ELECTROCHEMICAL EQUILIBRIUM

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1 Laurea Magistralis Corso di in Laurea MEDICINE Specialistica and SURGERY in MEDICINA HARVEY e CHIRURGIA corso integrato FISICA - disciplina FISICA Integrated Course/Discipline: PHYSICS ELECTROCHEMICAL EQUILIBRIUM - ELECTRO-CHEMICAL EQUILIBRIUM (Δµ 0) - DONNAN-GIBBS RELATION - ONCOTIC PRESSURE - ELECTRO-CHEMICAL EQUILIBRIUM (J S total 0) D. SCANNICCHIO /1

2 ELECTRO-CHEMICAL POTENTIAL n moli n moles / n / gr-ioni n g-ion 1 1 energia chemical potenziale potential chimica energy µ RT ln C + µo energia electric potenziale potential elettrica energy U q V energia electro-chemical potenziale elettro-chimica potential energy µ RT ln C + q V + µo Ze No electric carica elettrica di un g-ione charge of one µ RT ln C + Ze NoV + µo potenziale elettrochimico (relativo a n 1 g-ione) electro-chemical potential energy for 1 g-ion D. SCANNICCHIO 009 0/1

3 ELECTRO-CHEMICAL EQUILIBRIUM: NERNST EQUATION potenziale elettrochimico electro-chemical potential stato di equilibrium: equilibrio µ 1 µ 0 µ RT ln C + Ze No V + µo RT ln C 1 + Ze NoV 1 RT ln C Ze NoV 0 RT ln C 1 RT ln C + Ze NoV 1 Ze NoV 0 Ze NoV 1 Ze NoV RT ln C RT ln C 1 ZNo e (V 1 V ) RT ln C C 1 No e F C D. SCANNICCHIO /1

4 ELECTRO-CHEMICAL EQUILIBRIUM: NERNST EQUATION ZNo e (V 1 V ) RT ln C C 1 No e F C V 1 V RT FZ ln C C 1 Nernst s equazione di Nernst equation equilibrium relazione condition equilibrio D. SCANNICCHIO /1

5 ELECTRO-CHEMICAL EQUILIBRIUM: NERNST EQUATION equazione Nernst s equation di Nernst V 1 V RT FZ ln C C 1 membrana permeable permeabile membrane equilibrium: equilibrio : C 1 C V 1 V membrana semipermeable semipermeabile membrane equilibrium: equilibrio : C 1 C V 1 V (equazione (Nernst s equation) di Nernst) symbol new definition of solute s concentration definizione formale concentrazione di soluto s C {s} D. SCANNICCHIO /1

6 ELECTRO-CHEMICAL EQUILIBRIUM: NERNST EQUATION oppure : otherwise: dynamic equilibrio equilibrium dinamico J EsM + J DsM 0 go vedi to # slide 14 #15 Nernst s equazione di equation Nernst V 1 V RT FZ ln C C 1 D. SCANNICCHIO /1

7 DONNAN-GIBBS CONDITION Nernst s equation applied to each solute: equazione di Nernst applicata per ogni soluto : Na +, K +, Ca ++, Cl, CO3H V 1 V RT F ln {Na + } {Na + } 1 RT {K + } ln F {K + } RT 1 F RT {Cl } ln 1 ln {CO3H } 1 F {Cl } RT {CO3H F } {Na + } {Ca ++ } {Ca ++ {Na + {K+ } {Cl } 1 } 1 {K + } 1 } 1 {Cl {CO3H } 1 } {CO3H } ln {Ca ++ } {Ca ++ } 1 {Na + } {Cl } 1 {Na + } {Cl } {Na + } 1 {Cl } {Na + } 1 {Cl } 1 condizione di equilibrio di Donnan-Gibbs Donnan-Gibbs equilibrium condition D. SCANNICCHIO /1

8 DONNAN-GIBBS CONDITION equazione Nernst s di equation Nernst V 1 V RT FZ ln C C 1 {Na + } {Cl } {Na + } 1 {Cl } 1 condizione Donnan-Gibbs di equilibrio equilibrium di Donnan-Gibbs condition {Cl } V 1 V 1 {Cl } {Na + } 1 {Na + } D. SCANNICCHIO /1

9 ONCOTIC PRESSURE π mmhg 5 19 oncotic pressione oncotica pressure π nrt V π kc RTC o 1 mm litro concentrazione concentration C dipendenza real dependence reale : : π C proteine proteins D. SCANNICCHIO /1

10 ONCOTIC PRESSURE memb PNa k P k( ) Na + π M HO (Na + ) (Cl ) compartimento COMPARTMENT 11 HO Na + Cl compartimento COMPARTMENT EXPERIMENTAL TEST membrane M: permeable for ions Na + and Cl semipermeable for ions P k( ) compartimento 1 COMPARTMENT 1 compartimento COMPARTMENT PNa k P k( ) + k Na + NaCl Na + + Cl D. SCANNICCHIO /1

11 START INIZIO 1 ONCOTIC PRESSURE C 1 g-ioni P k( ) + kc 1 g-ioni Na + C g-ioni Cl + C g-ioni Na + EQUILIBRIUM EQUILIBRIO (carica neutral elettrica electric neutra) charge in each compartment 1 C 1 g-ioni P k( ) + x g-ioni Cl + (x + kc 1 ) g-ioni Na + (C x) g-ioni Cl + (C x) g-ioni Na + ions for which the membrane is permeable: ioni cui la membrana é permeabile {Cl } 1 x {Na + } 1 kc 1 + x {Cl } C x {Na + } C x condizione di equilibrio di Donnan-Gibbs : Donnan-Gibbs equilibrium condition: D. SCANNICCHIO /1

12 ONCOTIC PRESSURE Donnan-Gibbs condizione di equilibrio equilibrium di Donnan-Gibbs condition: : x (kc 1 + x) (C x) x kc1 + C C {Cl } 1 C kc 1 + C {Na + } 1 kc 1 + kc1 + C C Σ 1 {Cl } C {Na + } C C kc 1 + C Σ C kc 1 + C D. SCANNICCHIO 009 1/1

13 ONCOTIC PRESSURE {Cl } 1 + C C {Na + } 1 + kc kc 1 + C 1 + kc 1 + C C + kc 1 C + k C 1 kc 1 + C Σ 1 C C {Cl } + {Na + } C + C kc1 + C kc1 + C C + kc 1 C kc 1 + C Σ D. SCANNICCHIO /1

14 equilibrio : equilibrium: ONCOTIC PRESSURE k C 1 Σ 1 Σ kc1 + C solute build-up (despite the membrane is permeable to the solutes) accumulo soluti (malgrado membrana sia ad essi permeabile) in the compartment with the solute to which the membrane is not nel permeable compartimento (semipermeable) con il soluto cui la membrana non é permeabile MEMBRANA CAPILLARE : aggiunta addition to di the pressione osmotic osmotica pressure pressione oncotica del plasma CAPILLARY MEMBRANE: plasma oncotic pressure C >> C 1 π RT C 1 + C 1 C proteine proteins k C 1 C π effettiva real π proteine proteins + π ΔΣ π oncotica D. SCANNICCHIO /1

15 dynamic equilibrio equilibrium dinamico : ELECTRO-CHEMICAL POTENTIAL J EsM + J DsM 0 Nernst s equation equazione di Nernst flusso total ionico ionic totale flux J sm out in assenza of equilibrium di equilibrio equilibrium: equilibrio : J sm 0 J (totale) sm J + J D d{s} (total) DsM µ EsM M s {s} dx ΔV Δx d{s} ZFDM V D M + {s} m ΔV V dx RT Δx m (x coordinata (coordinate attraverso x through la membrana the membrane 0 < x 0 < x Δx) < x) flusso ionic flux ionico inside nella the membrane membrana constant stazionario : J sm D. SCANNICCHIO 009 (total) constant inside the membrane (totale) costante nella membrana dj sm dx 0 15/1

16 ELECTRO-CHEMICAL POTENTIAL V m d{s} ZFDM J sm (total) (totale) D M + {s} dx RT Δx dj sm dx 0 d {s} ZFD M V d{s} D M dx + m 0 RT Δx dx soluzione : solution: {s} k e Ax + h sostituendo replacing we si obtain: ottiene : V m A + RT ZF Δx D. SCANNICCHIO /1

17 ELECTRO-CHEMICAL POTENTIAL soluzione solution: : {s} k e Ax + h sostituendo replacing we si ottiene obtain: : V m A + RT ZF Δx x 0 x Δx {s} α {s} 1 k e A0 + h k + h {s} α {s} k e AΔx + h α {s} α {s} 1 k e AΔx + h k h k (e AΔx 1) D. SCANNICCHIO /1

18 ELECTRO-CHEMICAL POTENTIAL k α {s} {s} 1 (e AΔx 1) h α {s} 1 k α {s} 1 eaδx {s} 1 {s} + {s} 1 (e AΔx 1) α {s} 1 eaδx {s} (e AΔx 1) {s} k e Ax + h α {s} {s} 1 (e AΔx 1) e Ax + α {s} 1 eaδx {s} (e AΔx 1) D. SCANNICCHIO /1

19 ELECTRO-CHEMICAL POTENTIAL {s} k e Ax + h d{s} ZFDM V J sm (total) (totale) D M + {s} m dx RT Δx D M k A e Ax + ZFD V M m (k RT Δx e Ax + h) D M ZF RT V m Δx k e Ax + ZFD M RT V m Δx (k eax + h) ZFD M RT V m Δx ( k e Ax + k e Ax + h) ZFD M V m ZFD h α {s} 1 eaδx {s} M V m RT Δx RT Δx (e AΔx 1) D. SCANNICCHIO /1

20 ELECTRO-CHEMICAL POTENTIAL ZFV {s} 1 e AΔx m D M α {s} RT Δx (e AΔx 1) ZFV m P RT s ZF V m RT {s} 1 e {s} ZF V m (e RT 1) (total) J sm (totale) dynamic equilibrium equilibrio dinamico ZFV m P s RT ZF V m RT {s} 1 e {s} ZF V m (e RT 1) 0 D. SCANNICCHIO 009 0/1

21 ELECTRO-CHEMICAL POTENTIAL dynamic equilibrio equilibrium dinamico : ZF V ZFV {s} e m RT m 1 {s} J sm (total) (totale) P RT s ZF V (e m RT 1) 0 ZF V m RT {s} e 1 {s} 0 e ZF V m RT {s} {s} 1 ZFV m RT ln {s} ln C {s} 1 C 1 V V V ΔV m 1 V 1 V RT ZF ln C C 1 equazione di Nernst Nernst s equation Q.V.D. D. SCANNICCHIO 009 1/1

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