1 / 17

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

chiko
Download Presentation

Mixing in water

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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)

More Related