Chapter06.pdf

Geochemistry

W. M. White

Chapter 6: Aquatic Chemistry

6.1 Introduction

ater continually transforms the surface of the Earth, through interaction with the solid surface

and transport of dissolved and suspended matter. Beyond that, water is essential to life and

central to human activity. Thus as a society, we are naturally very concerned with water qual-

ity, which in essence means water chemistry. Aquatic chemistry is therefore the principal concern of

many geochemists.

In this chapter, we learn how the tools of thermodynamics and kinetics are applied to water and its

dissolved constituents. We develop methods, based on the fundamental thermodynamic tools already

introduced, for predicting the species present in water at equilibrium. We then examine the interaction

of solutions with solids through precipitation, dissolution, and adsorption.

Most reactions in aqueous solutions can be placed in one of the following categories:

• Acid-base, e.g., dissociation of carbonic acid:

H 2 CO 3 ® H + + HCO −

• Complexation, e.g., hydrolysis of mercury:

Hg 2+ + H 2 O ® Hg(OH) + + H +

• Dissolution/Precipitation, e.g., dissolution of orthoclase:

KAlSi 3 O 8 + H + + 7H 2 O ® Al(OH) 3 + K + + 3H 4 SiO 4

• Adsorption/Desorption, e.g., adsorption of Mn on a clay surface:

≡S + Mn 2+ ® ≡S–Mn

(where we are using ≡ S to indicate the surface of the clay).

In this chapter, we will consider these in detail. We return to the topic of aquatic chemistry in Chapter

13, we examine the weathering process, that is reaction of water and rock and development of soils,

and the chemistry of streams and lakes.

6.2 Acid-Base Reactions

The hydrogen and hydroxide ions are often participants in all the foregoing reactions. As a result,

many of these reactions are pH dependent. In order to characterize the state of an aqueous solution,

e.g., to determine how much CaCO 3 a solution will dissolve, the complexation state of metal ions, or the

redox state of Mn, the first step is usually to determine pH. On a larger scale, weathering of rock and

precipitation of sediments depend critically on pH. Thus pH is sometimes called the master variable in

aquatic systems. We note in passing that while pH represents the hydrogen ion, or proton concentra-

tion, the hydroxide ion concentration is easily calculated from pH since the proton and hydroxide con-

centrations are related by the dissociation constant for water, i.e., by:

K W = a H + a OH −

6.1

The value of K W , like all equilibrium constants, depends on temperature, but is 10 –14 at 25°C.

Arrhenius defined an acid as a substance that upon solution in water releases free protons. He de-

fined a base is a substance that releases hydroxide ions in solution. These are useful definitions in most

cases. However, chemists generally prefer the definition of Brønstead, who defined acid and base as

proton donors and proton acceptors respectively. The strength of an acid or base is measured by its

tendency to donate or accept protons. The dissociation constant for an acid or base is the quantitative

measure of this tendency and thus is a good indication of its strength. For example, dissociation of

HCl:

HCl ® H + + Cl –

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K HCl = a H + a Cl −

a HCl

= 10 3

has a dissociation constant:

HCl is a strong acid because only about 3% of the HCl molecules added will remain undissociated. The

equilibrium constant for dissociation of hydrogen sulfide:

H 2 S ® H + + HS –

K H 2 S = a H + a HS −

= 10 −7.1

is:

a H 2 S

Thus H 2 S is a weak acid because very few of the H 2 S molecules actually dissociate except at high pH.

Metal hydroxides can either donate or accept protons, depending on pH. For example, we can repre-

sent this in the case of aluminum as:

+ H + ® Al(OH) 2+ + H 2 O

Al(OH)

+ OH – ® Al(OH)

+ H 2 O

Compounds that can either accept or donate protons are said to be amphoteric .

Metals dissolved in water are always surrounded by solvation shells. The positive charges of the hy-

drogens in the surrounding water molecules are to some extent repelled by the positive charge of the

metal ion. For this reason, water molecules in the solvation shell are more likely to dissociate and give

up a proton more readily than other water molecules. Thus the concentration of such species will affect

pH.

Most protons released by an acid will complex with water molecules to form hydronium ions, H 3 O +

or even

Al(OH)

H 5 O + . However, in almost all cases we need not concern ourselves with this and can treat the

H + ion as if it were a free species. Thus we will use [H + ] to indicate the concentration of H + + H 3 O + +

H 5 O + +...

6.2.1 Proton Accounting, Charge Balance, and Conservation Equations

6.2.1.1 Proton Accounting

Knowing the pH of an aqueous system is the key to understanding it and predicting its behavior.

This requires a system of accounting for the H + and OH – in the system. There are several approaches to

doing this. One such approach is the Proton Balance Equation (e.g., Pankow, 1991). In this system, both

H + and OH – are considered components of the system, and the proton balance equation is written such

that the concentration of all species whose genesis through reaction with water caused the production of OH – are

written on one side, and the concentration of all species whose genesis through reaction with water caused the

production of H + are written on the other side . Because water dissociates to form one H + and one OH – , [H + ]

always appears on the left side and OH – always appears on the right side of the proton balance equa-

tion. The proton balance equation for pure water is thus:

[H + ] = [OH – ]

6.2 †

Thus in pure water the concentrations of H + and OH – are equal.

Now, consider the example of a nitric acid solution. H + will be generated both by dissociation of wa-

ter and dissociation of nitric acid:

HNO 3 ®H + +NO -

Since one NO - ion is generated for every H + , the proton balance equation becomes:

[H + ] = [OH - ] + [NO - ]

6.3

† Be careful not to confuse algebraic expressions, written with an equal sign, such as the proton balance equation,

with chemical reactions, written with the reaction symbol, ® . In this case, it is obvious that this is not a balanced

chemical reaction, but that will not always be the case.

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Next consider a solution of calcium carbonate. We specify the calcium and carbonate ions as compo-

nents. Hydrogen ions may be generated by hydrolysis of calcium:

Ca 2+ + H 2 O ® H + + Ca(OH) +

and hydroxide ions may be generated by:

CO 2- + H 2 O ® HCO - + OH -

The proton balance equation for this reaction is:

[H + ]+[HCO - ] = [OH - ]+[Ca(OH) + ] 6.4

Now consider a solution of a diprotonic acid such as H 2 S. H 2 S can undergo 2 dissociation reactions:

H 2 S ® H + + HS – 6.5

HS – ® H + + S 2– 6.6

For every HS – ion produced by dissociation of H 2 S, one H + ion would have been produced. For every

S 2– ion, however, 2 H + would have been produced, one from the first dissociation and one from the sec-

ond. The proton balance equation is thus:

[H + ] = [OH – ] + [HS – ] + 2[S 2– ] 6.7

An alternative approach to the proton balance equation is the TOT H proton mole balance equation used

by Morel and Hering (1993). In this system, H + and H 2 O are always chosen as components of the system

but OH – is not. The species OH – is the algebraic sum of H 2 O less H + :

OH – = H 2 O – H + 6.8

An implication of this selection of components is that when an acid, such as HCl is present, we

choose the conjugate anion as the component, so that the acid, HCl is formed from components:

HCl = Cl - + H +

For bases, such as NaOH, we choose the conjugate cation as a component. The base, NaOH is formed

from components as follows:

NaOH = Na + + H 2 O – H +

Because aquatic chemistry almost always deals with dilute solutions, the concentration of H 2 O may

be considered fixed at a mole fraction of 1, or 55.4 M. Thus in the Morel and Hering system, H 2 O is

made an implicit component, i.e., its presence is assumed but not written, so that equation 6.8 becomes:

OH – = –H + 6.9

The variable TOTH is the total amount of component H + , rather than the total of species H + . Every species

containing the component H + contributes positively to TOT H while every species formed by subtract-

ing component H + contributes negatively to TOT H. Because we create the species OH – by subtracting

component H + from component H 2 O, the total of component H + for pure water will be:

TOT H = [H + ] – [OH – ]

Thus TOT H in this case is the difference between the concentrations of H + and OH – . Of course, in pure

water, [H + ] = [OH – ], so TOT H = 0.

Now let’s consider our example of the CaCO 3 solution. In addition to H + and H 2 O, we choose Ca 2+

and CO 2 - as components. In the proton mole balance equation, HCO - counts positively (since HCO -

= CO 2 - + H + ) and CaOH + (since CaOH + = Ca 2+ + H 2 O – H + ) negatively:

TOT H = [H + ] + [ HCO - ] – [OH – ] – [Ca(OH) + ] 6.10

Comparing equations 6.10 and 6.4, we see that the TOT H is equal to the difference between the left and

right hand sides of the proton balance equation, and that in this case TOT H = 0. This makes sense, be-

cause, having added neither [H + ] nor [OH - ] to the solution, the total of the component H the solution

contains should be 0.

Now consider the dissolution of CO 2 in water to form carbonic acid:

CO 2 + H 2 O ® H 2 CO 3

6.11

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Under the right conditions of pH, this carbonic acid will dissociate to form bicarbonate ion:

H 2 CO 3 ® H + + HCO − 6.12

If we choose CO 2 as our component, bicarbonate ion would be made from components CO 2 , H 2 O, and

H + :

HCO − = CO 2 + H 2 O - H +

Thus in the TOTH proton mole balance equation, bicarbonate ion would count negatively, so TOT H is:

TOT H = [H + ] – [OH – ] – [ HCO − ]

6.13

Alternatively, had we defined CO 2 - as a component, then species HCO - is formed by the components:

HCO − = H + + CO 2−

In this case, the proton mole balance equation is:

TOT H = [H + ] – [OH – ] + [ HCO − ]

6.13a

Here we see that TOT H depends on how we define our components.

6.2.1.3 Conservation Equations

A further constraint on the composition of a system is provided by mass balance . Acid-base reactions

will not affect the total concentration of a substance. Thus regardless of reactions 6.5 and 6.6, and any

other complexation reactions, such as

Pb 2+ + S 2– ® PbS aq

the total concentration of sulfide remains constant. Thus we may write:

Σ S = [H 2 S] + [HS – ] + [S 2– ] + [PbS aq ] + ...

We can write one mass balance, or conservation , equation for each component in solution. Of course for

components, such as Na, that form only one species, Na + in this case, the mass balance equation is triv-

ial. Mass balance equations are useful for those components forming more than one species.

While the charge balance constraint is an absolute one and always holds, mass balance equations can

be trickier because other processes, such a redox, precipitation, and adsorption, can affect the concen-

tration of a species. We sometimes get around this problem by writing the mass balance equation for

an element, since an elemental concentration is not changed by redox processes. We might also define

our system such that it is closed to get around the other problems. Despite these restrictions, mass bal-

ance often provides a useful additional constraint on a system.

6.2.1.2 Charge Balance

As we saw in Chapter 3, solutions are electrically neutral; that is, the number of positive and negative

charges must balance:

∑

m i z i

= 0

6.14

where m is the number of moles of ionic species i and z is the charge of species i . Equation 6.14 in

known as the charge balance equation and is identical to equation 3.99. This equation provides an im-

portant constraint on the composition of a system. Notice that in some cases, the proton balance and

charge balance equations are identical (e.g., equations 6.2 and 6.7).

For each acid-base reaction an equilibrium constant expression may be written. By manipulating

these equilibrium constant expressions as well proton balance, charge balance, and mass balance equa-

tions, it is possible to predict the pH of any solution. In natural systems where there are many species

present, however, solving these equations can be a complex task indeed. An important step in their so-

lution is to decide which reactions have an insignificant effect on pH and neglect them.

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6.2.3 The Carbonate System

We now turn our attention to carbonate. Water at the surface of the Earth inevitably contains dis-

solved CO 2 , either as a result of equilibration with the atmosphere or because of respiration by or-

ganisms. CO 2 reacts with water to form carbonic acid :

CO 2 + H 2 O ® H 2 CO 3

6.15

Some of the carbonic acid dissociates to form bicarbonate and hydrogen ions:

H 2 CO 3 ® H + + HCO −

6.16

Some of the bicarbonate will dissociate to an additional hydrogen ion and a carbonate ion:

HCO − ® H + + CO 2−

6.17

We can write three equilibrium constant expressions for these reactions:

K sp = a H 2 CO 3

f CO 2

6.18

a H + a HCO 3 −

a H 2 CO 3

6.19

K 1 =

a H + a CO 2−

a HCO 3 −

K 2 =

6.20

The equilibrium constants for these reactions are given in Table 6.1 as a function of temperature.

In the above series of reactions, we have simplified things somewhat and have assumed that dis-

solved CO 2 reacts completely with water to form H 2 CO 3 . This is actually not the case, and much of the

dissolved CO 2 will actually be present as distinct molecular species, CO 2(aq) . Thus reaction 6.15 actually

consists of the two reactions:

CO 2(g) ® CO 2(aq) 6.15a

CO 2(aq) + H 2 O ® H 2 CO 3 6.15b

The equilibrium for the second reaction favors CO 2(aq) . However, it is analytically difficult to distin-

guish between the species CO 2(aq) and H 2 CO 3 . For this reason, CO 2(aq) is often combined with H 2 CO 3

when representing the aqueous species. The combined total concentration of CO 2(aq) + H 2 CO 3 is some-

times written as H 2 CO

* . We will write it simply as H 2 CO 3 .

The importance of the carbonate system is that by dissociating and providing hydrogen ions to solu-

tion, or associating and taking up free hydrogen ions, it controls the pH of many natural waters. Example

Table 6.1. Equilibrium Constants for the Carbonate System

T (°C)

pK CO 2 £

pK 1

pK 2

pK cal

pK arag

pK CaHCO + *

pK CaCO 0

†

1.11

6.58

10.63

8.38

8.22

–0.82

–3.13

1.19

6.52

10.55

8.39

8.24

–0.90

–3.13

1.27

6.46

10.49

8.41

8.26

–0.97

–3.13

1.34

6.42

10.43

8.43

8.28

–1.02

–3.15

1.41

6.38

10.38

8.45

8.31

–1.07

–3.18

1.47

6.35

10.33

8.48

8.34

–1.11

–3.22

1.52

6.33

10.29

8.51

8.37

-1.14

-3.27

1.67

6.29

10.20

8.62

8.49

–1.19

–3.45

1.78

6.29

10.14

8.76

8.64

–1.23

–3.65

1.90

6.34

10.13

8.99

8.88

–1.28

–3.92

1.94

6.38

10.14

9.12

9.02

–1.31

–4.05

*K CaHCO + = a CaHCO + /( a Ca 2+ a HCO − )

† K CaCO 0 = a CaCO 0 /( a Ca 2+ a CO 2− )

£ pressure in units of bars.

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