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Mixing in water

Mixing in water. Solutions dominated by water (1 L=55.51 moles H 2 O) a A =k H X A where K H is Henry’s Law coefficient – where is this valid? Low concentration of A. 1.0. Raoult’s Law – higher concentration ranges (higher X A ): m A = m A 0 +RTln G A X A

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Mixing in water

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  1. Mixing in water • Solutions dominated by water (1 L=55.51 moles H2O) • aA=kHXA where KH is Henry’s Law coefficient – where is this valid? Low concentration of A 1.0 Raoult’s Law – higher concentration ranges (higher XA): mA=mA0+RTlnGAXA where GA is Rauolt’s law activity coefficient aH2O aA Activity Ideal mixing 0.0 0.0 1.0 H2O Mol fraction A A

  2. Activity • Activity, a, is the term which relates Gibbs Free Energy to chemical potential: mi-G0i = RT ln ai • Why is there now a correction term you might ask… • Has to do with how things mix together • Relates an ideal solution to a non-ideal solution

  3. Activity II • For solids or liquid solutions: ai=Xigi • For gases: ai=Pigi = fi • For aqueous solutions: ai=migi Xi=mole fraction of component i Pi = partial pressure of component i mi = molal concentration of component i

  4. Activity Coefficients • Where do they come from?? • We think of ‘ideal’ as the standard state, but for dissolved ions, that is actually an infinitely dilute solution • Gases, minerals, and bulk liquids (H2O) are usually pretty close to 1 in waters • Dissolved molecules/ ions are have activity coefficients that change with concentration (ions are curved lines relating concentration and activity coefficients, molecules usually more linear relation)

  5. Application to ions in solution • Ions in solutions are obviously nonideal mixtures! • Use activities (ai) to apply thermodynamics and law of mass action ai = gimi • The activity coefficient, gi, is found via some empirical foundations

  6. Dissolved species gi • First must define the ionic strength (I) of the solution the ion is in: Where mi is the molar concentration of species i and zi is the charge of species I

  7. Activity Coefficients • Debye-Huckel approximation (valid for I: • Where A and B are constants (depending on T, see table 10.3 in your book), and a is a measure of the effective diameter of the ion (table 10.4)

  8. Different ways to calculate gi • Limiting law • Debye-Huckel • Davies • TJ, SIT models • Pitzer, HKW models

  9. Neutral species • Setchnow equation: • Logan=ksI For activity coefficient (see table 4-2 for selected coefficients)

  10. Law of Mass Action • Getting ‘out’ of the standard state: • Accounting for free energy of ions ≠ 1: m=m0 + RT ln P • Bear in mind the difference between the standard state G0 and m0 vs. the molar property G and m (not at standard state  25 C, 1 bar, a mole) GP – G0 = RT(ln P – ln P0) GP – G0 = RT ln P

  11. Equilibrium Constant • For a reaction of ideal gases, P becomes: for aA + bB  cC + dD • Restate the equation as: DGR – DG0R = RT ln Q • AT equilibrium, DGR=0, therefore: DG0R = -RT ln Keq where Keq is the equilibrium constant

  12. Assessing equilibrium If DGR – DG0R = RT ln Q, and at equilibrium DG0R = 0, then: Q=K Q  reaction quotient, aka Ion Activity Product (IAP) is the product of all products over product of all reactants at any condition K  aka Keq, same calculation, but AT equilibrium

  13. Solubility Product Constant • For mineral dissolution, the K is Ksp, the solubility product constant • Use it for a quick look at how soluble a mineral is, often presented as pK (table 10.1) DG0R = RT ln Ksp • Higher values  more soluble CaCO3(calcite) Ca2+ + CO32- Fe3(PO4)2*8H2O  3 Fe2+ + 2 PO43- + 8 H2O

  14. Ion Activity Product • For reaction aA + bB  cC + dD: • For simple mineral dissolution, this is only the product of the products  activity of a solid phase is equal to one CaCO3 Ca2+ + CO32- IAP = [Ca2+][CO32-]

  15. Saturation Index • When DGR=0, then ln Q/Keq=0, therefore Q=Keq. • For minerals dissolving in water: • Saturation Index (SI) = log Q/K or IAP/Keq • When SI=0, mineral is at equilibrium, when SI<0 (i.e. negative), mineral is undersaturated

  16. Calculating Keq DG0R = -RT ln Keq • Look up G0i for each component in data tables (such as Appendix F3-F5 in your book) • Examples: • CaCO3(calcite) + 2 H+ Ca2+ + H2CO3(aq) • CaCO3(aragonite) + 2 H+ Ca2+ + H2CO3(aq) • H2CO3(aq)  H2O + CO2(aq) • NaAlSiO4(nepheline) + SiO2(quartz)  NaAlSi3O8(albite)

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