Introduction Strong Electrolyte Weak Electrolyte Dissociation depends on concentration, model as reaction 8.2 Colligative properties Electrolyte dissociation changes concentration more than non-electrolyte (large dilution effect). Freezing pt. 5 g each acl 58.44g/mol, EG 62.7 g/mol, glucose 8 g/mol. Tf 27. K 27.7 K 272.7K. mole of each Tf 269.6 K 27.3 K 27.3 K smotic pressure,. mole of each Π 4.89 MPa 2.5 MPa 2.5 MPa Boiling pt elevation,. mole each Tb C.5 C.5C 2 8.3 Speciation H 2 l () H + ( aq) + H ( aq) K a, 298 H + [ ][ H ] 4 K a, 298 ΔG o 298 exp( RT) a H + a H --------------------- a H2 8.4 8.4 Concentration Scales and Standard States entity, superficial, apparent, nominal -- true -- molal - m i mol/(kg solvent) molarity - M i mol/l Standard States for electrolytes Standard State for water. K a 298, ( m H +γ H + m H γ H ) ( m o H + m o H a H2 ) m H +m H [ H + ][ H ] 3 4
8.5 Definition of ph ph log ( a H + ) 8.7 ph log [ H + ] 8.8 Solvent is important. 8.6 Thermodynamic etwork 8.7 Perspectives on Speciation 2H 2 () l H 3 + aq + Charge Balance ( ) H ( aq) AcH ( aq) + H 2 () l H 3 + aq + ( ) Ac ( aq) K VLE K SLE C 2 A ( v) C 2 A ( aq) C + aq C 2 A ( s) K a + ( ) CA ( aq) K sp K a2 2C + ( aq) + A 2 ( aq) 5 6 8.8 Acids and Bases Strong/Weak - Leveling effect - H 3 + H 2 H+ 4 + H Strong Acids - completely dissociate, superficial C A [Cl ] C A material balance for complete dissociation K a,w [H + ][H ] 4 equilibrium [H + ] [Cl ] + [H ] charge balance Proton Condition - [H + ] C A + [H ] proton condition Condition becomes [H + ] C A + K a,w /[H + ] Strong Bases - e.g. ah [a + ] C B material balance for dissociation K a,w [H + ][H ] 4 equilibrium [H + ] + [a + ] [H ] charge balance Proton Condition [H + ] + C B [H ] proton condition Condition becomes [H + ] + C B K a,w /[H + ] 7 8
Flood diagram -log [C(mol/L)] 2 4 6 8 2 4 4 4 2 4 6 8 2 2 8 6 4 2 - -2 Strong acid Strong Base -3-4 -5 Weak monoprotic acid - [A ] + [HA] C A material balance K a,a [H + ][A ]/[HA] equilibrium K a,w [H + ][H ] 4 equilibrium [H + ] [A ] + [H ] charge balance [HA] C A [ H + ] ([ H + ] + K aa, ) [ A ] K a, A C A ([ H + ] + K aa, ) undissociated acid (8.3) conjugate base (8.3) -6-7 -8 9 Weak monoprotic base - [a + ] [HA] + [A ] C B material balance K a,b [HA][H ]/[A ] equilibrium K a,w [H + ][H ] 4 equilibrium [H + ] + [a + ] [A ] + [H ] charge balance pk aa, + pk ab, pk aw, or K aa, K ab, K a, w Use pk a,a to plot Fluconazole + H 2 Fluconazole + + H ln(k a ).28 8/T F H F 8.9 Sillen Diagrams - seven steps. coordinates, strong acid/base lines. 2. material balance. 3. equil in acid form. 5. sketch acid and base equations. 6. proton condition to find intersection. 7. Check 2
Example 8.5 C B E-2 mol/l aac Step : The lines for [H + ] and [H ] have been drawn and labeled in the figure. Step 2: [a + ] [HAc] + [Ac ] C B material balance Step 3: K a [Ac ][H + ]/[HAc] equilibrium K w [H + ][H ] 4 equilibrium Step 4: [H + ] + [a + ] [Ac ] + [H ] charge balance Proton Condition - eliminate large terms from charge balance Polyprotic Acids (H 3 P 4, H 2 P 4, HP 2 4, P 3 4 ) [H 2 P 4 ] K -------------------- ---------- a [ H 3 P 4 ] [ H + ] [HP 2 4 ] K -------------------- a2 [HP 2 ---------- or 4 ] K -------------------- a K ---------------- a2 [H 2 P 4 ] [ H + ] [ H 3 P 4 ] [ H + ] 2 [P3 4 ] K -------------------- a3 [P3 ---------- or 4 ] K -------------------- a K a2 K ------------------------- a3 [HP 2 4 ] [ H + ] [ H 3 P 4 ] [ H + ] 3 The material balance on phosphorous is C [ H 3 P 4 ] + [ H 2 P 4 ] + [ HP2 4 ] + [P3 4 ] 3 4 ----- α 3 C [ H -------------------- 2 P 4 ] [ HP2 --------------------- 4 ] [P3 --------------------- 4 ] + + + -------------------- [ H 3 P 4 ] [ H 3 P 4 ] [ H 3 P 4 ] [ H 3 P 4 ] K a K ---------- a K a2 K ---------------- a K a2 K + + + ------------------------- a3 [ H + ] [ H + ] 2 [ H + ] 3 [ H α 3 P 4 ] 3 -------------------- C [ H + ] -------------------------------------------------------------------------------------------------------------- 3 [ H + ] 3 + K a [ H + ] 2 + K a K a2 [ H + ] + K a K a2 K a3 [ H α 2 P 4 ] [ H 2 --------------------- 3 P 4 ][ -------------------- H 2P 4 ] K --------------------- α a C C [ H 3 P 4 ] 3 ---------- [ H + ] ah 2 P 4, E-2 M, HCl, 5E-3 M ph 2 3 4 5 6 7 8 9 2 3 4 [H + ] [H ] - [H 3 P 4 ] [H 2 P 4 ] [HP 2 4 ] -2 5E-3 2 log[c(mol/l)] -3 [P 3 4 ] -4 [H + ]+[H 3 P 4 ] -5-6 -7-8 5 6
Amino Acids, H 2 H CH, pk a,a 2.35 H 2, pk a,a 9.78 glycinium glycine glycinate H 2 Gly + HGly Gly ph < 2.35 2.35 < ph < 9.78 ph > 9.78 + H 3 CH 2 CH + H 3 CH 2 C H 2 CH 2 C pk a 2.35 pk a 9.78 H 2 pk a,a.79 H 2 Lysine (Lys, K) H H pk a,a 3.9 H 2 H H H 2 Tryptophan (Trp, W) Aspartic Acid (Asp, D) H. M Glycine log[c(mol/l)] ph 2 3 4 5 6 7 8 9 2 3 4 - -2-3 -4-5 -6-7 -8 7 8 Buffers Isoelectric point mg /cm 3 4.5 4 3.5.5..2 3. 2.5 2.5.5 4.6 4.8 5 5.2 5.4 5.6 5.8 ph Salting In Donnan Equilibria membrane impermeable to DA α side a + Cl Cl a + β side Cl za + a + Cl DA z- a+ a + Cl Cl a + Salting ut 9 2
Solubility and Ksp Fluconazole, Example 8.8 and ln(k SLE ) 8.474 372.9/T K SLE a fluc( aq) Common Ion Effect KCl s ( ) K + ( aq) + Cl ( aq) K sp a K +a Cl K a,a [fluc][h + ]/([fluc + ]a H2 ) 2 22 Redox reactions - ILRIG Methane combustion - Li-Ion battery - LiC 6 C 6 + Li + + e, Co 2 Li + e + + LiCo 2, LiC 6 + Co 2 C 6 + LiCo 2 Half-cell rxns, relative to 2H + + 2e - H 2 g ( ) E E red E ox Potential per electron! Voltage and Gibbs Energy ΔG Faraday constant - 96,485 J/V. n e FE RTlnK a ΔG n e FE red + n e FE ox (equilibrium condition - dead when K a is reached. v v ΔG ΔG + RTln a i i or n e FE n e FE RTln a i i RT v E E -------- a i.596 v ernst Eq. n e F ln i E ------------------ a n log i i e Balancing, including non-redox. 23 24
Alkaline Battery Zn (s) and γ-mn 2(s) Zn (s), α-mnh (s)..596 E E ------------------ a Zn a log-------------------------------- MnH 2 a Zn a Mn2 a H2 Binding polynomials P 3 4 binding receptor for H + ligands Fuel Cell Biological Reactions Degree of reduction C d H a b c γ red (4d + a 2b)/d Glucose --> Ethanol 25 K bind a K a3 C P 3 [ H [ 4 ] + ] [ H ---------- + ] 2 [ H ---------------- + ] + + + ------------------------- 3 K a3 K a3 K a2 K a3 K a2 K a P 4 3 [ ]( + K bind a [ H + ] + K bind a K bind a2 [ H + ] 2 + K bind a K bind a2 K bind a3 [ H + ] 3 ) i ( ( ) + K [ H + ] + 2K 2 [ H + ] 2 + 3K 3 [ H + ] 3 ) -------------------------------------------------------------------------------------------------------- t P bind i P bind ik i [ x] i ---------- [ x] dpbind dlnp ------------- ------------------- bind dx [ ] dln[ x] P bind 26 Energy Carriers catabolic - anabolic exergonic - energonic coupling - ATP ADP + H 2 Adenine - - - - P P P 5' 4' H H D-Ribose ' H H 3' 2' H H Adenosine icotinamide (reduced) (oxidized) H H H - H 2 H 2 P + D-Ribose H H H 2 Adenine P - D-Ribose H P - - ATP 4, HATP 3, H 2 ATP 2, H 3 ATP, H 4 ATP, H 5 ATP + Standard State Transformed Gibbs Energy () Constant ph, pmg (2) Use apparent concentrations [ATP] sum of all ATP species ΔG ΔG + RT [] i ν i ln ΔG RTlnK c i ATP + H 2 ADP+ H 3 P 4 or ATP + H 2 ADP + P i [ ADP] [ P K c i ] ------------------------- [ ATP] ΔG f, ADP + ΔG f, Pi ΔG f, ATP ΔG exp f, H2 -------------------------------------------------------------------------------------------------------------- RT 27 28
Biological Fuel Cells Glucose --> Gluconolactone 2 --> H 2 2 on-ideal Solutions μ i μ i + RTln( m i γ i ) a a or m γ c γ ø Real Solution Ideal Solution air sat d V For biology, usually a ø e glucose --- ---- r r 2 r 2 Φ ρ ------- ± ( r) --------------- r ε r is radial position, Φ is electric potential, ρ ± (r) is charge distribution as a function of radial distance, ε ε o D, where ε o is the permittivity of a vacuum and D is the dielectric constant g(r) ~ exp( u Coul /kt) z log γ i2 A γ I i ---------------------- up to I. m + Ba I log γ s 2A γ M w, s ------------------------- Ba I ( Ba) 3 + ---------------------- 2 ln( + Ba I) + Ba I m or c standard state concentration m or c 2 3 a Φ -------------------------------------- lna s osmotic coefficient M w s, m i electrolytes 29 3 M w, s m i RT electrolytes Π ------ --------------------------------------Φ osmotic pressure V s Gibbs energies for electrolytes ΔG --------- T RT C ΔG T ----------- + ln a RT i i ΔG o 298 G f, 298 H + G f, 298 H + [ ] ν i Δ ( ) + ΔG f, 298 ( H ) ΔG o f, 298 ( H 2 () l ) Δ ( ) + ΔG f, 298 ( H ) + 237.8 79.98 kj/mol Transformed Gibbs Energies G' U TS + PV H μ H + Mg μ Mg 2+ Δ ΔG f T i,, H, i G f, T, H + I Mg, i G f, T, Mg 2+ I G f, T, j I Δ G f j,, ( I ph pmg) ΔG f, T, i () I { Δ () RTpH c ln( ) } { Δ () RTpMgln( ) } () ΔG f, T, j ( I) RTln( )z j2 A γ ( I ( + Ba I) ) T, ( I) --------------- ΔG 298.5 f, 298.5, j ( I) T + --------------- ΔH 298.5 f, 298.5, j ( I) 3 32
Gibbs Energies of Pseudoisomers ΔG f, T, i ( I, ph c, pmg) ΔG f, T, i( ) ( I, ph c, pmg) RTlnP bind ΔG P bind f, i( ) ΔG + -------------------------------------------------- f, i( 2) exp RT ΔG f, i( ) ΔG + exp-------------------------------------------------- f, i( 3) + RT P bind + --------- + -------------------- + ------------------------------ K a3 K a3 K a2 K a3 K a2 K a ( + K bind a + K bind a K bind a2 + K bind a K bind a2 K bind a3 ) r j ---------- P exp ΔG f, i( ) ΔG ------------------------------------------------- f, i() j bind RT ΔG f, T, i ΔG exp ------------------------------------------------ f, i() j ( RT) Example, ph c 7, pmg c 3, I.25 mol/kg [ ------------------- ATP 4 ] ---------- ---------------. P i P bind 9.7452 [ HATP 3 ] ------------------------ [ MgATP].2863 ----------------------- ---------------.3 9.7452 P i P i [ MgATP 2 ] 8.48 ---------------------------- ---------------.84 P i 9.7452 ΔG f, Pi ΔG f, Pi ( ) RTlnP bind 229.9.834( 298.5) ln9.7452 2297.5 kj/mol 33 34 Coupled Reaction and Phase Equilibria (Ideal Solutions only) Cl 2(aq) + H 2 H + + Cl + HCl (aq) a H +a Cl a HCl K a -------------------------------------- ( aq) E-3.348 a Cl2 a ( aq) H2 HCl (aq) H + + Cl a K H + a Cl a2 --------------------- a H 2 H + + H K H +a H w ------------------- a H2 a HCl ( aq) E-4 Write the VLE as reactions H K w a W /(y w P) / (P sat 2 ( v) H 2 () l w ) Ε 7.555 35 Cl 2( v) Cl 2( aq) log[c(mol/l)] K H [Cl 2(aq) ]/(y Cl2 P), Henry s Law ph 2 3 4 5 6 7 8 9 234 - -2-3 -4-5 -6-7 -8 [HCl] [Cl ] [H ] [H + ] 36