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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
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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
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
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)
Law of Mass Action • Mathematical model that explains and predicts behaviors of solutions in equilibrium • Valid only for reversible reactions • For reaction: aA + bBcC + 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
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
Law of Mass Action • For reaction: aA + bBcC + 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…
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 undersaturatedwith respect to that mineral • If SI > 0, solution is oversaturated with respect to that mineral • Example…
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.”
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
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?
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
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
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
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
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
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
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
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
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
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)
Second Law of Thermodynamics • Not all heat is convertible to work • Every system left to itself will, on average, assume maximum randomness • Entropyis a measure of this “randomness”
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 alwaysincreases in a closed system • Entropy can decrease in an open system only if energy is received from an outside source
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
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
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 standardstate in introduced
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)
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)
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
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
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)
Entropy: Examples • Molecules in gas phase are more randomly distributed than liquid phase • Solutes more random than solid
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
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
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
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
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+ bBcC+ dD • Keq= [(C)c(D)d] [(A)a(B)b] • The Law of Mass Action can be derived from Gibbs free energy • GR = -RT lnKeq • R is the gas constant = 8.314 J/(T(K) mol) • GR = -5.708 log Keqat 25°C
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
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
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
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)
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= iCi • a = activity (effective concentration) • = activity coefficient (usually < 1) • C = concentration in moles • i = specific species • a < C in most situations
Equilibrium Constant and Activity • aA + bBcC + 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
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)
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
Activity coefficient • Recall a = m • decreases with increasing ionic strength and increasing charge • Calculated using empirical equations • Debye-Hückel (basic and extended) • Davies • Pitzer
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)