Solubility of Salts

1. Solubility of Salts • A saturated solution of a salt is in a state of equilibrium • The solubility of a salt is the amount that dissolves at equilibrium • Usually reported as weight/volume (g/L or mg/L) • Can determine from equilibrium expression and amount of ions produced (use stoichiometric relationships) • Use saturation index to determine whether a solution is saturated with respect to a mineral • Can predict how much salt must dissolve or precipitate to reach equilibrium • Point at which IAP = Ksp

2. Changing solution composition due to precipitation • As salts precipitates, ratios of ions changes • The precipitation of a salt reduces the concentrations of ions and changes the chemical composition of remaining solution • The initial ratio of species can affect which minerals precipitate • GEOCHEMICAL DIVIDE • End up with a different final solution • May lead to precipitation of different minerals

3. Precipitation of Salts in Natural Waters • If 2 minerals have a common ion, we can determine the ratio of the couterions at equilibrium • The more insoluble mineral contributes a relatively small amount of the common ion • Replacement of 1 mineral by another is common in geology • Introduction of a common ion causes solution to become supersaturated with respect to the less soluble compound • Thus the more soluble compound is always replaced by less soluble • Makes sense: less soluble happier as solid, more soluble happier dissolved (relatively)

4. Supersaturation • Solutions in nature become supersaturatedwith respect to a mineral by: • Introduction of a common ion • Change in pH • Evaporative concentration • Temperature variations • In general solubilities increase with increasing T, but not always (e.g., CaCO3)

5. Calcite Solubility • Dissolution of calcite done primarily by acid • In natural systems, primary acid is CO2 • CO2(g) CO2(aq) • CO2(aq) + H2O  H2CO3 • CaCO3 + H2CO3 Ca2+ + 2HCO3- • Increasing PCO2 increases H2CO3, which increases amount of CaCO3 dissolved • Calcite cannot persist in even mildly acidic waters • Solubility of calcite decreases with increasing temperature

6. H2CO3

7. Incongruent Dissolution • KAlSi3O8 + 9H2O + 2H+ Al2Si2O5(OH)4 + 2K+ + 4H4SiO4 • If products such as K+and/or H4SiO4are removed by flowing groundwater, achieving equilibrium (saturation) may not be possible • Water/rock ratio is a key variable whether a chemical reaction achieve equilibrium in nature • The higher the water/rock ratio, the more likely the reaction goes to completion, not equilibrium • Products removed • If the ratio is small, the reactions can control the environment and equilibrium is possible

8. Geochemical Cycles and Kinetics (reaction rates)

9. Geochemical Cycles • Material is being cycled continuously in the Earth’s surface system • All chemical elements are cycled • We can think of the Earth’s surface as consisting of several reservoirs connected by “pipes” through which matter moves

10. Transfers between reservoirs d4,1n dt Reservoir 1 d1,2n dt Reservoir 4 Reservoir 2 d3,4n dt d2,3n dt Reservoir 3 n = component concentration t = time dn = rate of transfer of a component dt from one reservoir to another = Flux

11. Steady State • Steady state means that the composition of reservoirs in a cycle does not change over time • No accumulation or loss of the material of interest • Input + any production in the reservoir = outflow + any consumption in the reservoir • The mass balance = 0; no creation or loss of material • In the Earth surface environment, especially the oceans and atmosphere, cycling of materials has been occurring at near steady-state

12. Steady State Reservoir 1 d1,2n dt d2,3n dt d1,2n dt = Reservoir 2 d2n dt = 0 d2,3n dt Reservoir 3

13. Residence Time • Residence time is the average time a molecule spends in a reservoir between the time it arrives and the time it leaves • Determined by dividing the amount in the reservoir by the flux in (or out) 2n d1,2n dt T =

14. Cycles and reaction rates • As materials cycle through the Earth, they are moved and transformed at various rates (the “pipes” connecting reservoirs) • Transport processes and chemical reactions take time • Kinetics is the study of reaction rates

16. Kinetics vs. Thermodynamics • Thermodynamics tells us what should happen • All reactions tend to move towards equilibrium • Not concerned with time or steps involved in reaction • Only starting and ending points are of interest • Reactions cannot occur in contradiction to thermodynamics • Kinetics tells us whether a reaction actually does occur in a reasonable interval of time • Most geochemical reactions take place slowly • The reaction pathway is important • Kinetics is the study of what goes on in between the start and end points

17. Reaction Pathway • CaCO3 + H2CO3 Ca2+ + 2HCO3- • This is the overall reaction for calcite dissolution; there are actually many steps: • Dissolution and hydration of CO2(g) (→ H2CO3) • Transport of H2CO3 to mineral surface • Adsorption of H2CO3 to mineral surface • Detachment of products (Ca2+, HCO3-) from mineral surface • Transport of products to the bulk solution • There is a rate associated with each of these steps, and the rates may not be constant

18. Reaction Rates • Controlled by a variety of factors • Temperature • Generally rates increase as T increases • Concentrations of reactants and products • Mass transfer rates • Etc. • An overall (complete) reaction is the end product of several elementary reactions • Elementary reactions = reaction that actually occurs as written at molecular level • Each elementary reaction proceeds at its own rate • The rate of an overall reaction is controlled by the slowest step in the process

19. Overall vs. Elementary Reactions • Consider dissolution of nephaline to produce gibbsite • Elementary reactions: • NaAlSiO4(s) + 4H+ Al3+ + Na+ + H4SiO4 • Al3+ + 3H2O  Al(OH)3(s) + 3H+ • Overall reaction: • NaAlSiO4(s) + H+ 3H2O  Al(OH)3(s) + Na+ + H4SiO4 • Al3+ is a reactive intermediate that doesn’t persist • Because it is being both produced and consumed, Al3+ never reaches equilibrium concentration with respect to either nephaline or gibbsite • Add elementary reactions to get overall reaction

20. Groundwater and Partial Equilibrium • Low temperature systems (groundwater) can usually be described by partial equilibrium • For faster reactions, there is equilibrium between the water and rocks • For slow reactions, equilibrium is not achieved • Residence time: the longer water is in contact with rock, the higher the probability of equilibrium being reached. • In general (for near surface groundwater): • High temperature primary minerals unstable at near surface temperatures, are rarely in equilibrium with groundwater • Remember Bowen’s reaction series • Low temperature secondary minerals are generally at or near equilibrium

21. Reaction Pathway • Each step in an overall reaction has a rate • Oftentimes there is one step significantly slower than the others • The complete reaction can proceed only as fast as the slowest individual step • This step controls the overall rate; called the rate-determining step

22. Rate-Determining Step • Climb rungs • Sit • Slide • Go back to ladder “Reaction” Steps

23. Reaction Rates and Equilibrium • Rates decline with time as a reaction reaches equilibrium or goes to completion • In other words, the further away from equilibrium a reaction is, the more rapidly it occurs (in relative terms)

24. Slow Fast

25. Reaction Order • The rate of change of the concentration of a reactant generally varies as some power of its concentration • X  Y + Z • The consumption of reactant X • -d(X) = k(X)n dt • (X) = concentration of reactant X • t = time • n = reaction order (determined experimentally) • k = specific rate constant (determined experimentally) • Negative sign indicates the rate decreases with time as X reacts; as X is used up there is less of it to react so the rate slows down

26. Reaction Order • Reaction order determined by measuring how the initial reaction rate varies with the initial concentration of X • -d(X) = k(X)1: first order dt • -d(X) = k(X)2: second order dt • -d(X) = k(X)0: zeroth order dt • (rate doesn’t depend on reactant concentration) • Could be a fraction as well (e.g., 1/2)

27. Reaction Order

28. Reaction Order Examples • Zero: • Biodegradation when organic compound concentration is high • 1st: • Radioactive decay • Biodegradation at lower concentrations

29. Reaction Rates • As reactants react, products are produced • Rates can be expressed in terms of an increase in concentration of a product as well as the decrease in a reactant

30. X Y + Z

31. Rate Constants • X  Y + Z • Rate constants are determined experimentally by measuring concentration of reactant at known intervals of time

32. X Y + Z

33. Rate Constants • X  Y + Z • Rate constants are determined experimentally by measuring concentration of reactant at known intervals of time • k = rate constant; the larger it is, the faster the reaction • For 1st order rate, units = time-1 • n = reaction order

34. Rate Constant

35. Rate Constant • Plot ln(X) vs. t, get a straight line • Negative slope, concentration of reaction X decreases with time • Absolute value of slope = k

36. X Y + Z

37. Slope = -0.079 k = 0.079 sec-1

38. Temperature dependence of rates • Temperature has a strong influence on reaction rates • Consider X + Y  Z • X and Y must collide with sufficient energy to form a bond • Minimum energy is activation energy (Ea) • Ea acts as a barrier that must be overcome • Reaction rates ultimately depend on frequency with which atoms/molecules of reactants achieve necessary energy to form bonds

39. Activation energy (Ea)

40. Activation energy (Ea) • Ea explains why quartz does not usually control aqueous SiO2 concentrations • Equilibrium thermodynamics say it should • However, there is a high Ea for quartz dissolution that results in a long rate • Also helps explain why quartz is very resistant to chemical weathering

41. Ea and Arrhenius Equation • Ea can be determined experimentally • The Arrhenius Equation relates reaction rate to Ea and T: • k = rate • A = experimental constant for a specific reaction • R = gas constant • T in Kelvin • k ~doubles for every 10°C increase

42. Ea and Arrhenius Equation • Can re-write as • Get a straight line by plotting 1/T vs. log k • y = mx + b • Slope = • y intercept = log A

43. Radioactive decay • Radioactive decay follows a first-order rate law • A = rate of disintegration • k = rate constant • t = time

44. Radioactive decay • A = A0e-kt • Ao = initial radioactivity • Sometimes λ is used instead of k • Decay constant

45. Half Lives • ln(1) – ln(2) = -kt½ • ln(1) = 0 • t1/2 = half-life; the length of time required to remove half the initial concentration • these are known with precision

46. Half Lives • ln(1) – ln(2) = -kt½ • ln(1) = 0 • t1/2 = half-life; the length of time required to remove half the initial concentration • these are known with precision

47. Tritium • Half life = 12.3 yr • Decay constant? • k = 0.693/12.3 = 0.0563 yr-1 • How long before 75% gone? • t = -ln(0.25) / (0.0563) = 24.6 yr

48. Mass Transfer • There are 2 main processes transferring mass in the subsurface • Advection • Diffusion

49. Advection • Advection involves the displacement of matter in response to action of a force; it is a Flux (mass per time) • Groundwater flow = advection • Movement may provide reactants and remove products for reactions • Darcy’s Law is the governing law for groundwater flow

50. Darcy’s Law • F = K(h/L) • h/L = the hydraulic gradient • h = change in head; difference in the water elevation (measured in boreholes) between 2 points of an aquifer • L = the distance between those 2 points measured along the flow path • K = hydraulic conductivity (units = distance/time) • K is a measure of how easily water can flow through the rock or sediments; it is related to permeability