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Aqueous Geochemistry

• Basically the study of water interacting with rocks/sediments– Mineral dissolution/precipitation, adsorption, cation

exchange– Some reactions occur only in the aqueous phase

• We evaluate reactions with respect to equilibrium– For water-rock reactions, we can determine mineral

solubilities and saturation states of the solution with respect to individual minerals

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Balancing Chemical Reactions

• All chemical reactions must be balanced with respect to mass and charge– We can’t create or destroy mass or charge

• Overall Reactions:– Summation of all reaction steps– Determining molar ratios of reactant and product

species• Assumptions:– Since all the reactions involve water, we have all the

H2O and H+ that we need

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Law of Mass Action

• The rate at which a substance reacts is directly proportional to its active mass

• Mathematical model that explains and predicts behaviors of solutions in equilibrium– Valid only for reversible reactions– At equilibrium, the forward reaction rate (uf) = the

backward reaction rate (ub)

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Law of Mass Action

• Mathematical model that explains and predicts behaviors of solutions in equilibrium– Valid only for reversible reactions

• For reaction: aA + bB cC + dD– Keq = [(C)c(D)d]

[(A)a(B)b] • (A), (B), (C), (D) are concentrations at equilibrium• [(C)c(D)d] is the reaction quotient (Q) [(A)a(B)b] • Q changes until equilibrium is achieved, then it is

constant

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Law of Mass Action• Keq = the equilibrium constant– Keq values have been determined in the lab

for many reactions– Keq is a constant, i.e., never changes for that

particular reaction– Knowing Keq and having a balanced reaction,

we know the ratio of products to reactants at equilibrium

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Law of Mass Action

• For reaction: aA + bB cC + dD– Keq = [(C)c(D)d] [(A)a(B)b] – If we disturb the system, e.g., add more “A”, we have

changed Q, so something else must change to re-establish equilibrium• Because Keq is constant, Q is also constant at equilibrium• If we increase (A), maybe also increase (C) or (D), or both;

or decrease (B)– N.B.: stoichiometric coefficients and concentrations

are not the same• Examples…

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Solubility Index Calculations• SI = log IAP – log Keq

– SI = saturation index– IAP = ion activity product = measured concentration (=

Q)– Keq = equilibrium constant (IAP at equilibrium)

• If SI = 0: equilibrium• If SI < 0: solution undersaturated with respect to

that mineral• If SI > 0, solution is oversaturated with respect to

that mineral• Example…

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Thermodynamics

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What is Thermodynamics?

• The study of energy transformations– All reactions either consume or produce energy

• Thermodynamics is the study of the connection between heat and work and the conversion of one into the other

• Many machines and devices change heat into work (e.g., automobile engine) or turn work into heat (or cooling, as in a refrigerator)

• “Everything happens because heat is flowing from a hot place to a cold place. Nothing happens without heat flow. There are no exceptions.”

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What is Thermodynamics?

• The fundamental assumption is equilibrium• It describes the world based on observable

measurements– e.g., volume, pressure, temperature, chemical composition

• It is useful for predicting:– Directions of chemical change– Composition of reaction mixtures at equilibrium– Response of properties to external changes

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Equilibrium and Disequilibrium

• Equilibrium is often not attained in surface and near surface environments

• If equilibrium is not reached, then is equilibrium thermodynamics useful?

• Yes! Predicts whether a reaction can spontaneously occur based on magnitude and sign of Gibbs free energy of reaction– Is mineral potentially dissolving or precipitating?

• Provides good approximation of reality– Predicts dissolved concentrations at equilibrium– Is a reaction controlling concentration?

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Thermodynamics Terms

• System: the part of the world we’re interested in– Open: matter can pass across boundary– Closed: matter cannot pass, although energy (e.g.,

heat) can– Isolated: impervious boundary, no E transfer

• Surroundings or Environment: the rest of the world in contact with the system

• Boundary: separates system from its surroundings

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System properties

• We can describe every system using some fundamental properties

• Intensive: independent of matter, don’t need to specify quantity of sample – e.g., pressure, temperature, density

• Extensive: dependent on mass and are additive– e.g., volume, mass

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More Terms

• Phases: separate parts of a system– e.g., minerals in rock– solid, liquid, or gas H2O

• Components: describe phases– e.g., components of rock could be elements or

oxides• Change in state (or phase change): trans-

formation from one state to another – e.g., compress a gas; freeze water

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Heat: the main measure of energy transformations

• Heat is not temperature• Heat is energy transferred (flows) from one body or

system to another (across a boundary) due to thermal contact when the systems are at different temperatures– Flow from high to low T– Positive when flow from surroundings to system– Negative when flow from system to surroundings

• Heat is something that flows and temperature difference is what makes heat flow

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Heat Flow: Analogous to Water Flow

• Consider 2 cylinders of water connected by a pipe at their base• Water will flow from the cylinder on the left into the cylinder

on the right until the levels are equal• Water level acts like temperature• Heat, like water, flows in such a way to produce a uniform

temperature level

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Zeroth Law of Thermodynamics

• There is no heat flow between objects that are the same temperature

• Consider a thermometer:– If you stick one in a pot of boiling water, heat flows

from the pot to the thermometer until it reaches the temperature of the water

– At the point, heat stops flowing between the pot and the thermometer

– The temperature of the pot = the temperature of the thermometer

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First Law of Thermodynamics• Heat cannot be created or destroyed• Every system contains a certain amount of internal

energy– e.g., heat content, gravity, electrical, magnetic, molecular,

atomic, nuclear – Amount of E can change when there is a change of state

• E = E2 – E1

• Ei = internal E of system in states 1 and 2• E is difference in energy between 2 states

– Doesn’t matter how the change took place as long as it is reversible

– Back to original state, E = 0

• Energy is Conserved

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First Law of Thermodynamics• Heat is work waiting to happen– Work will be done (or wasted) when heat flows

from a hot place to a cold place• Consider an unlit candle– The wax has some potential energy– There is no heat flow when unlit, so it can’t do any

work– A lit candle does not create heat • Heat cannot be created or destroyed

– A burning candle liberates heat

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First Law of Thermodynamics• Heat flows from the flame and hot wax into

the cooler atmosphere• This heat could do some useful work– e.g., boil a pot of water which would create steam

and power an engine

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Work

• The transfer of energy from one system to another; completely convertible into lifting of a weight– Movement of a body from one position to another

against some physical resistance, such as friction or gravity

– e.g., hammer a nail into wood (wood resists)

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Second Law of Thermodynamics• Not all heat is convertible to work • Every system left to itself will, on average,

assume maximum randomness • Entropy is a measure of this “randomness”

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Second Law of Thermodynamics• Entropy is a quantifiable measure of how

evenly distributed heat is– When heat flows from a hot spot to a cold spot,

entropy increases– When heat flows from a cold spot to a hot spot,

entropy decreases• Entropy always increases in a closed system• Entropy can decrease in an open system only

if energy is received from an outside source

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Third Law of Thermodynamics

• An ideal engine would convert 100% of the heat into useful work only if its exhaust temperature were absolute zero– 100% efficiency is impossible– No perpetual motion machines– Also, there are no truly reversible reactions; all

processes have a natural direction which causes entropy to increase

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Thermodynamics: Key Facts

• There is a fixed amount of heat in the universe. Heat is neither created nor destroyed

• Heat is "organized" when there are some places that are hotter than others

• Heat always tries to disorganize itself by moving from a hot place to a cold place, spreading itself out as evenly as possible

• Entropy is a measure of how evenly spread out the heat is– Entropy is a measure of heat disorder

• As heat flows from one place to another, it either does work or wastes the opportunity to do work

• Natural processes cannot violate these laws

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First Law of Thermodynamics

• E = heat (q) flowing across a boundary minus work (w) done by system– E = q – w– dE = dq – dw – Measured using Enthalpy, or Heat of Reaction (H)

• We can’t directly measure H, so we need to establish an arbitrary scale so that we can compare ΔH’s. To do this, the concept of reference or standard state in introduced

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Standard State• Standard state: 25°C, 1 atmosphere pressure, infinitely

dilute solution• Enthalpy (H) of a pure substance in the standard state

= 0• Once this scale is established, we can experimentally

measure the enthalpy of ions and compounds that are formed from elements in their standard state

• For every ion or compound, we define:– ΔHf°: H of formation in the standard state– ° refers to the standard state, f = formation– SI units kJ/mol (English kcal)

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Enthalpy of a Reaction

• Enthalpy of a Reaction– > 0 = endothermic; reaction consumes heat – < 0 = exothermic; reaction produces heat

• Consider creation of sulfuric acid from H2 and S– H2 + S H2S– This produces 20.5 kiloJoules (kJ) of heat– H2 + S H2S + 20.5 kJ

– HR = -20.5 kJ/mol• R = reaction• = standard state• Negative sign = heat produced (+ = heat required)

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Enthalpy of a Reaction

• HR = niHfi(products) – niHfi(reactants)– i = specific ion or compound – n = molar coefficient of ion or compound

• Hf values have been measured experimentally and are tabulated in reference books

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Enthalpy: Examples

• If forward reaction is exothermic, increase in T favors backward reaction – consumes heat to counteract the increase in T

• If forward reaction is endothermic, increase in T favors forward reaction

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Second Law of Thermodynamics

• Not all enthalpy is convertible to work • Entropy (S) measures randomness– Positive value indicates reaction produces more

“randomness”– Negative values indicates reaction produces more

“order”

• ΔSR° = Σni Si° (products) - Σni Si° (reactants)

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Entropy: Examples• Molecules in gas phase are more randomly

distributed than liquid phase • Solutes more random than solid

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J. Willard Gibbs (1839-1903)

J. Willard Gibbs, a 19th century chemist noted that most of the heat involved in a reaction went to ΔH; however, some went to ΔS

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Gibbs Free Energy• Gibbs Free Energy (G) is a measure of enthalpy

(heat) taking entropy (randomness) into account– G = H – TS – For a chemical reaction: ΔGR° = ΔHR° - T ΔSR°

• T is in Kelvins (K) [25°C = 298.15 K]

• ΔGR° is a measure of the driving force of a reaction – GR < 0; forward reaction has excess energy, thus

favors forward reaction– GR > 0; forward reaction has deficiency of E, thus

favors reverse reaction

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Gibbs Free Energy

• GR is usually calculated from the free energies of formation (Gf) of the reaction products and reactants– GR = niGfi(products) – niGfi(reactants)

– Gf values for many compounds have been determined by chemists, and can be looked up in reference books

• Gibbs free energy is the basis of thermodynamic calculations

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Gibbs Free Energy: Examples

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Gibbs Free Energy

• For a reaction 2A + 3B A2B3

– If GR < 0, reaction, forward reaction proceeds until equilibrium is reached• Product (A2B3) becomes more abundant, reactants (A

and B) less abundant– Equilibrium constant (Keq) will be large• Keq = [A2B3] / ([A]2[B]3)

– Sign and magnitude of GR can be used to predict direction reaction runs at standard state and magnitude of Keq

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Gibbs Free Energy and the Law of Mass Action• The Law of Mass Action was used to determine the

equilibrium constant (Keq) for a reaction from the products and reactants– For reaction: aA + bB cC + dD– Keq = [(C)c(D)d] [(A)a(B)b]

• The Law of Mass Action can be derived from Gibbs free energy– GR = -RT ln Keq

• R is the gas constant = 8.314 J/(T(K) mol)– GR = -5.708 log Keq at 25°C

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Gibbs Free Energy and the Law of Mass Action: Example

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Thermodynamics

• Helps us determine – What reactions should be occurring– The response of reactions and properties to

external changes• It is the basis for geochemical equilibrium

computer models

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Activities and Concentrations

• We have been using concentrations in terms of values measured in the lab. In reality we should be using the “effective concentrations”, or activities (ai), of species

• Usually the activity of a species is less than its measured concentration– Due to interactions in solution caused by charges

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Activities and Concentrations

• Ions in solution interfere with each other– Ions are surrounded by a “cloud” of

counterions (opposite charge)– Ions can also be surrounded by polar (H2O)

molecules

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Activities and Concentrations

• Ions are less able to interact with each other than expected from their measured concentrations– Cloud of ions can repel ions of the same charge to

prevent bonding with ion at center of cloud• Therefore, the activity of ions < concentrations• Key variables are ion charge and ion radius

(charge density)

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Activity• To apply equilibrium principles to ions and

molecules, we need to replace concentrations with activities– Need to correct for interference by other ions – ai = i Ci • a = activity (effective concentration)• = activity coefficient (usually < 1)• C = concentration in moles• i = specific species

– a < C in most situations

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Equilibrium Constant and Activity

• aA + bB cC + dD– Keq = [C]c[D]d [A]a[B]b

– square brackets indicate activity • In very dilute solutions, the difference

between activity and concentration is unimportant, as ≈ 1.0

• But for most natural waters, we must use activities

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Conventions for Reactions and Equilibria

• Activities expressed in moles– is unitless

• Activities of pure solids and H2O = 1• Gas concentrations expressed as partial

pressure (Pp) in atmospheres• Reactions assumed to be at 25°C and 1 atm

(standard T and P)

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Activities are a function of Ionic Strength

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Calculation Ionic Strength (I)• I = ½ mi zi2– m = molar concentration– z = charge for each ion i– Need a complete chemical analysis– Uncharged ions are not considered– H+ and OH- considered only at extreme pHs

• Typical values– Lakes/streams: 0.001 mol– Old groundwater: 0.1 mol– Seawater: 0.7 mol– Oil Field brines: > 5 mol

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Activity coefficient

• Recall a = m• decreases with increasing ionic strength and

increasing charge• Calculated using empirical equations– Debye-Hückel (basic and extended)– Davies– Pitzer

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Debye-Hückel Theory

• For dilute solutions (I < 5 x 10-3)– log = -Az2I½

• A = 0.5085 (water at 25°C)• z = ion charge (if charge = 0, = 1)

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Debye-Hückel Theory

• For less dilute solutions (5 x 10-3 < I < 0.1), use extended Debye-Hückel Equation – log = - Az2I½ (1 - aBI½)• A and B = dielectric constants of solvent (function of T,

P; look up)• a = effective diameter of ion (look up)• Ion size becomes important as I increases

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Equations for High Ionic Strengths

• At higher I, D-H fails to adequately work• Davies Equation:

– 0.3 could be 0.2 or 0.24– a, B terms are dropped because it ~ 1

• At highest I values, Pitzer Equations are used

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At Very High Ionic Strengths, activities increase

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Effective I Ranges for Equations

• Debye-Hückel: I < 5 x 10-3M• Extended Debye-Hückel: 5 x 10-3 < I < 0.1• Davies or Truesdell-Jones: 0.1 < I < 0.5• Pitzer: I > 0.5• All these equations are empirical (based on lab

measurements, not theory)