山东大学：《物理化学》课程教学资源（讲义资料）7.5 Theories for strong electrolyte

8 7.5 Theories for strong electrolyte Out-class extensive reading Levine, pp. -300-304 10.8 The Debye-Huckel theory of electrolyte solution

§7.5 Theories for strong electrolyte Out-class extensive reading: Levine, pp.- 300-304 10.8 The Debye-Hückel theory of electrolyte solution

87.5 Theories for strong electrolyte Goals of this class (1) Be able to make theoretical thinking; (2) Be able to stablish a simplified theoretical model (3)Be able to make model improvement; (4)Be able to think critically

Goals of this class (1) Be able to make theoretical thinking; (2) Be able to stablish a simplified theoretical model; (3) Be able to make model improvement; (4) Be able to think critically. §7.5 Theories for strong electrolyte

87.5 Theories for strong electrolyte Empirical formula for electrolyte solution Dynamic property Stationary property ny

= −A I    m m A c ln  = − Dynamic property Stationary property Empirical formula for electrolyte solution §7.5 Theories for strong electrolyte

87.5 Theories for strong electrolyte Stationary property Theoretical evaluation of w 1ny± Before 1894: solution was treated as ideal gas For ideal solution: 1918-1920: Ghosh -crystalline structure u,=u(T)+RTInm (△G) Tp=RT In For nonideal solution: =1°(T)+ RTIn m2+RTny y RT

= −A I  ln Stationary property For ideal solution: ( ) ln   i i i = + T RT m For nonideal solution: ( ) ln ln    i i i i = + + T RT m RT ( ) ln ' G T ,P = RT i = −Wr  RT Wr i ' ln = − Theoretical evaluation of Wr ’ §7.5 Theories for strong electrolyte Before 1894: solution was treated as ideal gas 1918-1920: Ghosh – crystalline structure

87.5 Theories for strong electrolyte 1. The Debye-Huckel theory PHYSIKALISCHE ZEITSCHRIFT 9. Redaktionech I. Mai 1923. uB fur No 24. Jahrgang INHALT Originalmittellunger Vorlesungsverzeiehnis fir das Sommersemester 1923 P Debye t. E. Huckel. Zur Theorie der Elektro. lyte. S, 185 ORIGINALMITTEILUNGEN Zur Theorie der Elektrolyte. hiermit eingefuhrte ,osmotische Koeffizient"/o . Gefrierpunktserniedrigung und ver. messen soll und als Funktion von Konzentration wandte Erscheinungen ruck und Temperatur beobachtbar ist. In Wirk Von P Debye und E. Hickel). lichkeit beziehen sich solche Beobachtungen §1. Einleitung h iationshypothese'die bei den Elektrolytlosungen thermodynamischen Grinden mit Hilfe desselben beobachteten abnormal en Werte von osmotic. schem Druck, Gefrierpunktserniedrigung usw an't Hoffschen Gesetz fur vollkommene durch die Existenz freier Ionen und der damit zation folgenden Grenzwerten ableitbar Hand in Hand gehenden Vermehrung der Zah Die nachstliegende Annahme zur Erklarung P W. Debye and E. Huckel, Zur Theorie der Elektrolyte I Gefrierpunktserniedrigung und verwandte Erscheinungen, Phys. Z. 24(1923):185-206

1. The Debye-Hückel theory §7.5 Theories for strong electrolyte P. W. Debye and E. Hückel, "Zur Theorie der Elektrolyte. I. Gefrierpunktserniedrigung und verwandte Erscheinungen," Phys. Z. 24(1923): 185-206

87.5 Theories for strong electrolyte 1. The Debye-Huckel theory (1)Model hypothesis lonic atmosphere Radius: 1-100 nm Basic assumptions Peter J. w. Debye 1)Point charge Germany. Netherlands 2)Only Coulombic attraction 1884/03/24~1966/1102 3)Dielectric constant keep unchanged Studies on dipole moments and the 4) Boltzmann distribution, Poisson equation diffraction of X rays

1. The Debye-Hückel theory Ionic atmosphere Radius:1~100 nm Basic assumptions 1) Point charge 2) Only Coulombic attraction 3) Dielectric constant keep unchanged 4) Boltzmann distribution, Poisson equation Peter J. W. Debye + + + + + + + + + + + + − − − − − − − − − − − + − − (1) Model hypothesis Germany, Netherlands 1884/03/24~ 1966/11/02 Studies on dipole moments and the diffraction of X rays §7.5 Theories for strong electrolyte

87.5 Theories for strong electrolyte The Debye-Huckel theory Shielded Coulombic potential (2)Theoretical treatment e b/r 4丌EnEr tEC I b=/5h7) Debye lengt th 4NAle po) Inyi- RT BTe e kTb In y =-Az2 e 4I(EoE, kr)

Shielded Coulombic potential 0 4 j r Z e r    = / 0 e 4 j b r r Z e r    − = 1 2 0 2 A 0 4 r kT b N Ie      =     kTb Z e r i i    0 2 2 8 ln − = 1 1 3 2 2 A 0 2 1 2 0 ln 4 ( ) i i r e N Z I kT      − = Debye length RT Wr i ' ln = − AZ I i i 2 ln  = − + (2) Theoretical treatment 1. The Debye-Hückel theory §7.5 Theories for strong electrolyte

87.5 Theories for strong electrolyte 1. The Debye-Huckel theory (3)Experimental verification Group exercise Deduce ny+=-AZ,Z )ILewis's empirical equation from ny AZ for aqueous solution at 298K In 1.172ZZ lg=-05092Z

AZ I i i 2 ln  = − AZ Z I  = − + − ln  Lewis’s empirical equation Group exercise: Deduce from for aqueous solution at 298 K Z Z I  = − 172 + − ln  1. Z Z I  = − 509 + − lg 0. (3) Experimental verification 1. The Debye-Hückel theory §7.5 Theories for strong electrolyte

87.5 Theories for strong electrolyte 1. The Debye-Huckel theory (4)Modification Zur Theorie der Elektrolyte Mit 5 Abbildungen. Debye-Huckel limiting law holds quite well for dilute solutions when <0.01 m. but must be modified to account for the drastic deviations that occur at high concentrations ZncI2 AZ.Z 0.509ZZ Igr 1+aB 1+ Valid for c<0.1 mol kg AZ,Z gy± +bⅠ 1,4 1+aB√I Davies equation 08 10 Valid for c< 1 molkg-I

Debye-Hückel limiting law holds quite well for dilute solutions when I < 0.01 m, but must be modified to account for the drastic deviations that occur at high concentrations. Valid for c < 0.1 mol·kg-1 bI I AZ Z I + + − = + −    1 lgValid for c < 1 mol·kg-1 (4) Modification Davies equation 1. The Debye-Hückel theory §7.5 Theories for strong electrolyte 0.509 lg = 1 1 A Z Z I Z Z I I I   + − + −  − = − + +

87.5 Theories for strong electrolyte 1. The Debye-Huckel theory The Debye-Huickel theory was proposed by Peter Debye and Erich Huckel as a theoretical explanation for departures from ideality in solutions of electrolytes and plasmas. It is a linearized poisson-Boltzmann model, which assumes an extremely simplified model of the electrolyte solution but nevertheless gave accurate predictions of mean activity coefficients for ions in dilute solution The Debye-Huckel equation provides a starting point for modern treatments of non-ideality of electrolyte solutions Limitations and extensions: hopelessly oversimplified (I)Complete dissociation; (2) Weak electrolytes; (3)Ions are spherical, point charge and polarized; (4) Role of the solvent https://en.wikipedia.org/wiki/debye-huckeltheory

The Debye–Hückel theory was proposed by Peter Debye and Erich Hückel as a theoretical explanation for departures from ideality in solutions of electrolytes and plasmas. It is a linearized Poisson–Boltzmann model, which assumes an extremely simplified model of the electrolyte solution but nevertheless gave accurate predictions of mean activity coefficients for ions in dilute solution. The Debye–Hückel equation provides a starting point for modern treatments of non-ideality of electrolyte solutions. https://en.wikipedia.org/wiki/Debye–Hückel_theory Limitations and extensions: hopelessly oversimplified (1) Complete dissociation; (2) Weak electrolytes; (3) Ions are spherical, point charge and polarized; (4) Role of the solvent 1. The Debye-Hückel theory §7.5 Theories for strong electrolyte