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 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

8 7.4 Activity and activity coefficient 2. Ionic strength on reaction rate-primary/kinetics salt effect 0.6 Effect of ionic strength on the rate of reaction between two ions 0.4 +4: Co(NH,) Br2++ hg2+ +2:S2O2-+I 0.2 +1: INO2NCO2C2H5F+OH- 0.0 0: CH3COOC2H5 OH 1: H,O+H+t+ Br -0.2 -2 Co(NH) Br2++ oh k -0.4 lOg Rs=2ZAZBAT 0.0 0.3 k

Effect of ionic strength on the rate of reaction between two ions. +4: Co(NH3 )5Br2+ + Hg2+ +2: S2O8 2- + I − +1: [NO2NCO2C2H5 ] − + OH− 0: CH3COOC2H5 + OH− -1: H2O2 + H+ + Br− -2: Co(NH3 )5Br2+ + OH− 0.0 -0.2 -0.4 0.2 0.4 0.6 0.0 0.1 0.2 0.3 I 0 log s k k §7.4 Activity and activity coefficient A B 0 log 2 s k Z Z A I k = 2. Ionic strength on reaction rate -primary/kinetics salt effect

87.5 Theories for strong electrolyte 2. Ionic strength on reaction rate -primary/kinetics salt effect Ax+B2÷[(A…B)]→→P k=B-K K K·( h k k YAYI C K ko A/B 2Z.ZA k For ionic reactions in solution, activity coefficients must be taken into consideration Therefore, the apparent rate constant depends on the ionic strength of the solution A substantial amount of inert salt(supporting electrolyte) was added to keep the ionic strength and therefore the activity coefficient of the solution essentially constant

2. Ionic strength on reaction rate -primary/kinetics salt effect For ionic reactions in solution, activity coefficients must be taken into consideration. Therefore, the apparent rate constant depends on the ionic strength of the solution. B c k T k K h  = 1 A B A B ( )n a c a K K c a a        − = =  B A B A B 1 0 ( )n s a k T k c K k h       −    =  = §7.5 Theories for strong electrolyte A B 0 log 2 s k Z Z A I k = A substantial amount of inert salt (supporting electrolyte) was added to keep the ionic strength and therefore the activity coefficient of the solution essentially constant

87.5 Theories for strong electrolyte 3. Debye-Huckel-Onsage theory In 1926, Onsager pointed out that as the ion distorted atmospheres moves across the solution its ionic atmosphere is repeatedly being destroyed and formed again The time for formation of a new ionic atmosphere (relaxation time)is ca. 10-s in an 0.01 mol kg" solution Under normal conditions the velocity of an ion is sufficiently slow so that the electrostatic force exerted by the atmosphere on the ion tends to retard its motion and hence to decrease the conductance 1)Relaxation effect 2)Electrophoretic effect L Onsager, Zur Theorie der Electrolyte I', in Physikali Zeitschrift, 27(1926), 388-392, and".II,, ibid., 28(1 277-298

3. Debye-Hückel-Onsage theory 1) Relaxation effect 2) Electrophoretic effect In 1926, Onsager pointed out that as the ion moves across the solution, its ionic atmosphere is repeatedly being destroyed and formed again. The time for formation of a new ionic atmosphere (relaxation time) is ca. 10-7 s in an 0.01 mol·kg-1 solution. Under normal conditions, the velocity of an ion is sufficiently slow so that the electrostatic force exerted by the atmosphere on the ion tends to retard its motion and hence to decrease the conductance. + − + − − − − − + + + + + − − − + + − − §7.5 Theories for strong electrolyte distorted atmospheres L. Onsager, “Zur Theorie der Electrolyte I”, in Physikalische Zeitschrift, 27 (1926), 388–392, and “…II”, ibid., 28 (1927), 277–298

87.5 Theories for strong electrolyte 3. Debye-Huckel-Onsage theory 2.08×102Zq124125(Z|+Z (E7)2(1+√q) 7 (a1+B) Valid for 3- 10-3 mol ks Lars Onsager, 1968 Noble prize Fuoss: valid for <0. 1 mol kg-I USA, Norway Falkenhagen: valid for 5 molkg-I 1903/11/27~1976/10/05 Studies on the thermodynamics of for LiCl: valid until 9 mol kg irreversible processes

6 3 2 2.08 10 41.25( ) ( ) (1 ) Z Z q Z Z I T T q         + − + −    +   = − +     +       ( ) I   = − + Valid for 310-5 ~ 10-3 mol·kg-1 Fuoss: valid for < 0.1 mol·kg-1 Falkenhagen: valid for < 5 mol·kg-1 , for LiCl: valid until 9 mol·kg-1 Lars Onsager， 1968 Noble Prize USA, Norway 1903/11/27~1976/10/05 Studies on the thermodynamics of irreversible processes §7.5 Theories for strong electrolyte 3. Debye-Hückel-Onsage theory

87.5 Theories for strong electrolyte 4. Summary Empirical law Process for establishing a theory Problem-orientation (1)Propose a simplified model Method-principle (2)Theoretical treatment Study-data ( )Experimental verification Results-analysis (4) Modification Empirical law (5)Theory

Process for establishing a theory Problem-orientation Method-principle Study-data Results-analysis Empirical law §7.5 Theories for strong electrolyte 4. Summary

87.5 Theories for strong electrolyte Progress of the theories for electrolyte 1800: Nicholson and Carlisle: electrolysis of water-conductivity 1805: Grotthuss: orientation of molecules- molecular wire 1857: Clausius: embryo of dissociation [upon electrolysis 1886: vant' Hoff: colligative property-vant Hoff factor 1887: Arrhenius: dissociation and ionization -electrolyte. ion 1918: Ghosh: crystalline structure- first structure model 1923: Debye-Huckel: Debye-Huckel theory -activity coefficient 1926: Bjerrum: conjugation theory -ionic pair 1927: Onsager: Debye-Huckel-Onsager theory 1948: Robinson and stokes: solvation theory -reason for ionization

Progress of the theories for electrolyte 1800: Nicholson and Carlisle: electrolysis of water—conductivity 1805: Grotthuss: orientation of molecules – molecular wire 1857: Clausius: embryo of dissociation [upon electrolysis] 1886: vant’ Hoff: colligative property – vant’ Hoff factor 1887: Arrhenius: dissociation and ionization – electrolyte, ion 1918: Ghosh: crystalline structure – first structure model 1923: Debye-Hückel: Debye-Hückel theory – activity coefficient 1926: Bjerrum: conjugation theory – ionic pair 1927: Onsager: Debye-Hückel-Onsager theory 1948: Robinson and Stokes: solvation theory – reason for ionization §7.5 Theories for strong electrolyte