Environmental Chemistry of Aqueous Systems

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2.  Carbon Dioxide in Water

Carbon dioxide can get into water by dissolution of gaseous CO2, or through the weathering of minerals such as CaCO3.  To get the full picture of what is going on, we must consider these two effects together, but we start by considering them in isolation.

CO2/H2O in the Atmosphere: Natural Acid Rain

CO2 dissolves in rain water.

                CO2(g)                  CO2(aq)                KH = 0.03 M atm-1

                                                                p(CO2) = 0.00035 atm

                        [CO2(aq)] = KH × 0.00035 atm = 1.1 × 10-5 M

                CO2(aq)        +        H2O                H+         HCO3-                K1 = 5 × 10-7 M

                        K1 = [H+][HCO3-]/[CO2(aq)]

                HCO3-                        H+        +        CO32-                        K2 = 5 × 10-11 M

                        K2 = [H+][CO32-]/[HCO3-]

Also

                [H+]         =        [HCO3-]        +        2[CO32-]

Manipulation of these equations gives:

                [HCO3-] = K1[CO2(aq)]/[H+]

                [CO32-] = K1K2[CO2(aq)]/[H+]2

                [H+]3 - K1[CO2][H+] – 2K1K2[CO2] = 0

Solution of the cubic equation: [H+]3 - K1[CO2][H+] – 2K1K2[CO2] = 0

Method A:  Simplification

                [CO32-]/[HCO3-] = K2/[H+]

Ratio is much less than 1 for [H+]>>5 × 10-11, which seems likely in this case, where H+ ions are generated in the system.

The third term can be ignored to give:

                        [H+]2 = K1[CO2];  [H+] =  = 2.3 × 10-6 M

Method B:  Newton's Approximation

Consider a general function f(x), with a solution for x at f(x) = 0.

Starting with a guess (x1), a better estimate (x2) can be obtained by extrapolation of the tangent of the function at x1, as shown in figure.

Simple algebra and calculus shows:

                x2 = x1 −

 Repeat until f(xn) is sufficiently close to zero.

Method C:  Spreadsheet

Use Excel to plot the function out and obtain [H+] when the function is equal to zero.

Results

What we can see is that natural water is expected to be mildly acidic.  We can also see that the reactions of CO2 in water mean that the total amount of CO2 in natural water is greater by about 20 % than expected on the basis of the Henry's Law solubility alone.  This effect can be very significant under other conditions (e.g. if the pH were lower) or if we were looking at a species that reacted more extensively in water.  Generally, Henry's Law constants lead to low solubilities of gases in water.

This approach can be applied to unpolluted rain water and fresh water in the Pre-Cambrian Shield regions (Canada and Scandinavia).

3.  CaCO3 in equilibrium with water.

CaCO3 is a common mineral (limestone, chalk) found in the bedrock and soil of many parts of Britain and the US, as well as in sediments on ocean and lake floors.  To look at the full picture, it is necessary to consider the CaCO3/water/CO2(g) interactions.

                

As a first approximation, consider just the dissolution of CaCO3.

                CaCO3  Ca2+ + CO32-                Ksp = 5 × 10-9 M2

        S = Solubility = [Ca2+] = [CO32-] =

S = 7 × 10-5 M

Effect of reaction of carbonate

        CO32- + H2O    HCO3- + OH-;        K3 = Kw/K2 = 2 × 10-4 M.

Combine to get CaCO3 + H2O == Ca2+ + HCO3- + OH-

                        K = KspK3         = 1 × 10-12 M3

                                        = [Ca2+][HCO3-][OH-]

Assuming this is the only important process, and it proceeds to completion,

                S = [Ca2+] = [HCO3-] = [OH-] = 1 × 10-4M

ie about 50 % higher than when the reaction of carbonate is ignored.

In fact, this calculation underestimates the solubility, because not all carbonate is converted to bicarbonate (we will cover this in a problem).

For [OH-] = 1 × 10-4 M, pOH = 4, and hence, pH = 10.  CaCO3 is thus a moderate base.

4.  CaCO3/H2O/CO2(g)

                        CaCO3  Ca2+ + CO32-                        Ksp = 5 × 10-9 M2

                        HCO3-                        H+        +        CO32-                K2 = 5 × 10-11 Mƒ

        CO2(aq)        +        H2O                H+         HCO3-                        K1 = 5 × 10-7 M

H2O                  H+        +        OH-                Kw = 10-14 M2

Maintaining Charge Neutrality

2[Ca2+]         +        [H+]   =    2[CO32-]         +        [HCO3-]        +        [OH-]        (I)

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Hence:

Substitute in (I)

which gives

Solution can be obtained using a spreadsheet, as shown below:  

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From the [H+] concentration, the concentrations of the other species can be obtained.

5.  Ion Concentrations in Natural Waters

Concentrations for fresh waters

What is observed is that there is good agreement between observations and predictions, although the calculations are approximate because of factors such as differences of temperature, omission of activity coefficients, non-saturation in natural waters, etc.

Other ions present in calcareous waters include:  magnesium, sulphate, chloride, chloride and some sodium.

In non-calcareous waters, concentrations of Na+ and K+ may be as high as Ca2+ and Mg2+ in calcareous waters, and HCO3- ions can be present from the weathering of aluminosilicates, e.g.

3KalSi3O8 + 2CO2 + 14H2O → 2KHCO3 + 6 H4SiO4 + KAl3Si3O10(OH)

        Feldspar

Hardness Index for Natural Waters

Hardness = [Ca2+] + [Mg2+]

This is defined in terms of the mass in milligrams per litre of calcium carbonate that contains the same total number of dipositive cations.

Alkalinity

Total Alkalinity = 2[CO32-] + [HCO3-] + [OH-] – [H+]

Usually this is determined using methyl orange as the indicator because it does not change colour until pH = 4, thus ensuring that the bicarbonate is neutralised.

The alkalinity can be defined using the indicator phenolphthalein.

Phenolphthalein alkalinity = [CO32-]

[Calculation:  Suppose that the hardness of a sample of water is 100 mg L−1.  This means that, if we convert this to mol L−1 of CaCO3, this will give us the total concentration of Ca2+ and Mg2+.

[Ca2+] + [Mg2+]         = 100 × 10−3 g L−1 / {(40.1 + 12.0 + 3 × 16.0) g mol−1}

                                = 100 × 10−3 g L−1/ 100.1 g mol−1

                                = 1.00 × 10−3 mol L−1                                        ]

6.  Acid Rain

As we have seen, natural rainwater is slightly acidic due to CO2, with a pH of around 5.6.  In the industrial world, rainwater is likely to have a much lower pH – typically of around 4 – perhaps as low as 2.4.  The cause of this acidity is the dissolution of acids that are generated in industrial processes.  Sulphuric acid is the primary acid, but nitric and hydrochloric may also be important.

Sulphuric acid.  The burning of sulphur rich fuels leads to sulphur dioxide emissions.  SO2 is the anhydride of sulphurous acid, which is a weak acid (pKa1 = 1.81, pKa2 = 6.91).  Therefore oxidation to SO3 is a key step in the route to acid rain.

                SO2        +        OH        →        HSO3

                HSO3        +        O2        →        SO3        +        HO2

The first reaction is rate limiting, and has a rate constant of about 1E-12 cm3 molecule-1 s-1 under normal conditions.  For [OH] – 1E6 molecule cm-3, this gives a lifetime of about 1E6 s, equivalent to about 10 days.

Nitric acid.  NO emitted from vehicles is oxidised to NO2 by reaction with peroxy radicals and then NO3 by reaction with ozone.  NO3 can react with aldehydes to form HNO3 or with NO2 to give N2O5, the anhydride of HNO3.  These reactions are more rapid than the processes that oxidise SO2 to SO3.

Hydrochloric acid.  HCl may be emitted after burning chlorine rich coal, and from the reaction of H2SO4 with sea salt aerosol.  It is very soluble and so will be removed from the atmosphere very rapidly.

In general terms, HCl is expected to be observed close to sources, while the [H2SO4]/[HNO3] ratio will increase as the age of an air parcel increases.  In recent years, coal with less sulphur has been used in the industrial nations, while vehicle use has increased.  Consequently, the ratio of [H2SO4]/[HNO3] has declined over the years.

Impact of Acid Rain

Calcareous waters.  In such waters, the CaCO3 tends to buffer the waters against pH changes

                CaCO3                  Ca2+         +         CO32-                

                CO32-         +         H2O                    HCO3- +         OH-

                CO2(aq)        +        H2O                H+         HCO3-

                H+        +        OH-                H2O

Any attempt to increase [H+] causes the loss of CO2 from solution and converts carbonate to bicarbonate, which in effect dissolves more CaCO3.  Thus the water should not change pH.  However, it should be noted that as more acidity is introduced, more CaCO3 is dissolved, so that the buffering action can be lost.

        CaCO3        +        H2SO4        →        CaSO4        +        CO2        +        H2O

Non-calcareous waters.  In this case, there is no buffering action and so the waters are very strongly affected by acid rain.  It should be noted that although the major sources of acid rain may be areas such as the US, Britain, and continental Europe, the major effects are observed in areas such as Canada and Scandinavia, where the soil and bedrock are non-calcareous.  The pH of non-calcareous waters can drop well below 5.

Aluminium.  One of the side effects of increased acidity is to bring more Aluminium into solution, through the dissolution of Al(OH)3.

                Al(OH)3        →        Al3+        +        3OH-;  Ksp = 10-33 M4

In neutral water, the solubility = [Al3+] = Ksp/(10-7)3 = 10-12 M.

However, its solubility increases dramatically as the pH reduces.

        [Al3+] = Ksp([H+]/Kw)3

The solubility is proportional to [H+]3!  One effect of Al3+ is that when it reaches the more alkaline gills of the fish, it precipitates as a gel, thus preventing the fish from breathing properly.  In addition, Al3+ has also been implicated in senile dementia.

7.  Summary

The aim of this short course has been to provide an introduction to the environmental chemistry of aqueous systems.  This has been achieved by examining the equilibrium behaviour of natural waters under the influence of CO2, CaCO3 and anthropogenic acid rain.  The principles introduced are more generally applicable to other aqueous systems; e.g., examining the effect of other ions on natural waters.

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