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Understanding Ionic Strength and Activity Coefficients in Aqueous Solutions

This text explores the differences between concentrations and activities in aqueous solutions, focusing on the interactions of charged species. It delves into electrostatic interactions and the importance of hydration shells formed by polar water molecules. The influence of these interactions on Gibbs free energy and the practical implications of salinity levels in seawater and fresh water are discussed. Additionally, it highlights the challenges in determining ionic strength in natural waters, and how ionic strengths can be estimated through total dissolved solids (TDS) and specific conductance (SpC) measurements.

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Understanding Ionic Strength and Activity Coefficients in Aqueous Solutions

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  1. Concentrations vs. Activities • Activities are not identical to concentrations • Result from interactions of charged species • Interactions • Electrostatic: between charged ions • Not complexes – that is dealt with differently • Hydration shells: water as a polar molecule • Interactions influence Gibbs free energy

  2. Practical applications • Most water less concentrated than seawater: • Salinity 3.5% • aseawater ≈ 0.98 mseawater • Fresh water • awater ≈ mwater • Recall • Activity coefficient, g = a/m

  3. Uncharged Species • Uncharged solutes in water close to ideal • E.g., a ~ m • There is no electrical interaction • Only change from hydration of ions

  4. For uncharged species: • g ~ 1 for dilute solution • Typically, g > 1 for concentrated solution • E.g., a > m • Why? • Results from hydration of charged species • “Removes” water from solution

  5. Activity coefficient of uncharged species: g = 100.1I Where I is ionic strength: I = ½ Smizi2

  6. Ionic Strengths • Complicated to determine in natural waters: • Need a total analyses of all dissolved solids, approximate with major elements • Possible to estimate with TDS or SpC

  7. Values depend on type of solution: • I ≈ 2X10-5(TDS); NaCl waters • I ≈ 2.5x10-5(TDS); “average” waters • I ≈ 2.8x10-5(TDS); CaHCO3 waters

  8. Or: • I ≈ 0.8X10-5(SpC); NaCl waters • I ≈ 1.7x10-5(SpC); “average” waters • I ≈ 1.9x10-5(SpC); CaHCO3 waters • SpC typically closer to ionic strength because it measures charge of solution

  9. Examples of Ionic strength • On board

  10. Charged Species • Problem • To determine gi = ai/mi, need to know how much G varies when m changes • Impossible to change just one ion (i), violates electrical neutrality • If one ion changes, then another oppositely charged specie changes • Generally calculated in terms of uncharge components, e.g., NaClo

  11. For dilute solution, assume change in single ion concentration • Can consider single ion activity coefficient

  12. Debye-Huckelfomulation • Reduction in “effective” concentrations results from: • Charged species surrouned by “cloud” of oppositely charge species – adds structure to solution • Charged species surrounded by “hydration sheath” – water as polar molecule

  13. Changes state variables: • Less random • Increases entropy • Reduces the G of the ion • Assumptions: • Charged species are point charges • All interaction are electrostatic • Boltzmann distribution around ions

  14. Expression for g • On board

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