Concentrations vs. Activities Activities ≠ concentrations Activities ≠ concentrations Activities are “effective” concentrations Activities are “effective” concentrations Interactions between ions and solutes that change chemical potential from standard state Interactions between ions and solutes that change chemical potential from standard state Cause “non-ideal” behavior of the ions in solution Cause “non-ideal” behavior of the ions in solution

Interactions Interactions Electrostatic: between charged ions Electrostatic: between charged ions Hydration shells: water as a polar molecule Hydration shells: water as a polar molecule Interactions add structure to solution: Interactions add structure to solution: Increase entropy Increase entropy reduces free energy e.g.,  G reduces free energy e.g.,  G May lower effect concentration of ions May lower effect concentration of ions Not complexes – these are specific species Not complexes – these are specific species May use  G to calculate stability - later May use  G to calculate stability - later

Examples Fresh water Fresh water a water ≈ m water a water ≈ m water Seawater: Seawater: Salinity 3.5% Salinity 3.5% Activity of water in seawater: a H2O, seawater ≈ 0.98 concentration of water in seawater: m H2O, seawater Activity of water in seawater: a H2O, seawater ≈ 0.98 concentration of water in seawater: m H2O, seawater a H2O,seawater = 0.98m H2O,seawater Recall Recall Activity coefficient,  = a/m Activity coefficient,  = a/m  seawater = 0.98  seawater = 0.98

How to determine  ? Must consider two types of solutes: Must consider two types of solutes: Uncharged species Uncharged species Charged species Charged species

Uncharged Species Uncharged solutes in dilute water (i.e. close to ideal) Uncharged solutes in dilute water (i.e. close to ideal) Here: a ~ m;  ~ 1 Here: a ~ m;  ~ 1 There is no electrical interaction There is no electrical interaction No hydration of the uncharged species No hydration of the uncharged species The charged ions are hydrated The charged ions are hydrated

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

Activity coefficient of uncharged species: Activity coefficient of uncharged species:  = I Where I is ionic strength: I ≡ ½  m i z i 2 Essentially sum of charges in solution

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

Values depend on type of solution: Values depend on type of solution: I ≈ 2 x (TDS); NaCl waters I ≈ 2 x (TDS); NaCl waters I ≈ 2.5 x (TDS); “average” waters I ≈ 2.5 x (TDS); “average” waters I ≈ 2.8 x (TDS); CaHCO 3 waters I ≈ 2.8 x (TDS); CaHCO 3 waters

Or: Or: I ≈ 0.8 x (SpC); NaCl waters I ≈ 0.8 x (SpC); NaCl waters I ≈ 1.7 x (SpC); “average” waters I ≈ 1.7 x (SpC); “average” waters I ≈ 1.9 x (SpC); CaHCO 3 waters I ≈ 1.9 x (SpC); CaHCO 3 waters SpC typically closer to ionic strength because it measures charge of solution SpC typically closer to ionic strength because it measures charge of solution

Examples of Ionic strength On board On board

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

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

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

Expression for  On board On board

Seawater Debye- Huckel range of I Extended Debye- Huckel range of I Davies range of I Debye- Huckel Extended Debye- Huckel Davies