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Re: total alkalinity and total hardness

> I think I understand that KH measures carbonate ion concentration and GH
> measures total dissolved solids. Knowing the total alkalinity and total
> hardness, and the concentrations of Cl-, NO3-, SO4--, Ca++ and Mg++ can
> we deduce CO3--, Na+ and K+ concentrations? (assuming typical ground
> water from a well)

KH normally measures bicarbonate rather than carbonate, and GH measures 
the concentration of alkaline earth elements (Ca, Mg, Sr, Ba), not total 
dissolved solids.

You can easily calculate CO3 from alkalinity and pH; CO3 is negligible 
until the pH gets well over 8.  The concentration of Na+K can be
estimated by a charge-balance calculation, but it isn't possible (without
additional information) to say how much of the total is Na and how much is

I've added some values to your table:

                       mg/l    mg/meq  meq/l
Chloride               45      -35.45  -1.27
Nitrate                22.2    -62.00  -0.36
Sulfate                24      -48.03  -0.50
Barium                 <0.02
Calcium                92       20.04   4.59
Magnesium              12.2     12.15   1.00
Ferrous iron           <0.02
Manganese              <0.02
Copper                 <0.02
Zinc                    0.36
Chromium               <0.02
Phosphate               0.041

pH                     7.1
Total Hardness         280     50.04
Total Alkalinity       330     50.04  -6.59

Na+K                   72      22.99   3.13
HCO3                  402      61.02
CO2                    51
CO3                     0.28

The values in the "mg/meq" column lists the weight in milligrams needed 
for each major constituent to make one millimole of charge - that is, one 
milliequivalent.  The values in the "meq/l" column show the concentration 
of electrical charge due to each major constituent; the sign of the value 
shows the the polarity of the ionic charge.

It's usually assumed that the water must be electrically neutral.  That
is, the sum of the milliquivalents for all major species must be near 0. 
The values listed above (excepting that shown for Na+K) total -3.13 meq/l. 
In order for the solution to have a net charge of 0 the Na+K in solution
must provide a balancing charge of +3.13 meq/l.  Sodium is usually more
common than potassium in natural freshwater but without additional
information it isn't possible to tell how much of the charge comes from
sodium and how much is from potassium.  The normal procedure is to
represent all that balancing charge as sodium, and call it Na+K as Na.
72 mg/l of Na are required to provide 3.13 meq/l. 

I assumed that the nitrate concentration is listed as nitrate.  If it is
shown as nitrogen, then this is polluted water.  Also, these calculations
need to be adjusted. 

The table also shows the calculated concentrations of the dissolved
inorganic carbon species.  The numbers are based on the alkalinity and pH
and the (usually good) assumption that the alkalinity is provided entirely
by bicarbonate (HCO3).  Bicarbonate is calculated by dividing alkalinity
in mg/l by 50.04 mg/meq, then multiplying that by 61.02 mg/meq for 
bicarbonate.  CO2 is calculated from bicarbonate and pH with

CO2 = HCO3*1.6*10^(6-pH)

and carbonate is calculated with

CO3 = HCO3*0.553*10^(ph-10)

which uses pK = 10.25.  The calculated CO3 concentration (0.28 mg/l) is
functionally zero because of the limited precision of the alkalinity
value.  If the CO3 concentration were significant then the assumption that
alkalinity is all provided by bicarbonate would be wrong and a more
complicated method would be needed. 

Calcium and magnesium together total 5.59 meq/l.  The general hardness 
due to calcium and magnesium is then 5.59*50.04 = 280 mg/l, exactly the 
value shown in your table for the general hardness.  

General hardness does not measure total dissolved solids (TDS).  You can
calculated the TDS concentration if you like:  sum all of the major
constituents other than bicarbonate, then add in 49% of the bicarbonate
concentration.  The total dissolved solids estimate is then about 393 mg/l
- substantially higher than the general hardness.  If your analysis
included silica then the calculated TDS would be more accurate and probably
10 or 20 mg/l higher.

The 49% correction on the bicarb concentration is to keep the estimate
consistent with wet-chemistry results.  The normal lab procedure calls for
drying the water sample at 105 degrees C, then weighing the residue to
determine the solids content.  Before the sample is completely dry the
bicarbonate breaks down by the reaction: 

2(HCO3-) -> H20 + CO2 + CO3--

The weight of CO3 that remains to be measured is 49% of the weight of the 
original bicarb.

Gee, I hope that's all worth it.

Roger Miller