Print version Updated: 18 September 2019 CEE 370 Environmental Engineering Principles Lecture #6 Environmental Chemistry IV: Thermodynamics, Equilibria, Acids-bases I Reading: Mihelcic & Zimmerman, Chapter 3 Davis & Masten, Chapter 2 Mihelcic, Chapt 3 David Reckhow CEE 370 L#6 1
Kinetics Base Hydrolysis of dichloromethane (DCM) Forms chloromethanol (CM) and chloride Classic second order reaction (molecularity of 2) − − − − d [ DCM ] d [ OH ] d [ CM ] d [ Cl ] − = = = = = Rate k [ DCM ][ OH ] dt dt dt dt First order in each reactant, second order overall 2 CEE 370 L#5 David Reckhow
Kinetic principles Law of Mass Action For elementary reactions + → k aA bB products rate = a b kC A C B where, C A = concentration of reactant species A, [moles/liter] C B = concentration of reactant species B, [moles/liter] a = stoichiometric coefficient of species A b = stoichiometric coefficient of species B k = rate constant, [units are dependent on a and b] 3 CEE 370 L#5 David Reckhow
Kinetics: zero order Reactions of order dc = − “n” in reactant “c” kc n dt When n=0, we 90 have a simple 80 = − c c kt zero-order 70 Concentration o 60 reaction 50 Example: 40 biodegradation of 30 Slope 2,4-D 20 = 10 k mg l / / min 10 dc 0 = − k 0 20 40 60 80 dt Time (min) 4 CEE 370 L#5 David Reckhow
Kinetics: First Order When n=1, dc = − 1 A => products kc we have a dt simple first- order reaction 90 80 This results in − = kt c c e 70 Concentration an o 60 “exponential 50 40 decay” 30 Example: 20 decay of − k = 1 0 032 . min 10 137 Cs from 0 Chernobyl 0 20 40 60 80 accident Time (min) 5 CEE 370 L#5 David Reckhow
Kinetics: First Order (cont.) dc = − 1 kc This equation dt can be linearized good for assessment of “k” from data 6 CEE 370 L#5 David Reckhow
dc Kinetics: Second Order = − 2 kc dt When n=2, we have a simple second-order reaction A + A => products This is a reaction 90 1 between two 80 = c c 70 + identical o 1 kc t Concentration 60 o molecules 50 More common to 40 = 0 0015 k . L mg / / min have different 30 20 molecules 10 reacting (see next 0 slide) 0 20 40 60 80 Time (min) 7 CEE 370 L#5 David Reckhow
Kinetics; Pseudo-1 st Order When you have two different species reacting via 2 nd order kinetics overall dc dc = = − A B kc c A + B => products A B dt dt If one reactant (c B ) is present in great excess versus the other, the concentration of that one can be treated as constant and folded into the rate constant to get a pseudo-first order reaction dc = − = A k c k kc where obs A obs B dt From here you can use the first order equations 8 CEE 370 L#5 David Reckhow
Comparison of Reaction Orders Curvature: 2nd>1st>zero 90 80 Zero Order 70 Concentration 60 First Order 50 Second Order 40 30 20 10 0 0 20 40 60 80 Time (min) 9 CEE 370 L#5 David Reckhow
Half-lives Time required for initial concentration to drop to half, ie., c=0.5c o For a zero order reaction: 0 . 5 c 1 = t o = − = − c c kt 0 . 5 c c kt k o o o 1 2 2 For a first order reaction: ln( 2 ) = t − kt − = = 1 kt 1 c c e 0 . 5 c c e k 2 2 o o o 0 . 693 = Try example 3.5 & 3.6 in Mihelcic k 10 CEE 370 L#5 David Reckhow
Temperature Effects Temperature Dependence • Chemist's Approach: Arrhenius Equation Activ ivat ation en ener ergy (ln ) = Pre re-exponen ential F Fac actor d k E a − = E / RT k Ae a a 2 dT RT T a a a R = universal gas constant − = E ( T 293 )/ RT 293 k k e a a a = 1.987 cal/ o K/mole T o 293 K T a = absolute temp ( o K) a • Engineer's Approach: Or more generally − = θ T T o − = θ k k T 20 C k k o where T o is any T T T o 20 C o “baseline” temperature Typical values: θ =1.02 to 1.15 11 David Reckhow
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 12 CEE 370 L#6 David Reckhow
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) 13 CEE 370 L#6 David Reckhow
Activity & Ionic Strength { } { } c d C D K = Equilibrium quotients are really written { } { } a b A B for activities, not concentrations in most natural waters activities are { } [ ] A ≈ A nearly equal to the molar concentrations [ ] { } = In saline waters, we must account for A f A A differences between the two [ ] { } = γ A A activity coefficients (f or γ ) are used for this A Ionic Strength (I or µ) is used to determine the extent of correction ∑ µ = 2 I or C i z 1 i 2 14 CEE 370 L#6 David Reckhow
µ Corrections From textbook Mihelcic & Zimmerman 15 CEE 370 L#6 David Reckhow
Correlations for ionic strength µ vs. specific conductance: Russell Approximation µ = 1.6 x 10 -5 x K (in µmho/cm) Equ 3.3 µ vs. TDS: Langlier approximation µ ~ 2.5 x 10 -5 x TDS (in mg/L) Equ 3.2 16 CEE 370 L#6 David Reckhow
Corrections to Ion Activity Approximation Equation Applicable Range for I <10 -2.3 Debye-Hückel = − 2 log f 0 . 5 z I <10 -1 Extended I = − 2 log f 0 . 5 z Debye-Hückel + 1 0 . 33 a I <10 -1 , solutions Güntelberg I = − 2 log f 0 . 5 z of multiple + 1 I electrolytes Davies <0.5 I = − 2 − log f 0 . 5 z 0 . 2 I + 1 I From Stumm & Morgan, Table 3.3 (pg.103) 0.3, based on Mihelcic 17 CEE 370 L#6 David Reckhow
Kinetic model for equilibrium Consider a reaction as The rates are: follows: b = r k { C }{ D } f = r k { A }{ B } b f And at equilibrium the A + B = C + D two are equal, r f =r b Since all reactions are = reversible, we have two k { A }{ B } k { C }{ D } f b possibilities We then define an equilibrium constant (K eq ) k + → + A B C D f k { C }{ D } ≡ f = K + ← + A B C D eq k { A }{ B } k b b 18 CEE 370 L#6 David Reckhow
Kinetic model with moles In terms of molar concentrations, the rates are: [ ] [ ] D [ ] [ ] B = γ γ = γ γ r k C D r k A B f f A b b C And at equilibrium the two are equal, r f =r b [ ] [ ] [ ] [ ] D γ γ = γ γ k A B k C D f A B b C And solving for the equilibrium constant (K eq ) [ ] [ ] [ ][ ] k γ γ γ γ C D C D ≡ f = = K C D C D [ ] [ ] [ ][ ] eq γ γ γ γ k A B A B b A B A B 19 CEE 370 L#6 David Reckhow
Equilibrium Chemistry Tells us what direction the reaction is headed in Doesn’t tell us how fast the reaction is going (kinetics) Solving equilibrium problems identify reactants and products formulate equations equilibrium equations mass balance equations electroneutrality equation solve equations 20 CEE 370 L#6 David Reckhow
Temperature Effects on K Need ∆ H (enthalpy change) ∆ H < 0, exothermic (heat evolved) ∆ H > 0, endothermic (heat absorbed) The Van’t Hoff Equation: ( ) ∆ o − K = H T T log 2 2 1 K 2 . 303 RT T 1 2 1 Log K recall that: ∑ ∆ ∆ o = ν o H H 1/T i f 21 CEE 370 L#6 David Reckhow
Acids & Bases pH of most mineral-bearing waters is 6 to 9. (fairly constant) pH and composition of natural waters is regulated by reactions of acids & bases chemical reactions; mostly with minerals carbonate rocks: react with CO 2 (an acid) CaCO 3 + CO 2 = Ca +2 + 2HCO 3 - other bases are also formed: NH 3 , silicates, borate, phosphate acids from volcanic activity: HCl, SO 2 Biological reactions: photosynthesis & resp. Sillen: Ocean is result of global acid/base titration 22 CEE 370 L#6 David Reckhow
Acids & Bases (cont.) Equilibrium is rapidly established proton transfer is very fast we call [H + ] the Master Variable because Protons react with so many chemical species, affect equilibria and rates Strength of acids & bases strong acids have a substantial tendency to donate a proton. This depends on the nature of the acid as well as the base accepting the proton (often water). 23 CEE 370 L#6 David Reckhow
pH: the intensity factor Alkalinity: a capacity factor 24 CEE 370 L#6 David Reckhow
Recommend
More recommend
