CEE 680 Lecture #15 2/18/2020 Print version Updated: 18 February 2020 Lecture #15 Kinetics and Thermodynamics: Fundamentals and Temperature effects (Stumm & Morgan, Chapt.2 ‐ 3 ) (Benjamin, Chapt 3,4) David Reckhow CEE 680 #15 1 Non ‐ ideal conditions Ionic strength (I or µ) Already talked about this (ionic strength corrections) Not zero (or infinite dilution) Temperature (T) Focus of this section Not 25°C Concentration (C ) Mostly of concern for G Not 1 M David Reckhow CEE 680 #15 2 1
CEE 680 Lecture #15 2/18/2020 Ionic Strength Effects Ideal or infinite dilution constants (K) are in terms of activity quotients These can be factored into molar concentrations and activity coefficients: { H } f [ B ] H B K B K f [ HB ] HB HB f [ H ] f [ B ] f { H }[ B ] B B H f [ HB ] f [ HB ] HB HB f f [ H ][ B ] B H K’ f [ HB ] HB c K David Reckhow CEE 680 #15 3 Operational Acidity Constants The common practice of using molar concentrations results in a conditional constant: [ H ][ B ] f c K K HB [ HB ] f f B H And pH measurements generally give us H + activity, so it’s often convenient to leave H + in these terms, which results in the mixed acidity constant: { H }[ B ] f C K Kf K HB H [ HB ] f B David Reckhow CEE 680 #15 4 2
CEE 680 Lecture #15 2/18/2020 Temperature Effects on rates Chemist's Approach: Arrhenius Equation Pre-exponential Factor Activation energy or frequency factor (ln ) 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 a T a = absolute temp ( o K) Engineer's Approach: Or more generally where T T o T 20 C k k k k o T o is any “baseline” T T T o 20 C o temperature Typical values: =1.02 to 1.15 David Reckhow 5 Determination of E a and A E / RT k Ae a a T Use Arrhenius equation a E 1 Take natural log of both ln k ln A a sides T R T a a Evaluate slope and intercept See: equation 3.4 (pg83) in Benjamin, 2015 David Reckhow CEE 680 #15 6 3
CEE 680 Lecture #15 2/18/2020 G Catalysis G A Catalyst enhances rates reactants by providing alternative pathways with lower activation products energies Reaction coordinate It is not “consumed” in the reaction Homogeneous Acid/base catalysis Trace metal catalysis Heterogeneous Reactions on particle surfaces Reactions mediated by microorganisms (enzymes) Engineered surface catalysis Catalytic converters, activated carbon David Reckhow CEE 680 #15 7 Chapt 2: Basics Thermodynamics Will tell you which reactions are favorable or “Possible” Sets limits composition of systems at equilibrium Won’t tell you how quickly the reactions proceed good for systems with constant P & T Air: 1.0 atm at sea level Water: 1.0 atm for each additional 10.7 m of water Earth: wt of overlying rock and soil Governing property @ const. T&P is the Gibbs Free Energy for constant T&V, it is the Helmholtz Free Energy David Reckhow CEE 680 #15 8 4
CEE 680 Lecture #15 2/18/2020 Gibbs Free Energy Combines enthalpy and entropy 1st and 2nd laws of thermodynamics Determines whether a reaction is favorable or spontaneous Practical form is based on an arbitrary datum the pure and most stable form of each element at standard state o o o G H T S David Reckhow CEE 680 #15 9 Standard State About: Standard State 1 mole/L for dissolved substances 1 atmosphere for gases Conditions: Unit activity (a=1) Rarely encountered in practice; but easier to base calculations on State variables: G o , µ o Non ‐ standard State Conditions: Non ‐ unit activity, often quite low This is the “real world” State Variables: G , µ David Reckhow CEE 680 #15 10 5
CEE 680 Lecture #15 2/18/2020 Enthalpy A fundamental thermodynamic variable enthalpy change is equal to heat of reaction (for systems at constant pressure) H<0, heat is given off exothermic H>0, heat is absorbed endothermic H can be calculated from standard enthalpies of formation ( H o f ) available in many texts o o H H e.g., Snoeyink & Jenkins, Table 3 ‐ 1 i f David Reckhow CEE 680 #15 11 Example H 2 O (g ) Evaporation of water H 2 O (l) H 2 O (l) = H 2 O (g) H 2 O (g) H 2 O (l) o o H H i f 1 mole 57 . 80 kcal 1 mole 68 . 32 kcal mole mole 10 . 52 kcal H>0, heat is absorbed endothermic However, this does not tell us if the reaction is favorable, or proceeds spontaneously to answer this we need to know the entropy change David Reckhow CEE 680 #15 12 6
CEE 680 Lecture #15 2/18/2020 Thermodynamic Constants for Species of Importance in Water Chemistry (Table 3 ‐ 1 from Snoeyink & Jenkins) Part I o o o o Species H G Species H G f f f f kcal/mole kcal/mole kcal/mole kcal/mole Ca +2 (aq) -2 (aq) CO 3 -129.77 -132.18 -161.63 -126.22 CH 3 COO - , CaC0 3 (s), calcite -288.45 -269.78 -116.84 -89.0 acetate H + (aq) CaO (s) -151.9 -144.4 0 0 C(s), graphite H 2 (g) 0 0 0 0 Fe +2 (aq) CO 2 (g) -94.05 -94.26 -21.0 -20.30 Fe +3 (aq) CO 2 (aq) -98.69 -92.31 -11.4 -2.52 CH 4 (g) Fe(OH) 3 (s) -17.889 -12.140 -197.0 -166.0 Mn +2 (aq) H 2 CO 3 (aq) -167.0 -149.00 -53.3 -54.4 - (aq) HCO 3 MnO 2 (s) -165.18 -140.31 -124.2 -111.1 Conversion: 1kcal = 4.184 kJ David Reckhow CEE 680 #15 13 Thermodynamic Constants for Species of Importance in Water Chemistry (Table 3 ‐ 1 from Snoeyink & Jenkins) Part II o o o o Species Species H G H G f f f f kcal/mole kcal/mole kcal/mole kcal/mole Mg +2 (aq) -110.41 -108.99 O 2 (g) 0 0 OH - (aq) Mg(OH) 2 (s) -221.00 -199.27 -54.957 -37.595 - (aq) NO 3 -49.372 -26.43 H 2 O (g) -57.7979 -54.6357 NH 3 (g) -11.04 -3.976 H 2 O (l) -68.3174 -56.690 -2 NH 3 (aq) -19.32 -6.37 SO 4 -216.90 -177.34 + (aq) NH 4 -31.74 -19.00 HS (aq) -4.22 3.01 HNO 3 (aq) -49.372 -26.41 H 2 S(g) -4.815 -7.892 O 2 (aq) -3.9 3.93 H 2 S(aq) -9.4 -6.54 Conversion: 1kcal = 4.184 kJ David Reckhow CEE 680 #15 14 7
CEE 680 Lecture #15 2/18/2020 A measure of a system’s Entropy randomness remove the partition and randomness T=0 V 1 , c 1 V 2 , c 2 increases 2nd law of Thermo. o o S S T=1 i f Spontaneous in isolated T=2 system Like water running downhill Or hot objects heating colder ones T=large David Reckhow CEE 680 #15 15 Gibbs Energy of a System Fig. 2.5 G Changes as reaction Pg. 45 progresses due to changing concentrations G reaches a minimum at the point of equilibrium dG G d Extent of reaction David Reckhow CEE 680 #15 16 8
CEE 680 Lecture #15 2/18/2020 o Convention The G f o values are essentially G’s for the Since the G f formation of chemical substances from the “most stable” (reference) forms of their constituent elements o values for those most stable elemental forms are The G f zero, by definition Examples Zero ‐ valent, Metallic Ag, Al, Fe, Mn, Pb, Zn graphite ‐ C, white ‐ P, rhombic ‐ S diatomic H 2 , I 2 , N 2 , O 2 David Reckhow CEE 680 #15 17 Simple examples Reaction o G H 2 (g) + S (s) = H 2 S (aq) -27.87 H 2 (g) + S (s) = H 2 S (g) -33.56 O 2 (g) + S (s) = SO 2 (g) -300.2 Hg (l) + S (s) = HgS (s) -43.3 H 2 (g) + ½O 2 (g) = H 2 O (l) -237.18 O 2(g) = O 2 (aq) 16.32 o equal to zero, i.e., they are In all of these cases reactants have a G f the reference forms of the elements so the G o is simply equal to the G f o of the product compound David Reckhow CEE 680 #15 18 9
CEE 680 Lecture #15 2/18/2020 Solving problems with G o o G Recall, at any T & P: i i G can be calculated at 25 o C from But for STP, we use: standard gibbs free energies of o o G G formation (G o f ) i f These are essentially G’s for the formation of chemical substances from the most stable forms of their constituent elements available in many texts e.g., Stumm & Morgan, Appendix 3 In: kJ/mole e.g., Benjamin, Table 2.1 In: kcal/mole e.g., Snoeyink & Jenkins, Table 3 ‐ 1 Conversion: 1kcal = 4.184 kJ David Reckhow CEE 680 #15 19 Ammonia Problem (1/7) Determine G o for dissolution of ammonia in water at 25 o C NH ( g ) NH ( aq ) 3 3 Based on example 2.5 in text Two approaches A. Determine G o directly from individual G o f ’s The easiest way B. Determine G o from H o and S o o o o G H T S David Reckhow CEE 680 #15 20 10
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