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Concentrations vs. Activities

Concentrations vs. Activities. Remember: activities are “effective” concentrations E.g. the concentrations that control difference in chemical potential from standard state Activities ≠ concentrations Result from interactions of charged species

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Concentrations vs. Activities

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  1. Concentrations vs. Activities • Remember: activities are “effective” concentrations • E.g. the concentrations that control difference in chemical potential from standard state • Activities ≠ concentrations • Result from interactions of charged species • Cause “non-ideal” behavior of the ions in solution

  2. Interactions • Electrostatic: between charged ions • Hydration shells: water as a polar molecule • Interactions adds structure to solution: • Increase entropy • reduces free energy e.g., DG • lowers activity of ions • Not complexes – these are specific species, deal with separately

  3. Examples • Seawater: • Salinity 3.5% • Activity of water in seawater: aH2O, seawater ≈ 0.98 concentration of water in seawater: mH2O, seawater aH2O,seawater= 0.98mH2O,seawater • Fresh water • awater ≈ mwater • Recall • Activity coefficient, g = a/m • gseawater = 0.98

  4. How to determine g? • Must consider two types of solutes: • Uncharged species • Charged species

  5. Uncharged Species • Uncharged solutes in dilute water (i.e. close to ideal) • Here: a ~ m; g ~ 1 • There is no electrical interaction • Only change from hydration of ions • Since no charge though, little hydration

  6. For uncharged species in concentration solutions: • g > 1 • E.g., a > m • Why? • Results from hydration of charged species • “Removes” water from solution

  7. Activity coefficient of uncharged species: g = 100.1I Where I is ionic strength: I = ½ Smizi2 Essentially sum of charges in solution

  8. Ionic Strengths • Complicated to determine in natural waters: • Need a total analyses of all dissolved solids • Commonly approximated with major elements • Possible to estimate with TDS or SpC using empirical relationships

  9. Values depend on type of solution: • I ≈ 2 x 10-5(TDS); NaCl waters • I ≈ 2.5 x 10-5(TDS); “average” waters • I ≈ 2.8 x 10-5(TDS); CaHCO3 waters

  10. Or: • I ≈ 0.8 x 10-5(SpC); NaCl waters • I ≈ 1.7 x 10-5(SpC); “average” waters • I ≈ 1.9 x 10-5(SpC); CaHCO3 waters • SpC typically closer to ionic strength because it measures charge of solution

  11. Examples of Ionic strength • On board

  12. Charged Species • Problem with calculating g • To determine gi of single dissolved species, need to know how much G varies as concentrations of single species changes • Impossible to change just one ion - violates electrical neutrality • Generally calculated in terms of uncharged components, e.g., NaClo

  13. For dilute solution, assume change in single ion concentration • With assumptions, can estimate single ion activity coefficient • Calculated using various models • Debye-Hückel • Extended Debye-Hückel • Güntelberg equation • Davies equation • Pitzer equations - Complicated, but thermodynamically more rigorous

  14. Assumptions of all these models: • Charged species are point charges – i.e. 1 D, not true, all ions have mass so are 3D • All interaction are electrostatic • Boltzmann distribution around ions

  15. Expression for g • On board

  16. Seawater Davies Debye- Huckel Extended Debye- Huckel Debye- Huckel Davies Extended Debye- Huckel

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