Updated: 6 March 2018 Print version Lecture #4 Kinetics and Thermodynamics: Fundamentals of water and Ionic Strength (Stumm & Morgan, pp.1 15 Brezonik & Arnold, pg 10 18) (Benjamin, 1.2, 1.3, 1.5) David Reckhow CEE 680 #4 1 Molecular Weight and boiling point Organic Compounds: Homologous series Image from: http://chemed.chem.purdue.edu/genchem/topicrevie Image from: https://socratic.org/questions/how-does-molar-massaffect-boiling-point w/bp/ch14/liquids.php David Reckhow CEE 680 #4 2 1
Water and related heteroatoms Water is different Groups hydrides Image From: http://schoolbag.info/chemistry/central/100.html David Reckhow CEE 680 #4 3 Structure of Water S&M: Fig. 1.3 sp 3 hybridization 2 bonding and 2 non bonding orbitals Dipolar Character Origin of Water s Unusual properties High melting and boiling point High heat of vaporization Expands upon freezing High surface tension Excellent polar solvent S&M: Fig. 1.4 B: Fig 1.2 David Reckhow CEE 680 #4 4 2
Water s intermolecular structure Dominated by Hydrogen Bonds Ice Open tetrahedral structure Water Flickering cluster model 100 ps lifetime 0.1 ps molecular vibration Fig. 1.5a Pg. 8 Fig. 1.5b Pg. 8 David Reckhow CEE 680 #4 5 Solutes in Water Great solvent for ionic or ionizable substances Ion dipole bonds improves stability Energy increases with charge of ion and decreases with size Solvent hole model As solute water bonding strengthens compared to water water bonding, solubility goes up Hydrophilic solute Weak solute water bonds reduce solubility Hydrophobic solutes S&M: Fig. 1.6 B: Fig 1.4 David Reckhow CEE 680 #4 6 3
Periodic Table David Reckhow CEE 680 #4 7 H 4.5 H 2 O -1.74-1.74 Li 6.3 Li + 4.6 Be BeOH + (?) 9.2 Na 7.7 Na + Mg 7 Mg +2, MgSO 4 0.33 3.57 1.27 3.77 K 6.7 K + 1.99 4.23 680 Periodic Table Ca 5.9 Ca +2, CaSO 4 1.99 3.42 Sr 6.6 Sr +2 4.05 Ba 4.5 Ba +2 B 7.0 H 3 BO 4 3.39 Al 2 Al(OH) - 4 7.1 C 4.9 HCO 3-2.64 3.0 Si 3.8 H 4 SiO 4 4.15 3.8 N 6.3 N 2, NO 3-1.97 P 4 HPO 4-2 5.3 As HAsO 4-2 7.3 O 4.5 H 2 O, O 2-1.74-1.74 Ocean residence time (log yr) Predominant species River Water conc. ( log M) Seawater conc. ( log M) F 5.7 F -, MgF + 4.17 5.3 S 6.9 SO -2 4,NaSO - 4 Cl 7.9 Cl - 1.55 3.92 0.26 3.66 Se 4 SeO 3-2 8.6 Br 8 Br - 3.08 I 6 I -, IO - 3 6.3 6.8 David Reckhow CEE 680 #4 After S&M:Fig. 1.7, Pg. 10 8 8.8 8.15 6.96 8.6 He Ne Ar Kr 4
Law of Mass Action The rate of an elementary reaction is proportional to the product of the concentrations of the participating molecules, atoms or ions Chemical equilibria comes from the combination of two competing rates Consider the autodecomposition of water Other examples Equilibrium Quotients acid dissociation, Precipitation, Redox, Adsorption, volatilization David Reckhow CEE 680 #4 9 Effect of ph, water temp, chlorine concentration and log reduction on required Ct for disinfection of Giardia with free chlorine (US EPA SWTR Guidance Manual) from US EPA SWTR Regulations (units of Ct are mg L -1 min ) Ct Values for 1 log Inactivation of Giardia by free Chlorine C ph (temp = 5.0 degrees C) ph (temp= 20 degrees C) (mg/l) 6.0 6.5 7.0 7.5 8.0 6.0 6.5 7.0 7.5 8.0 0.1 32 39 46 55 66 12 15 17 28 33 0.5 33 40 47 56 67 12 15 18 28 34 1.0 35 42 50 60 72 13 16 19 30 36 1.5 37 44 52 63 77 14 17 20 32 38 2.0 39 46 55 67 81 15 17 21 33 41 Ct Values for 3 log Inactivation of Giardia by free Chlorine C ph (temp = 5.0 degrees C) ph (temp= 20 degrees C) (mg/l) 6.0 6.5 7.0 7.5 8.0 6.0 6.5 7.0 7.5 8.0 0.1 97 117 139 166 198 36 44 52 83 99 0.5 99 119 141 169 201 37 45 53 85 101 1.0 105 125 149 179 216 39 47 56 90 108 1.5 110 131 157 190 230 42 50 59 95 115 2.0 116 138 165 200 243 44 52 62 100 122 Borrowed David Reckhowfrom John Tobiason CEE 680 #4 10 5
Activity Activity is the effective or apparent concentration, which may be slightly different from the true analytical concentration These two differ substantially in waters with high TDS, such as sea water. We identify these two as follows: Curved brackets ({X}) indicate activity Square brackets ([X]) indicate concentration Usually this is molar concentration This may also be used when we re not very concerned about the differences between activity and concentration David Reckhow CEE 680 #4 11 Why the difference? Mostly long range interactions between uninterested bystanders (chemical species that are not involved in the reaction) and the two dancers of interest (those species that are reacting) Relative importance in determining activity Concentration >> charge > polarity > MW David Reckhow CEE 680 #4 12 6
Activity & Ionic Strength Equilibrium quotients are really written for activities, not concentrations in most natural waters activities are nearly equal to the molar concentrations In saline waters, we must account for differences between the two activity coefficients (f or γ) are used for this Ionic Strength (I) is used to determine the extent of correction David Reckhow CEE 680 #4 13 I A A K A 1 2 c d C D A a B b A f A A A A m i z i 2 Correlations for ionic strength µ vs. specific conductance: Russell Approximation µ = 1.6 x 10-5 x K (in µmho/cm) µ vs. TDS: Langlier approximation µ ~ 2.5 x 10-5 x TDS (in mg/l) David Reckhow CEE 680 #4 14 7
Equilibrium Constants Consider a simple acid/base reaction HA = H + + A The activity based constant is: The concentration based constant is: c K And a mixed constant would be: K K A HA K H A HA H A HA K H A H A H A HA HA HA H H A HA HA H A HA A David Reckhow CEE 680 #4 15 Corrections to Ion Activity Approximation Equation Applicable Range for I Debye-Hückel 2 log f 0.5z I <10-2.3 Extended Debye-Hückel Güntelberg Davies 2 I log f 0.5z <10-1 1 0.33a I I <10-1, solutions 2 log f 0.5z 1 I of multiple electrolytes I <0.5 2 log f 0.5z 0. 2I 1 I Based on: S&M, Table 3.3; B, Table 1.4a note: Mihelcic cites 0.3 David Reckhow CEE 680 #4 16 8
Ion Size Parameter Ion Size Ions Parameter, a (Å) 9 H + 8 Al +3, Fe +3 6 Mg +2 5 Ca +2, Zn +2, Cu +2, Sn +2 Mn +2, Fe +2 4 Na +, HCO - 3, H 2 PO - 4, CH 3 COO -, SO -2-4, HPO 4 2-3, PO 4 3 K +, Ag +, NH 4 +, OH -, Cl -, ClO 4 -, NO 3 -, I -, HS - See also: B, Table 1.4b David Reckhow CEE 680 #4 17 Debye Hückel Effect of charge (z) 1.2 f 1 0.8 0.6 0.4 0.2 0 Debye-Hückel -5-4 -3-2 -1 0 Log I z=1 z=2 z=3 z=4 David Reckhow CEE 680 #4 18 9
Extended Debye Hückel Benjamin: Figure 1.6a David Reckhow CEE 680 #4 19 Activity Coefficients compared Different approximations at low charge a=3 f 1.2 1 0.8 0.6 0.4 0.2 0 a=3 z=1-5 -4-3 -2-1 0 Log I DH EDH Guntelberg Davies David Reckhow CEE 680 #4 20 10
Act. Coeff. Comparison (cont.) Different Approximations at low charge a = 9 1.2 1 f 0.8 0.6 0.4 0.2 0 a=9 z=1-5 -4-3 -2-1 0 Log I DH EDH Guntelberg Davies David Reckhow CEE 680 #4 21 Act. Coeff. Comparison (cont.) Different Approximations at high charge 1.2 1 f 0.8 0.6 0.4 0.2 0 a=3 z=3-5 -4-3 -2-1 0 Log I DH EDH Guntelberg Davies David Reckhow CEE 680 #4 22 11
Comparison: CaCl 2 dissolution Benjamin, Figure 1.6b SIT is the specific interaction model Incorporates interactions between specific ions Quite accurate for high brines, but requires more coefficients David Reckhow CEE 680 #4 23 Activity Coefficients (cont.) For neutral species: log = ki k is a function of species, T and P k=0.13 for O 2 in NaCl in fresh water, I=0.002, O2 = 1.0006 Molar vs. Molal in principle, activity predictions are based on molal concentrations (mole/kg solvent), but since we are often most concerned with dilute solutions, we frequently use molar concentrations David Reckhow CEE 680 #4 24 12
Salting out Coefficients Compound k s (L/mole) Reference Tetrachloroethene 0.213 Gossett, 1987 Trichloroethene 0.186 Gossett, 1987 1,1,1-Trichloroethane 0.193 Gossett, 1987 1,1-Dichloroethane 0.145 Gossett, 1987 Chloroform 0.140 Gossett, 1987 Dichloromethane 0.107 Gossett, 1987 Benzene 0.195 Schwarzenbach et al., 1993 Toluene 0.208 Schwarzenbach et al., 1993 Naphthalene 0.220 Schwarzenbach et al., 1993 Oxygen 0.132 Snoeyink & Jenkins, 1980 David Reckhow CEE 680 #4 25 Activity for isotopes Most subtle of the effects For saline waters (chloride is counterion) Deuterium Oxygen 18 0.0022 0.0051 0.0016 0.0047 0.0025 0.0061 0.0111 Where () represents the molal concentration (moles/kg water) David Reckhow CEE 680 #4 26 13
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