Unit08a-aqgeochem

8/10/2019 Unit08a-aqgeochem

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Unit 08a : Advanced Hydrogeology

Aqueous Geochemistry


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Aqueous Systems

In addition to water, mass exists in thesubsurface as:

Separate gas phases (eg soil CO 2) Separate non-aqueous liquid phases (eg

crude oil) Separate solid phases (eg minerals

forming the pm) Mass dissolved in water (solutes eg Na +,

Cl-)


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Chemical System in Groundwater

Ions, molecules and solid particles in waterare not only transported.

Reactions can occur that redistribute massamong various ion species or between thesolid, liquid and gas phases.

The chemical system in groundwatercomprises a gas phase, an aqueous phaseand a (large) number of solid phases


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Solutions

A solution is a homogeneous mixture whereall particles exist as individual molecules or

ions. This is the definition of a solution. There are homogeneous mixtures where the

particle size is much larger than individualmolecules and the particle size is so smallthat the mixture never settles out.

Terms such as colloid, sol, and gel are usedto identify these mixtures.


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Concentration Scales

Mass per unit volume (g/L, mg/L, g/L)is the most commonly used scale for

concentration Mass per unit mass (ppm, ppb, mg/kg,

g/kg) is also widely used

For dilute solutions, the numbers arethe same but in general:mg/kg = mg/L / solution density (kg/L)


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Molarity Molar concentration (M) defines the

number of moles of a species per litre ofsolution (mol.L -1)

One mole is the formula weight of asubstance expressed in grams.


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Molarity Example

Na 2SO 4 has a formula weight of 142 g A one litre solution containing 14.2 g of

Na 2SO 4 has a molarity of 0.1 M (mol.L -1) Na 2SO 4 dissociates in water:

Na 2SO 4 = 2Na + + SO 42-

The molar concentrations of Na + andSO 42- are 0.2 M and 0.1 M respectively


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Seawater Molarity Seawater contains roughly 31,000 ppm of NaCl

and has a density of 1028 kg.m -3. What is themolarity of sodium chloride in sea water?

M = (m c/FW) * rwhere m c is mass concentration in g/kg;

r is in kg/m 3; andFW is in g.

Formula weight of NaCl is 58.45 31 g is about 0.530 moles Seawater molarity = 0.530 * 1.028 = 0.545 M

(mol.L -1)


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Molality

Molality (m) defines the number ofmoles of solute in a kilogram of solvent(mol.kg -1)

For dilute aqueous solutions attemperatures from around 0 to 40 oC,

molarity and molality are similarbecause one litre of water has a massof approximately one kilogram.


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Molality Example

Na 2SO 4 has a formula weight of 142 g One kilogram of solution containing 0.0142 kg

of Na 2SO 4 contains 0.9858 kg of water. The solution has a molality of 0.101 m(mol.kg -1)

Na 2SO 4 dissociates in water:

Na 2SO 4 = 2Na + + SO 42- The molal concentrations of Na + and SO 42-

are 0.202 m and 0.101 m respectively


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Seawater Molality Seawater contains roughly 3.1% of NaCl. What

is the molality of sodium chloride in sea water?m = (m c/FW)/(1 TDS)

where m c is mass concentration in g/kg;TDS is in kg/kg andFW is in g.

Formula weight of NaCl is 58.45

31 g is about 0.530 moles Average seawater TDS is 35,500 mg/kg (ppm) m = (31/58.45)/ (1- 0.0355) = 0.550 mol.kg -1


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Molar and Molal

The molarity definition is based on thevolume of the solution. This makes molarity a

temperature-dependent definition. The molality definition does not have a

volume in it and so is independent of anytemperature changes.

The difference is IMPORTANT forconcentrated solutions such as brines.


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Brine Example

Saturated brine has a TDS of about 319 g/L Saturated brine has an average density of

1.203 at 15o

C The concentration of saturated brine istherefore 265 g/kg or 319 g/L

The molality m = (265/58.45)/(1-0.319)) is

about 6.7 m (mol.kg-1

) The molarity M = (265/58.45)*1.203 is about

5.5 M (mol.L -1)


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Equivalents

Concentrations can be expressed inequivalent units to incorporate ionic

chargemeq/L = mg/L / (FW / charge)

Expressed in equivalent units, the

number of cations and anions in diluteaqueous solutions should approximatelybalance


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Partial Pressures

Concentrations of gases are expressedas partial pressures.

The partial pressure of a gas in amixture is the pressure that would beexerted by the gas if it occupied thevolume alone.

Atmospheric CO 2 has a partial pressureof 10 -3.5 atm or about 32 Pa.


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Mole Fractions

In solutions, the fundamental concentrationunit in is the mole fraction Xi; in which for jcomponents, the ith mole fraction is

Xi = n i/(n 1 + n 2 + ...n j),

where the number of moles n of a componentis equal to the mass of the componentdivided by its molecular weight.


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Mole Fractions of Unity

In an aqueous solution, the mole fraction ofwater, the solvent, is always near unity.

In solids that are nearly pure phases, e.g.,limestone, the mole fraction of the dominantcomponent, e.g., calcite, will be near unity.

In general, only the solutes in a liquid solutionand gas components in a gas phase will havemole fractions that are significantly differentfrom unity.


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Structure of Water

Covalent bonds between H and O 105 o angle H-O-H Water molecule is polar Hydrogen bonds join molecules

tetrahedral structure

Polar molecules bind to chargedspecies to hydrate ions in solution

105 o -

+

+


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Chemical Equilibrium

The state of chemical equilibrium for a closedsystem is that of maximum thermodynamic

stability No chemical energy is available to

redistribute mass between reactants andproducts

Away from equilibrium, chemical energydrives the system towards equilibriumthrough reactions


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Kinetic Concepts

Compositions of solutions in equilibrium withsolid phase minerals and gases are readily

calculated. Equilibrium calculations provide no

information about either the time to reachequilibrium or the reaction pathway.

Kinetic concepts introduce rates and reactionpaths into the analysis of aqueous solutions.


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Reaction Rates

After Langmuir and Mahoney, 1984

Mineral Recrystallization

Solute-Solute

Hydrolysis of multivalent ions (polymerization)

Adsorption-Desorption

Mineral-Water Equilibria

Secs Mins Hrs Days Months Years Centuries My

Gas-Water

Solute-Water

Reaction Rate Half-Life


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Relative Reaction Rates

An equilibrium reaction is fast if it takesplace at a significantly greater rate than thetransport processes that redistribute mass.

An equilibrium reaction is slow if it takesplace at a significantly smaller rate than thetransport processes that redistribute mass.

Slow reactions in groundwater require akinetic description because the flow systemcan remove products and reactants beforereactions can proceed to equilibrium.


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Partial Equilibrium Reaction rates for most important reactions

are relatively fast. Redox reactions are oftenrelatively slow because they are mediated by

micro-organisms. Radioactive decayreactions and isotopic fractionation areextremely variable.

This explains the success of equilibrium

methods in modelling many aspects ofgroundwater chemistry. Groundwater is best thought of as a partial

equilibrium system with only a few reactions

requiring a kinetic approach.


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Equilibrium Model

Consider a reaction where reactants A and B react toproduce products C and D with a,b,c and d being therespective number of moles involved.

aA + bB = cC + dD For dilute solutions the law of mass action describes

the equilibrium mass distributionK = (C) c(D)d

(A)a(B)b where K is the equilibrium constant and (A),(B),(C), and

(D) are the molal (or molar) concentrations


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Activity

In non-dilute solutions, ions interact electrostaticallywith each other. These interactions are modelled byusing activity coefficients ( g) to adjust molal (or molar)concentrations to effective concentrations

[A] = ga(A) Activities are usually smaller for multivalent ions than

for those with a single charge The law of mass action can now be written:

K = gc(C) c gd(D)d = [C]c[D]d ga(A)a gb(B)b [A]a [B]b


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Debye-Hckel Equation

The simplest model to predict ion ion activitycoefficients is the Debye-Hckel equation:

log gi = - Az i2(I)0.5

where A is a constant, z i is the ion charge, and I is theionic strength of the solution given by:

I = 0.5 SMiz i2

where (M i) is the molar concentration of the ith

species The equation is valid and useful for dilute solutionswhere I < 0.005 M (TDS < 250 mg/L)


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Extended Debye-Hckel Equation

The extended Debye-Hckel equation is usedto increase the solution strength for whichestimates of g can be made:

log gi = - Az i2(I)0.5

1 + Ba i(I)0.5 where B is a further constant, a i is the ionic

radius This equation extends the estimates to

solutions where I < 0.1 M (or TDS of about5000 mg/L)


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More Activity Coefficient Models

The Davis equation further extends theionic strength range to about 1 M

(roughly 50,000 mg/L) using empiricalcurve fitting techniques

The Pitzer equation is a much more

sophisticated ion interaction model thathas been used in very high strengthsolutions up to 20 M


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Monovalent Ions

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.001 0.01 0.1 1 10

Ionic Strength

A c

t i v

i t y

C o e

f f i c i e n

t

Debye-Huckel

Extended

Davis

Pitzer


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Divalent Ions

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.001 0.01 0.1 1 10

Ionic Strength

A c

t i v

i t y

C o e

f f i c i e n

t

Debye-Huckel

Extended

Davis

Pitzer


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Activity and Ionic Charge

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.001 0.01 0.1 1 10

Ionic Strength

A c

t i v

i t y

C o e

f f i c i e n

t

Debye-Huckel

Extended

Davis

Pitzer

Monovalent

Divalent


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Non-Equilibrium

Viewing groundwater as a partial equilibriumsystem implies that some reactions may notbe equilibrated.

Dissolution-precipitation reactions arecertainly in the non-equilibrium category.

Departures from equilibrium can be detected

by observing the ion activity product (IAP)relative to the equilibrium constant (K) whereIAP = [C]c[D]d = products

[A]a[B]b reactants


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Dissolution-PrecipitationaA + bB = cC + dD

If IAP1) then the reaction isproceeding from right to left.

If the reaction is one of mineral dissolutionand precipitation IAP/K1 the system is supersaturated and is

moving towards saturation by precipitation


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Saturation Index

Saturation index is defined as:SI = log(IAP/K)

When a mineral is in equilibrium withthe aqueous solution SI = 0

For undersaturation, SI < 0 For supersaturation, SI > 0


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Calcite The equilibrium constant for the calcite dissolution

reaction is K = 4.90 x 10 -9 log(K) = -8.31 Given the activity coefficients of 0.57 for Ca 2+ and 0.56

for CO 32- and molar concentrations of 3.74 x 10 -4 and5.50 x 10 -5 respectively, calculate IAP/K.

Reaction: CaCO 3 = Ca 2+ + CO 32-

IAP = [Ca 2+][CO 32-] = 0.57x3.37x10 -4x0.56x5.50x10 -5 [CaCO 3] 1.0

= 6.56 x 10 -9 and log(IAP) = -8.18 {IAP/K}calcite = 6.56/4.90 = 1.34log{IAP/K}calcite = 8.31 - 8.18 = 0.13

The solution is slightly oversaturated wrt calcite.


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Dolomite The equilibrium constant for the calcite dissolution reaction

is K = 2.70 x 10 -17 and log(K) = -16.57 Given activity coefficients of 0.57, 0.59 and 0.56 for Ca 2+ ,

Mg2+ and CO 32- and molar concentrations of 3.74 x 10 -4,

8.11 x 10-5

and 5.50 x 10-5

respectively, calculate IAP/K. Reaction: CaMg(CO 3)2 = Ca 2+ + Mg 2+ + 2 CO 32-

Assume the effective concentration of the solid dolomitephase is unity

log[Ca2+

] = -3.67 log[Mg2+

] = -4.32 log[CO 32-

] = -4.51log(IAP)=log([Ca 2+][Mg2+][CO 32-]2)= -3.67-4.32-9.02= -16.31

log{IAP/K}dolomite = 16.57 17.01 = -0.44 The solution is undersaturated wrt dolomite.


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Kinetic Reactions Reactions that are slow by comparison with

groundwater transport rates require a kineticmodel

k1

aA + bB = cC + dDk2 where k 1 and k 2 are the rate constants for the forward (L to R)and reverse (R to L) reactions

Each constituent has a reaction rate:r A = dA/dt; r B = dB/dt; r c = dC/dt; r D = dD/dt;

Stoichiometry requires that:-r A/a = -r B/b = r C/c = r D/d


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Rate Laws

Each consituent has a rate law of theform:

r A = -k 1(A)n1 (B)n2 + k 2(C) m1 (D)m2 where n 1, n 2, m 1 and m 2 are empirical orstoichiometric constants

If the original reaction is a single step(elementary) reaction then n 1=a, n 2=b,m 1=c and m 2=d


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Elementary Reactions

Fe 3+ + SO 42- = FeSO 4+

d(Fe 3+)/dt = -k 1(Fe 3+ )(SO 42-) + k 2(FeSO 4+)

The reaction rate depends not only onhow fast ferric iron and sulphate are

being consumed in the forward reactionbut also on the rate of dissociation ofthe FeSO 4+ ion.

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