Alkalinity and Acidity for Aqueous Carbonate Systems Alkalinity and acidity are defined, respectively, as the equivalent sum of the bases that are titratable with strong acid and the e
Trang 1AQUATIC CHEMICAL EQUILIBRIA
In this section a few example will be given that demonstrate
how elementary principles of physical chemistry can aid in
the recognition of interrelated variables that establish the
composition of natural waters Natural water systems
usu-ally consist of numerous mineral assemblages and often of
a gas phase in addition to the aqueous phase; they nearly
always include a portion of the biosphere Hence, natural
aquatic habitats are characterized by a complexity seldom
encountered in the laboratory In order to distill the
perti-nent variables out of a bewildering number of possible ones,
it is advantageous to compare the real systems with their
idealized counterparts
Thermodynamic equilibrium concepts represent the
most expedient means of identifying the variables relevant
in determining the mineral relationships and in establishing
chemical boundaries of aquatic environments Since
mini-mum free energy describes the thermodynamically stable
state of a system, a comparison with the actual free energy
can characterize the direction and extent of processes that
are approaching equilibrium Discrepancies between
equi-librium calculations and the available data of real systems
give valuable insight into those cases where chemical
reac-tions are not understood sufficiently, where non-equilibrium
conditions prevail, or where the analytical data are not
suf-ficiently accurate or specific
Alkalinity and Acidity for Aqueous Carbonate
Systems
Alkalinity and acidity are defined, respectively, as the
equivalent sum of the bases that are titratable with strong
acid and the equivalent sum of the acids that are titratable
with strong base; they are therefore capacity factors which
represent, respectively, the acid and base neutralizing
capacities of an aqueous system Operationally, alkalinity
and acidity are determined by acidimetric and alkalimetric
titrations to appropriate pH end points These ends points
(equivalence points) occur at the infection points of
titra-tion curves as shown in Figure 1 for the carbonate system
The atmosphere contains CO 2 at a partial pressure of
3 104 atmosphere, while CO 2 , H 2 CO 3 , HCO3 and CO32
are important solutes in the hydrosphere Indeed, the
carbon-ate system is responsible for much of the pH regulation in
natural waters
The following equations define for aqueous carbonate systems the three relevant capacity factors: Alkalinity (Alk),
Acidity (Acy), and total dissolved carbonate species ( C T ): †
2
H CO2 3 HCO3 CO32
*
where [H 2 CO 3 * ] [CO 2 (aq)] [H 2 CO 3 ]
These equations are of analytical value because they represent rigorous conceptual definitions of the acid neutral-izing and the base neutralneutral-izing capacities of carbonate sys-tems The definitions of alkalinity and acidity algebraically
† Brackets of the form [ ] refer to concentration, e.g., in moles per liter.
FIGURE 1 Alkalinity and acidity titration curve for the aque-ous carbonate system The conservative quantities alkalinity and acidity refer to the acid neutralizing and base neutralizing capacities of a given aqueous system These parameters can be determined by titration to appropriate equivalence points with strong acid and strong base The equations given below define the various capacity factors rigorously Figure from Stumm, W
and J Morgan, Aquatic Chemistry, Wiley-Interscience, New
York, 1970, p 130.
9 7 5
pH
[CO2–Acy] [CO32– –Alk]
[Acy]
Addition of Acid Addition of Base [H + –Acy] [Alk]
[OH –– Alk]
Trang 2express the net proton deficiency and net proton excess of
the systems with repect to specific proton reference levels
(equivalance points) The definitions can be readily
ampli-fied to account for the presence of buffering components
other than carbonates For example, in the presence of borate
and ammonia the definition for alkalinity becomes
2
4 3
⎦⎦
(4)
Although individual concentrations or activities, such as
[H 2 CO 3 * ] and pH, are dependent on pressure and
tempera-ture, [Alk], [Acy], and C T are conservative properties that are
pressure and temperature independent (Alkalinity, acidity,
and C T must be expressed in terms of concentration, e.g., as
molarity, molality, equivalents per liter or parts per million as
CaCO 3 ) Note that 1meq/l 5 50 ppm as CaCO 3
The use of these conservative parameters facilitates the
calculation of the effects of the addition or removal of acids,
bases, carbon dioxide, bicarbonates, and carbonates to
servative quantities remains constant for particular changes
in the chemical composition The case of the addition or
removal of dissolved carbon dioxide is of special interest
Respiratory activities of aquatic biota contribute carbon
diox-ide to the water whereas photosynthetic activities decrease
the concentration of this weak acid An increase in carbon
dioxide increases both the acidity of the system and C T ,
the total concentration of dissolved carbonic species, and
it decreases the pH, but it does not affect the alkalinity
Alternatively, acidity remains unaffected by the addition
or removal of CaCO 3 (s) or Na 2 CO 3 (s) C T , on the other
hand, remains unchanged in a closed system upon addition
of strong acid or strong base For practical purposes,
sys-tems may be considered closed if they are shielded from
the atmosphere and lithosphere or exposed to them only for
short enough periods to preclude significant dissolution of
CO 2 or solid carbonates
Dissolution of Carbon Dioxide
Though much of the CO 2 which dissolves in solution may
ion-ize to form HCO3 CO3
2 , depending upon the pH, only a small fraction (0.3% at 25C) is hydrated as H 2 CO 3 Hence, the
concentration of the unhydrated dissolved carbon dioxide,
CO 2 (aq), is nearly identical to the analytically determinable
concentration of H 2 CO 3 * ( [CO 2 (aq)] [(H 2 CO 3 ])
The equilibrium of a constituent between a gas phase and a
solution phase can be characterized by a mass law relationship
for the characterization of the CO 2 dissolution equilibrium
A water that is in equilibrium with the atmosphere (Pco2
103.5 atm) contains at 25C approximately 0.44 milligram per
liter (105 M) of CO 2 ; K H (Henry’s Law constant) at 25C is
101.5 mole per liter-atm
Dissolved Carbonate Equilibria
Two systems may be considered: (1) a system closed to the atmosphere and (2) one that is in equilibrium with the atmosphere
Closed Systems In this case H 2 CO 3 * is considered a non-volatile acid The species H 2 CO 3 * , HCO 3 , CO32 and are interrelated by the equilibria: †
[H][CO] [ HCO]
3 2
3 K2
where K 1 and K 2 represent the equilibrium constants (acidity constants)
The ionization fractions, whose sum equals unity (see
Eq (3)), can be defined as follows:
a1 3 [HCO C] T
(8)
2
From Eqs (3) to (9) the ionization fractions can be expressed
in terms of [H ] and the equilibrium constants:
2 1
1
( K [H]K K [H] ) (10)
1
1
([H] K K [H ]) (11)
2
1
1
([H] K K [H] K ] (12)
1 2
HCO3 and CO3 may form complexes with other ions in the systems (e.g., in sea water, MgCO 3 , NaCO3 , CaCO3 ,
MgHCO3, it is operationally convenient to define a total concentration of the species to include an unknown number
of these complexes For example,
3 2
3 2
3
The distribution of carbonate species in sea water as a
Systems Open to the Atmosphere A very elementary model showing some of the characteristics of the carbonate system in natural waters is provided by equilibrating pure water with a gas phase (e.g., the atmosphere) containing CO 2
at a constant partial pressure Such a solution will remain in
† To facilitate calculations the equilibria are written here in terms of concentration quotients The activity corrections can be considered incorporated into the equilibrium “constants” which therefore vary with the particular solution Such constants for given media of con-stant ionic strength, as well as the true thermodynamic concon-stants, are listed in Tables 2A and 2B.
Table 1 gives the various expressions and their interrelations
Values for K and K are given in Tables 2A and 2B Because aqueous systems As shown in Figure 2, each of these
con-tion of pH is given in Figure 3
Trang 3equilibrium with pco , despite any variation of pH by the
addi-tion of strong base or strong acid This simple model has its
counterpart in nature when CO 2 reacts with bases of rocks,
for example with clays and silicates
such a model A partial pressure of CO 2 equivalent to that
in the atmosphere and equilibrium constants valid at 25C
have been assumed The equilibrium concentrations of the
individual carbonate species can be expressed as a function
of and [H ] 2 From Henry’s Law,
and Eqs (5) to (9), one obtains
C T 1 K p H
0
2
HCO
H
3 1 0
1
FIGURE 2 Closed system capacity diagram: pH contours for
alkalin-ity versus C T (total carbonate carbon) The point defining the solution composition moves as a vector in the diagram as a result of the addition (or removal) of CO2, NaHCO3, and CaCO3 (Na2CO3) or CB (strong base)
and C (strong acid) (After K.S Deffeyes, Limnol., Oceanog., 10, 412,
1965.) Figure from Stumm, W and J Morgan, Aquatic Chemistry,
Wiley-Interscience, New York, 1970, p 133.
CaCO3
Na2CO3
Dilution
1
1 1
2
0 –0.5 0 1 2
3
11.5 11.4
11.3
11.2
11.1
11.0
10.9
10.8
10.6
10.4 10.3
10.1 10.0 9.9
9.8
9.6
9.7 9.5
9.0
8.5
8.0
7.5
7.0 6.9 6.7 6.6 6.5 6.4 6.3 6.2 6.1 6.0 5.9 5.8
5.3 5.2 5.1 5.0 4.5 4.0 3.9 3.8 3.7 3.6 3.5 3.4
CT(Total Carbonate carbon; millimoles/liter)
F
igure 4 shows the distribution of the solute species of
Trang 4TABLE 1 Solubility of gases
Example a : CO2(g) CO2(aq) Assumptions: Gas behaves ideally; [CO2(aq)] [H2CO 3 ]
I Expressions for Solubility Equilibriumb
(1) Distribution (mass law) constant, K D:
K D [CO 2 (aq)]/[CO2(g)] (dimensionless) (1) (2) Henry’s law constant, K H:
In (1), [CO2(g)] can be expressed by Dalton’s law of partial pressure:
Combination of (1) and (2) gives [CO2 (aq)] (K D /RT)pCO
2 K H pCO
where K H K D /RT (mole liter1 atm –1 ) (3) Bunsen absorption coefficient, a B: [CO2(aq)] ( B/22.414)pCO
where 22.414 RT/p (liter mole–1 ) and
Partial Pressure and Gas Composition
pCO
2 xCO2 (P T – w) (6) where XCO
2 mole fraction or volume fraction in dry gas, P T total pressure and w water vapor pressure
Values of Henry’s Law Constants at 25 C
Carbon Dioxide CO2 33.8 10 –3
a Same types of expressions apply to other gases
b The equilibrium constants defined by (1)–(4) are actually constants only if the equilibrium expressions are formulated in terms of activities and fugacities
Table from Stumm, W and J Morgan, Aquatic Chemistry, Wiley-Interscience, New York, 1970, p 125
and
CO
H
3
0
1 2 2
It follows from these equations that in a logarithmic
2 3
*
HCO32, CO32 have slopes of 0, 1, and 2, respectively
If we equilibrate pure water with CO 2 , the system is
defined by two independent variables, for example,
temper-ature and Pco2, In other words, the equilibrium
concentra-tions of all solute components can be calculated by means of
Henry’s Law, the acidity constants and the proton condition
or charge balance if, in addition to temperature, one variable,
such as Pco2, [H 2 CO 3 * ] or [H ], is known or measured Use
of the proton condition instead of the charge balance gener-ally facilitates calculations because species irrelevant to the calculation need not be considered The proton condition merely expressed the equality between the proton excess and the proton deficiency of the various species with respect
graphic illustration of its use
Solubility Equilibria
Minerals dissolve in or react with water Under different physico-chemical conditions minerals are precipitated and accumulate on the ocean floor and in the sediments of rivers and lakes Dissolution and precipitation reactions impart to the water and remove from it constituents which modify its chemical properties
to a convenient proton reference level Figure 4 furnishes a
c oncentration—pH diagram (Figure 4) the lines of H CO ,
Trang 5TABLE 2B First acidity constant: H2CO3 HCO 3
K1
3
{ }{ }
{ * }
H HCO
1
3
{ }[ ]
[ * ]
H HCO
H CO
K1
3
[ ][ ]
[ * ]
H HCO
H CO
Temp., °C
Medium
→ 0 Seawater, 19% Cl Seawater 1 M NaClO4
25 6.352 a 6.00 b , 6.09 d — 6.04 g
a H S Harned and R Davies, Jr., J Amer Chem Soc , 65, 2030 (1943)
b After Lyman (1956), quoted in G Skirrow, Chemical Oceanography, Vol I, J P Riley and G
Skirrow, Eds., Academic Press, New York, 1965, p 651
c A Distèche and S Distèche, J Electrochem Soc , 114, 330 (1967)
d Calculated as log (K1/fHCO3) as determined by A Berner, Geochim Cosmochim Acta, 29, 947 (1964)
e D Dyrssen, and L G Sillén, Tellus, 19, 810 (1967)
f D Dyrssen, Acta Chem Scand , 19, 1265 (1965)
g M Frydman, G N Nilsson, T Rengemo, and L G Sillén, Acta Chem Scand , 12, 878 (1958)
Ref.: Stumm, W and J Morgan, Aquatic Chemistry, Wiley-Interscience, New York, 1970, p 148
TABLE 2A Equilibrium constant for CO 2 solubility Equilibrium: CO 2 (g) aq H 2 CO 3
Henry’s law constant: K [H 2 CO3]/pCO
2 (M.atm –1 ) Temp., C → 0 Medium, 1 M NaClO 4 Seawater, 19% C1 –
–log K –log cK –log cK
25 1.47 a 1.51 c 1.53 a
a Values based on data taken from Bohr and evaluated by K Buch,
Meeresforschung, 1951
b A.J Ellis, Amer J Sci , 257, 217 (1959)
c G Nilsson, T Rengemo, and L G Sillen, Acta Chem Sand , 12, 878 (1958)
Ref.: Stumm, W and J Morgan, Aquatic Chemistry, Wiley-Interscience,
New York, 1970, p 148
It is difficult to generalize about rates of precipita-tion and dissoluprecipita-tion other than to recognize that they are usually slower than reactions between dissolved species
Data concerning most geochemically important solid-solu-tion reacsolid-solu-tions are lacking, so that kinetic factors cannot be assessed easily Frequently the solid phase initially formed
is metastable with respect to a thermodynamically more stable solid phase Relevant examples of such metastabil-ity are the formation of aragonite under certain conditions instead of calcite, the more stable form of calcium car-bonate, and the over-saturation of quartz in most natural waters This over-saturation persists due to the extremely slow establishment of equilibrium between silicic acid and quartz
The solubilities of most inorganic salts increase with increasing temperature However, a number of compounds
of interest in natural waters (e.g CaCO 3 , CaSO 4 ) decrease in solubility with increasing temperature The dependence of solubility on pressure is very slight but must be considered for the extreme pressures encountered at ocean depths For example, the solubility product of CaCO 3 will increase by approximately 0.2 logarithmic units for a pressure of 200 atmospheres (ca 2000 meters)
Trang 60 1 2 3 4 5 6 7 8 9 10 11 12 13 13 7
0 –1 –2 –3 –4 –5 –6 –7
0 –1 –2 –3 –4 –5 –6 –7
HC –
OH –
C2–
B–
HC–
HB
H2C
P1
P2
B –
C2–
HC –
HB
H2C
seawater
pH
FIGURE 3 Logarithmic concentration—pH equilibrium diagram for seawater as a
closed system For seawater log B T 3.37, log CT 2.62 and the following pK
values: 6.0 for H2CO3, 9.4 for and pK 13.7 BT total borate boron and CT total carbonate carbon Arrows gives [H ] for seawater (pH 8.0) and for two equivalence points (points of minimum buffer intensity): P1, corresponding to a proton reference level of HB HC H 2 O, and P2, corresponding to a proton reference level of HB
H2C H 2O (From Dyrssen, D and L.G Sillén, Tellus, 19, 110, 1967).
TABLE 2B (continued)
Solid acidity constant: HCO3 H CO 3
K2
3 3
{ }{ } { }
H CO
T
2
3 3
{ }[ ]
[ ]
H CO HCO
3 3
[ ][ ] [ ]
H CO HCO
Temp., °C
Medium
→ 0 Seawater 0.75 M NaCl 1 M KclO4
— log K2 log K2 log K2 log c K2
a H S Harned and S R Scholes, J Amer Chem Soc , 63, 1706 (1941)
b After Lyman, quoted in G Skirrow, Chemical Oceanography, Vol I, J P Riley and G Skirrow,
Eds., Academic Press, New York, p 651
c A Distèche and S Distèche, J Electrochem Soc , 114, 330 (1967)
d M Frydman, G N Nilsson, T Rengemo, and L G Sillén, Acta Chem Scand , 12, 878 (1958)
Ref.: Stumm, W and J Morgan, Aquatic Chemistry, Wiley-Interscience, New York, 1970, pp 149
and 150
Trang 7Solubility of Oxides and Hydroxides
If pure solid oxide or hydroxide is in equilibrium with free
ions in solution, for example,
Me(OH) 2 (s) Me 2 2OH (18)
MeO(s) H 2 O Me 2 2OH (19)
the conventional (concentration) solubility product is given by
*
where the subscript “0” refers to solution of the simple,
uncom-plexed forms of the metal ion
Sometimes it is more appropriate to express the solubility
in terms of reaction with protons, for example,
Me(OH) 2 (s) 2H Me 2 2H 2 O (21)
MeO(s) 2H Me 2 H 2 O (22)
In the general case for a cation of charge z, the solubility equilibrium for Eqs (21) and (22) is characterized by
K
K
z
w z
s
s
0
0
[ ] [
where K w is the ion product of water This constant and also a
number of solubility equilibrium constants relevant to
natu-Equation (23) can be written in logarithmic form to express the equilibrium concentration of a cation Mez as a function of pH:
*
Equation (24) is plotted for a few oxides and hydroxides in
pKH
H+
H2CO3
CT
CO3
OH –
TRUE H2CO3 HCO3
P
pH
a
-1
-2
-3
-4
-5
-6
-7
-8
*
–
-2
FIGURE 4 Logarithmic concentration—pH equilibrium diagram for the aque-ous carbonate system open to the atmosphere Water is equilibrated with the
at-mosphere (pCO2 = 103.5 atm) and the pH is adjusted with strong base or strong acid Eqs (14), (15), (16), (17) with the constants (25C) pKH 1.5, pK1 6.3,
pK2 10.25, pK(hydration of CO2 ) 2.8 have been used The pure CO 2 solu-tion is characterized by the proton condisolu-tion [H ] [HCO 3
] 2[CO 3
]+[OH ]
see point P) and the equilibrium concentrations log[H ] log[HCO 3
] 5.65; log[CO 2 aq] log[H 2 CO3] 5.0; log[H 2 CO3] 7.8; log[CO 3
]
8.5 Ref.: Stumm, W and J Morgan, Aquatic Chemistry, Wiley-Interscience, New
York, 1970, p 127.
ral waters are given in Table 3
Figure 5
Trang 8TABLE 3 Equilibrium constants for oxides, hydroxides, carbonates, hydroxide carnonates, sulfates, silicates, and acids
Reaction
Symbol for equilibrium constants log K (25C) I
I OXIDES AND HYDROXIDES
13.77 1M NaClO4 (am)Fe(OH)3(s) Fe 3 3OH Ks0 38.7 3M NaClO4 (am)Fe(OH)3(s) FeOH 2 2OH Ks1 27.5 3M NaClO4 (am)Fe(OH)3(s) Fe(OH) 2
(am)Fe(OH)3(s) OH FE(OH) 4 Ks4 4.5 3M NaClO4 2(am)Fe(OH)3(s) Fe 2 (OH)2 4OH Ks22 51.9 3M NaClO4 (am)Fe(OOH)(s) 3H Fe 3 2H 2 O * Ks0 3.55 3M NaClO4
a—FeOOH(s) 3H Fe 3 2H 2 O *Ks0 1.6 3M NaClO4
a—Al(OH)3(gibbsite) 3H Al 3 3H 2
g—Al(OH)3(bayerite) 3H Al 3 3H 2 O *Ks0 9.0 0 (am)Al(OH)3(s) 3H Al 3 3H 2 O *Ks0 10.8 0
Al 3 4OH Al(OH) 4
CuO(s) 2H Cu 2 H 2 O *Ks0 7.65 0
Cu 2 4OH Cu(OH) 4
ZnO(s) 2H Zn 2 H 2 O *Ks0 11.18 0
Zn 2 3OH Zn(OH) 3
Cd(OH)2(s) 2H 2 Cd 2 2H 2 O *Ks0 13.61 0
Mn(OH)2(s) Mn 2 2OH Ks0 12.8 0 Mn(OH)2(s) OH Mn(OH) 3
Fe(OH)2(active) Fe 2 2OH Ks0 14.0 0 Fe(OH)2(inactive) Fe 2 2OH Ks0 14.5 (15.1) 0
Fe(OH)2(inactive) OH Fe(OH) 3 Ks3 5.5 0 Mg(OH)2 Mg 2 2OH Ks0 9.2 0 Mg(OH)2(brucite) Mg 2 2OH Ks0 11.6 0
Ca(OH)2(s) Ca 2 2OH Ks0 5.43 0 Ca(OH)2(s) CaOH OH Ks1 4.03 0 Sr(OH)2(s) Sr 2 2OH Ks0 3.51 0 Sr(OH)2(s) SrOH OH Ks1 0.82 0
II CARBONATES AND HYDROXIDE CARBNONATES
CO2(g) H 2 O H HCO 3
7.5 Seawater
5 C, 200 atm
seawater HCO3 H CO 3
9.0 Seawater
(Continued)
Trang 9TABLE 3 (continued )
Reaction
Symbol for equilibrium constants log K (25C) I
9.0 5 C, 200 atm
seawater
CaCO3(calcite) Ca 2 CO 3
6.2 Seawater CaCO3(aragonite) Ca 2 CO 3
6.8 Seawater ZnCO3(s) 2H Zn 2 H 2 O CO 2 (g) *Kps0 7.95 0 Zn(OH)1.2(CO3)0.4(s) 2H Zn 2 H 2 O
CO2(g)
Cu(OH)(CO3)0.5(s) 2H Cu 2 3/2H 2 O
1/2CO2(g)
Cu(OH)0.67(CO3)0.67(s) 2H Cu 2
4/3H2O 2/3CO 2 (g)
MgCO3(magnesite) Mg 2 CO 3
MgCO3(nesquehonite) Mg 2 CO 3
Mg4(CO3)3(OH)2.3H2O(hydromagnesite) 4Mg 2
3CO3 2OH
CaMg(CO3)2(dolomite) Ca 3 Mg 2 2CO 3
FeCO3(siderite) Fe 2 2CO 3
CdCO3(s) 2H CD 2 H 2 O CO 2 (g) Kps0 6.44 1M NaCl4
III SULFATES, SULFIDES, AND SILICATES
CaSO4(s) Ca 2 SO 4
MnS(green) Mn 2 S 2 Ks0 12.6 0 MnS(pink) Mn 2 S 2 Ks0 9.6 0 FeS(s) Fe 2 S 2 Ks0 17.3 0 SiO2(quartz) 2H 2 H 4 SiO4 Ks0 3.7
(am)SiO2(s) 2H 2 O H 4 SiO4 Ks0 2.7 0
IV ACIDS
The constants given here are taken from quotations or selections in (a) L G Sillén and A E Martell, Stability
Constants of Metal Ion Complexes, Special Publ., No 17, the Chemical Society, London, 1964: (b) W Feitknecht
and P Schindler, Solubility Constants of Metal Oxides, Metal Hydroxides and Metal Hydroxide Salts in Aqueous
Solutions, Butterworths, London, 1963; (c) P Schindler, “Heterogeneous Equilibria Involving Oxides, Hydroxides,
Carbonates and Hydroxide Carbonates”, in Equilibrium Concepts in Natural Water Systems, Advance in Chemistry
Series, No 67, American Chemical Society, Washington, DC, 1967, p 196; and (d) J N Butler, Ionic Equilibrium,
A Mathematical Approach, Addison-Wesley Publishing, Reading, Mass., 1964 Unless otherwise specified a pressure
of 1 atm is assumed.
a Most of the symbols used for the equilibrium constants are those given in Stability Constants of Metal-Ion Complexes
Table from Stumm, W and J Morgan, Aquatic Chemistry, Wiley-Interscience, New York, 1970, pp 168 and 169
Trang 10The relations in Figure 5 do not fully describe the
solu-bility of the corresponding oxides and hydroxides, since
in addition to free metal ions, the solution may contain
hydrolyzed species (hydroxo complexes) of the form The
solubility of the metal oxide or hydroxide is therefore
expressed more rigorously as
n
z n n
1
for ferric hydroxide, zinc oxide, and cupric oxide
Solubility of Carbonates
The maximum soluble metal ion concentration is a function
of pH and concentration of total dissolved carbonate species
Calculation of the equilibrium solubility of the metal ion for a
given carbonate for a water of a specific analytic composition
discloses whether the water is over-saturated or undersaturated
with respect to the solid metal carbonate In the case of calcite
Ca
CO
3 2
0 2
C
Since a2 is known as a function of pH, Eq (26) gives the
equilibrium saturation value of Ca 2 as a function of C T
and pH An analogous equation can be written for any
metallic cation in equilibrium with its solid metallic
car-bonate These equations are amenable to simple graphical
representation in a log concentration versus pH diagram as † Note that this solubility product is expressed for activities, as
represented by {}.
1 2 3 4 5 6
Fe 3+ Al 3+
Cu 2+ CuO(s)
Cu 2+ Zn 2+ Fe 2+
Cd 2+ Mg 2+
Ag +
CO 2+
pH
FIGURE 5 Solubility of oxides and hydroxides: free metal ion concentration
in equilibrium with solid oxides ore hydroxides As shown explicitly by the equi-librium curve for copper, free metal ions are constrained to concentrations to the left of (below) the respective curves Precipitation of the solid hydroxides and oxides commences at the saturation concentrations represented by the curves The formation of hydroxo metal complexes must be considered for the evaluation of complete solubility of the oxides or hydroxides Ref.: Stumm, W and J Morgan,
Aquatic Chemistry, Wiley-Interscience, New York, 1970, p 171.
Control of Solubility
Solubility calculations, such as those exemplified above, give thermodynamically meaningful conclusions, under the speci-fied conditions (e.g., concentrations, pH, temperature and pres-sure), only if the solutes are in equilibrium with that solid phase for which the equilibrium relationship has been formulated
For a given set of conditions the solubility is controlled by the solid giving the smallest concentration of solute For example, within the pH range of carbonate bearing natural waters, the stable solid phases regulating the solubility of Fe(II), Cu(II), and Zn(II) are, respectively, FeCO 3 (siderite), CuO (tenorite) and Zn (OH) (CO 3 ) (hydrozincite)
Unfortunately, it has not yet been possible to determine precise solubility data for some solids important in the reg-ulation of natural waters Among these are many clays and dolomite (CaMg(CO 3 ) 2 ), a mixed carbonate which con-stitutes a large fraction of the total quantity of carbonate rocks The conditions under which dolomite is formed in nature are not well understood and attempts to precipitate
it in the laboratory from solutions under atmospheric con-ditions have been unsuccessful These difficulties in ascer-taining equilibrium have resulted in a diversity of published figures for its solubility product, ({Ca2 }{Mg2 }{Co32 }2}†, ranging from 1016.5 to 1019.5 (25C)
The Activity of the Solid Phase
In a solid-solution equilibrium, the pure solid phase is defined
as a reference state and its activity is, because of its constancy, Plots of this equation as a function of pH are given in Figure 6
illustrated in Figure 7