Precipitative Softening Description + Example Analysis
1. Characterizing Chemical Equilibrium
The numerical value of any equilibrium constant is the ratio of the concentrations of the products
to the concentrations of the reactants. The equilibrium constant is a dimensionless number, but
for it to be meaningful, conventions need to be established for the units to use for the
concentrations of the different species. These conventions are as follows:

For species that are dissolved in a large amount of a bulk phase (e.g., species of interest
to us, which are dissolved in water), the concentrations are expressed in mol/L

For constituents that make up the bulk of a condensed phase (e.g., bulk water, or a pure
solid that has precipitated and just happens to be suspended in the water), the
concentrations are expressed in terms of the fraction of that phase that the species
represents. In all cases of interest to us, this fraction will be so close to 1.0 that we can
use the approximation that the concentration is exactly 1.0.

For gases, the concentrations are expressed in terms of the pressure that the species exerts
(i.e., its partial pressure), in atmospheres.
Often, we are interested in equilibria that only involve species dissolved in water, and the water
itself. For example, the following equilibria are especially important:
Kw
 H  OH    H  OH  

K a1
 H  HCO   10




 H 2O 
1.0

 H  OH   10


14.0

3
 H 2CO3 
 H  CO   10

 HCO 

Ka2

6.3
2
3
10.3

3
where (i) refers to a dimensionless number that represents the concentration of a species i, in
units that are consistent with the conventions described above.
The carbonate acid/base system is particularly important in environmental chemistry, including
the chemistry of precipitation. The sum of the concentrations of the three carbonate species is
sometimes represented as TOTCO3:
TOTCO3   H 2CO3    HCO3    CO32 
By manipulating the equilibrium constants Ka1 and Ka2, it can be shown that the relative
concentrations of the various carbonate species depend on solution pH but not on TOTCO3. This
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dependence is often shown as in the following graph, where each species is represented as a
percentage of TOTCO3.
H2CO3/TOT CO3
1.0

HCO3 /TOTCO3
2
CO3 /TOTCO3
0.9
Conc'n / TOT CO3
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
2
3
7
6
5
4
8
9
10
11
12
pH
2. Other Equations that Characterize Systems of Interest
In addition to equilibrium constants, mass balance equations can be used to describe the
status of systems of interest. These mass balance equations often focus exclusively on the
dissolved phase. Two mass balance equations of particular interest are the following:

 
TOTCO3   H2CO3   HCO3  CO32

 
 

  
ALK  HCO3  2 CO32  OH  H 
TOTCO3 is important because it characterizes the total amount of dissolved carbonate species
in the solution. These species are easily interconverted, so TOTCO3 represents a limiting value
for the maximum concentration of any one of the species. The relative amounts of the different
species depend only on pH, with the speciation shifting from H2CO3 to HCO3 to CO32 as pH
increases, as shown in the preceding diagram.
ALK is important as a measure of the capacity of the solution to acquire and neutralize acid
without rather severe ecological consequences occurring. The value of ALK can be determined
experimentally by titrating a sample to pH 4.5. The amount of acid (mol/L, often expressed as
2
equiv/L) needed to carry out this titration is the alkalinity of the original water (not the water that
has been titrated).
Alkalinity is expressed in a variety of units, not all of which are intuitive. The need for these
units arises from the fact that the alkalinity includes contributions from several different
compounds. One equivalent (equiv) of alkalinity refers to one mole of "H+ binding capacity."
Thus, one mole of HCO3 has the capacity to combine with one mole of H+, so one mole of
HCO3 is one equivalent of alkalinity. On the other hand, one mole of CO32 has the capacity to
combine with two moles of H+, so one mole of CO32 is two equivalents of alkalinity. Because
the total alkalinity is a composite parameter that is not really the number of moles of any
particular chemical, the units equiv/L are used. The idea is that, with respect to H(+) binding, one
mole of CO32 is "equivalent" to two moles of HCO3.
Historically, alkalinity has often been reported in units of “mg/L as CaCO3.” The meaning of
this phrase is that the water being discussed has the same amount of alkalinity as would water
that contained the specified number of mg/L of CaCO3. Note that this does not mean that the
water actually contains that amount of CaCO3, or for that matter that it contains any CaCO3 at
all. When CaCO3 dissolves in water, it releases one Ca2+ and one CO32 ion. The Ca2+ does not
combined with or release H+, so it has no effect on the alkalinity. On the other hand, the CO32
ion has the capacity to combine with two H+ ions. Therefore, one mole of CaCO3 represents two
equivalents of alkalinity. Because the molecular weight of CaCO3 is 100, the “equivalent
weight” of CaCO3 is 50 g/equiv, or 50 mg/meq. (Conventionally, the abbreviation for
equivalents is equiv, but that for milliequivalents is meq.)
Example. Determine the carbonate speciation in a solution with the following, experimentally
determined characteristics:
pH = 7.0; ALK = 1.0 x 103 equiv/L; (Ca2+) = 3 x 103 mol/L = 120 mg/L
We first use equilibrium constants to find some other values that characterize the solution:

 
 
  
ALK  HCO3  2 CO32  OH  H 
1.0x10
3
 HCO  K
2 H
 


 HCO3

3

a2

Kw
H 

 
 H

1010.3  1014.0
 HCO3 1  2 7.0   7.0  107.0
10

 10




 HCO3 1  103.0   107.0  107.0

 1.001 HCO3

3
3
 HCO   1.0x10
1.001

3

 1.0x103
 HCO  K
 H
 

CO3

3
a2


103.01010.3
 106.3
7.0
10
 HCO  H   10
 H CO  


3
2
3
K a1

3.0
107.0
106.3
 
 103.7  2x104
TOTCO3   H2CO3   HCO3  CO32

 2.0x104  1.0x103  5x107  1.2x103
The results indicate that almost all the alkalinity is contributed by HCO3. They also indicate
that the majority of the carbonate is present as HCO3, but that H2CO3 also contributes a
substantial fraction; on the other hand, the contribution of CO32 to either ALK or TOTCO3 is
negligible. This result is consistent with the carbonate speciation figure shown above.
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