Introduction Strong Electrolyte Weak Electrolyte Dissociation depends on concentration, model as reaction 1
18.2 Colligative properties Electrolyte dissociation changes concentration more than non-electrolyte (large dilution effect). Freezing pt. 5 g each NaCl 58.44g/mol, EG 62.07 g/mol, glucose 180 g/mol. Tf 270.0 K 271.7 K 272.7K 0.1 mole of each Tf 269.6 K 271.3 K 271.3 K smotic pressure, 0.1 mole of each Π 4.89 MPa 2.5 MPa 2.5 MPa Boiling pt elevation, 0.1 mole each Tb 101 C 100.5 C 100.5C 2
18.3 Speciation H 2 l + () H + ( aq) H ( aq) 18.4 K a, 298 H + [ ][ H ] 10 14 K a, 298 ΔG o 298 exp( RT) a H + a H --------------------- a H2 3
18.4 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 ] 4
18.5 Definition of ph ph log 10 ( a H + ) ph log 10 [ H + ] Solvent is important. 18.6 Thermodynamic Network C 2 A ( v) 18.7 18.8 K VLE K SLE C 2 A ( aq) C + aq C 2 A ( s) K a1 + ( ) CA ( aq) K sp K a2 2C + ( aq) + A 2 ( aq) 5
18.7 Perspectives on Speciation 2H 2 () l H 3 + aq Charge Balance + ( ) H ( aq) AcH ( aq) + H 2 () l H 3 + aq + ( ) Ac ( aq) 6
18.8 Acids and Bases Strong/Weak - Leveling effect - NH 3 + H 2 NH+ 4 + H Strong Acids - completely dissociate, superficial C A [Cl ] C A material balance for complete dissociation K a,w [H + ][H ] 10 14 equilibrium [H + ] [Cl ] + [H ] charge balance 7
Proton Condition - [H + ] C A + [H ] proton condition Condition becomes [H + ] C A + K a,w /[H + ] Strong Bases - e.g. NaH [Na + ] C B material balance for dissociation K a,w [H + ][H ] 10 14 equilibrium [H + ] + [Na + ] [H ] charge balance Proton Condition [H + ] + C B [H ] proton condition Condition becomes [H + ] + C B K a,w /[H + ] 8
Flood diagram 0 2 4 6 8 10 12 14 0 0 14 14 0 2 4 6 8 10 12 12 10 8 6 4 2-1 -2 -log [C(mol/L)] -3-4 -5 Strong acid Strong Base -6-7 -8 9
Weak monoprotic acid - [A ] + [HA] C A material balance K a,a [H + ][A ]/[HA] equilibrium K a,w [H + ][H ] 10 14 equilibrium [H + ] [A ] + [H ] charge balance [HA] C A [ H + ] ([ H + ] + K aa, ) [ A ] K a, A C A ([ H + ] + K aa, ) undissociated acid (18.30) conjugate base (18.31) 10
Weak monoprotic base - [Na + ] [HA] + [A ] C B material balance K a,b [HA][H ]/[A ] equilibrium K a,w [H + ][H ] 10 14 equilibrium [H + ] + [Na + ] [A ] + [H ] charge balance pk aa, pk ab, + pk aw, or K aa, K ab Use pk a,a to plot, K a, w 11
Fluconazole N N N N N N + H 2 Fluconazole + + H H F ln(k a ) 1.28 8000/T F 18.9 Sillen Diagrams - seven steps 1. 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 12
Example 18.5 C B 1E-2 mol/l NaAc Step 1: The lines for [H + ] and [H ] have been drawn and labeled in the figure. Step 2: [Na + ] [HAc] + [Ac ] C B material balance Step 3: K a [Ac ][H + ]/[HAc] equilibrium K w [H + ][H ] 10 14 equilibrium Step 4: [H + ] + [Na + ] [Ac ] + [H ] charge balance Proton Condition - eliminate large terms from charge balance 13
Polyprotic Acids (H 3 P 4, H 2 P 4, HP 4 2, P 4 3 ) [H 2 P 4 ] -------------------- [ H 3 P 4 ] [HP 2 4 ] -------------------- [H 2 P 4 ] [P3 4 ] -------------------- [HP 2 4 ] K a1 ---------- [ H + ] K a2 ---------- [ H + ] K a3 ---------- [ H + ] or or [HP 2 4 ] -------------------- [ H 3 P 4 ] [P3 4 ] -------------------- [ H 3 P 4 ] K a1 K ---------------- a2 [ H + ] 2 The material balance on phosphorous is K a1 K a2 K ------------------------- a3 [ H + ] 3 C [ H 3 P 4 ] + [ H 2 P 4 ] + [ HP2 4 ] + [P3 4 ] 14
----- 1 α 3 C [ H -------------------- 1 2 P 4 ] [ HP2 --------------------- 4 ] [P3 --------------------- 4 ] + + + -------------------- [ H 3 P 4 ] [ H 3 P 4 ] [ H 3 P 4 ] [ H 3 P 4 ] K 1 a1 K ---------- a1 K a2 K ---------------- a1 K a2 K + + + ------------------------- a3 [ H + ] [ H + ] 2 [ H + ] 3 [ H α 3 P 4 ] 3 -------------------- C -------------------------------------------------------------------------------------------------------------- [ H + ] 3 [ H + ] 3 + K a1 [ H + ] 2 + K a1 K a2 [ H + ] + K a1 K a2 K a3 [ H α 2 P 4 ] [ H 2 --------------------- 3 P 4 ][ -------------------- H 2P 4 ] K --------------------- α a1 C C [ H 3 P 4 ] 3 ---------- [ H + ] 15
NaH 2 P 4, 1E-2 M, HCl, 5E-3 M -1-2 5E-3 log[c(mol/l)] ph 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14-3 -4-5 [H + ] [H ] [H 3 P 4 ] [H 2 P 4 ] [HP 4 2 ] 2 1 [P 3 4 ] [H + ]+[H 3 P 4 ] -6-7 -8 16
Amino Acids, N H 2 H CH, pk a,a 2.35 NH 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 NCH 2 CH + H 3 NCH 2 C H 2 NCH 2 C pk a 2.35 pk a 9.78 H 2 N pk a,a 10.79 H 2 N Lysine (Lys, K) H H pk a,a 3.9 H 2 N H NH H 2 N Tryptophan (Trp, W) Aspartic Acid (Asp, D) H 17
0.1 M Glycine ph 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14-1 -2 log[c(mol/l)] -3-4 -5-6 -7-8 18
Buffers Isoelectric point mg N/cm 3 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 Salting In 0.005N 0.01N 0.02N 0.001N 4.6 4.8 5 5.2 5.4 5.6 5.8 ph Salting ut 19
Donnan Equilibria membrane impermeable to DNA α side Na + Cl Cl Na + β side Cl zna + Na + Cl DNA z- Na+ Na + Cl Cl Na + 20
Solubility and Ksp Fluconazole, Example 18.8 and ln(k SLE ) 8.474 3721.9/T K SLE a fluc( aq) K a,a [fluc][h + ]/([fluc + ]a H2 ) 21
Common Ion Effect KCl s + K sp a K +a Cl ( ) K + ( aq) Cl ( aq) 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 ( ) 23
E E red E ox Potential per electron! Voltage and Gibbs Energy Faraday constant - 96,485 J/V. ΔG n e FE red + n e FE ox (equilibrium condition - dead when K a is reached. or ΔG Balancing, including non-redox. n e FE RTlnK a v v ΔG ΔG + RTln a i i n e FE n e FE RTln a i i RT v E E -------- a i 0.05916 v n e F ln i E ------------------ a i n log i e Nernst Eq. 24
Alkaline Battery Zn (s) and γ-mn 2(s) Zn (s), α-mnh (s). E E Fuel Cell 0.05916 ------------------ a Zn a log-------------------------------- MnH 2 a Zn a Mn2 a H2 Biological Reactions Degree of reduction C d H a b N c γ red (4d + a 2b)/d Glucose --> Ethanol 25
Binding polynomials P 3 4 binding receptor for H + ligands K bind a1 1 K a3 C [ P 3 4 ] 1 i + [ ---------- H + ] + ---------------- [ H + ] 2 + ------------------------- [ H + ] 3 K a3 K a3 K a2 K a3 K a2 K a1 [ P 3 4 ] 1 K bind a1 H + ( + [ ] + K bind a1 K bind a2 [ H + ] 2 + K bind a1 K bind a2 K bind a3 [ H + ] 3 ) ( 01 ( ) + 1K 1 [ H + ] + 2K 2 [ H + ] 2 + 3K 3 [ H + ] 3 ) -------------------------------------------------------------------------------------------------------- t P 1 bind i 0 P bind ik i [ x] i ---------- [ x] dp ------------- bind dx [ ] P bind dlnp ------------------- bind dln[ x] 26
Energy Carriers catabolic - anabolic exergonic - energonic coupling - ATP NADP + - - P - P - P N NH 2 N N 5' 4' 1' H H H 3' 2' H H H N Adenosine Adenine D-Ribose ATP 4, HATP 3, H 2 ATP 2, H 3 ATP, H 4 ATP, H 5 ATP + Standard State Nicotinamide (oxidized) - P P - H H H 2 N N N H N + H P - - N N NH 2 D-Ribose D-Ribose H N Adenine (reduced) H NH 2 27
Transformed Gibbs Energy (1) Constant ph, pmg (2) Use apparent concentrations [ATP] sum of all ATP species ΔG ATP ΔG + RT [] i ν i ln ΔG RTlnK c i + 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 28
Biological Fuel Cells Glucose --> Gluconolactone 2 --> H 2 2 Non-ideal Solutions μ i μ i + RTln( m i γ i ) air sat d V e glucose a 1 a 1 or m 1 γ 1 c 1 γ 1 ø Real Solution For biology, usually a ø 1 Ideal Solution 1 0 1 m 1 or c 1 standard state concentration m 1 or c 1 2 3 a 1 29
--- 1 ---- 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 10 γ i2 A γ I i ---------------------- 1 + Ba I log 10 γ s Φ up to I 0.1 m 2A γ M w, s ------------------------- 1 + Ba I 1000( Ba) 3 -------------------------------------- 1000 lna s M w s, m i electrolytes 1 ---------------------- 2 ln( 1 + Ba I) 1 + Ba I osmotic coefficient 30
M w, s m i RT electrolytes Π ------ --------------------------------------Φ osmotic pressure V s 1000 Gibbs energies for electrolytes ΔG --------- T RT NC ΔG T ----------- + ln a RT i ΔG o 298 G f, 298 H + G f, 298 H + i 1 [ ] ν i Δ ( ) + ΔG f, 298 ( H ) ΔG o f, 298 ( H 2 () l ) Δ ( ) + ΔG f, 298 ( H ) + 237.18 79.908 kj/mol 31
Transformed Gibbs Energies G' U TS + PV N H μ H + N Mg μ Mg 2+ Δ G f, T, j I Δ ΔG f T i,, N H, i G f, T, H + I N Mg, i G f, T, Mg 2+ I G f j,, ( I ph pmg) ΔG f, T, i () I { Δ () RTpH c ln( 10) } { Δ () RTpMgln( 10) } () ΔG f, T, j ( I0) RTln( 10)z j2 A γ ( I ( 1 + Ba I) ) T, ( I0) --------------- ΔG 298.15 f, 298.15, j ( I0) T + 1 --------------- ΔH 298.15 f, 298.15, j ( I0) 32
Gibbs Energies of Pseudoisomers ΔG f, T, i ( I, ph c, pmg) G f T i( 1) G f, i( 1) Δ Δ,, ( I, ph c, pmg) RTlnP bind Δ G P bind 1 + exp -------------------------------------------------- f, i( 2) RT ΔG f, i( 1) ΔG + exp-------------------------------------------------- f, i( 3) + RT P bind 1 + --------- 1 + -------------------- 1 + ------------------------------ 1 K a3 K a3 K a2 K a3 K a2 K a1 ( 1 + K bind a1 + K bind a1 K bind a2 + K bind a1 K bind a2 K bind a3 ) 1 G r j ---------- exp Δ f, i( 1) ΔG ------------------------------------------------- f, i() j RT ΔG f, T, i ΔG exp ------------------------------------------------ f, i() j ( RT) P bind Example, ph c 7, pmg c 3, I 0.25 mol/kg 33
[ ------------------- ATP 4 ] ---------- 1 --------------- 1 0.10 P i P bind 9.7452 [ HATP ------------------------ 3 ] [ ----------------------- MgATP] 0.2863 --------------- 0.03 9.7452 P i P i [ ---------------------------- MgATP 2 ] --------------- 8.148 0.84 P i 9.7452 ΔG f, Pi ΔG f, Pi ( 1) RTlnP bind 2291.9 0.008314( 298.15) ln9.7452 2297.5 kj/mol 34
Coupled Reaction and Phase Equilibria (Ideal Solutions only) Cl 2(aq) + H 2 H + + Cl + HCl (aq) K a1 a H +a Cl a HCl -------------------------------------- ( aq) a Cl2 a ( aq) H2 1E-3.348 HCl (aq) H + + Cl a K H + a Cl a2 --------------------- a HCl ( aq) 1Ε 7.555 a H 2 H + + H K H +a H w ------------------- Write the VLE as reactions H 2 ( v) H 2 l () a H2 1E-14 K w a W /(y w P) 1/ (P w sat ) 35
Cl 2( v) Cl 2( aq) K H [Cl 2(aq) ]/(y Cl2 P), Henry s Law ph 0 1 2 3 4 5 6 7 8 9 1011121314 0-1 [HCl] log[c(mol/l)] -2-3 -4-5 [Cl ] [H ] -6 [H + ] -7-8 36