:


Reagents

REFERENCE: 

	
______________________________________________________________________________
-- 

Fernando J. Pineda
2-254
The Applied Physics Laboratory