每日一句 Academic life was fascinating. I used to sit in on lots of classes I hadn’t even signed up for. I worked day and night on this little extra credit project. What I remember above all about Harvard was being in the midst of so much energy and intelligence. It could be exhilarating, intimidating, sometimes even discouraging, but always challenging Speech at Harvard by Bill Gates, Jun. 7, 2007.

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

Goals of this class (1)Knew the theoretical deduction of Lewis and Kohlrausch’s empirical laws (2)Understand the process for developing theory; (3)Learn how to establish a simplified model; (4)Know the importance of activity.

Process for establishing a theory (1) Propose a simplified Model (2) Theoretical treatment (3) Experimental verification (4) Modification (5) Theory Empirical law

Stationary property Dynamic property For ideal solution:For nonideal solution: Theoretical evaluation of W r ’ Before 1894: treated solution as ideal gas : Ghosh – crystalline structure 1923: Debye-Hückel: ionic atmosphere Empirical formula for electrolyte solution

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) Simplified Model Germany, Netherlands 1884/03/24~ 1966/11/02 Studies on dipole moments and the diffraction of X rays

Shielded Coulombic potential Debye length + (2) Theoretical treatment

Lewis’s empirical equation Group exercise: Deduce from for aqueous solution at 298 K (3) Experimental verification

Debye-Hückel limiting law holds quite well for dilute solutions (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 Valid for c < 1 mol·kg -1 (4) Modification Davies equation

2. Debye-Hückel-Onsage theory 1) Relaxation effect 2) Electrophoretic effect In 1927, 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 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.

Valid for 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

Progress of the theories for electrolyte 1800: Nicholson and Carlisle: electrolysis of water 1805: Grotthuss: orientation of molecules 1857: Clausius: embryo of dissociation 1886: vant’ Hoff: colligative property 1887: Arrhenius: dissociation and ionization 1918: Ghosh: crystalline structure 1923: Debye-Hückel: Debye-Hückel theory 1926: Bjerrum: conjugation theory 1927: Onsager: Debye-Hückel-Onsager theory 1948: Robinson and Stokes: solvation theory

Discussion section Very useful concepts: activity and activity coefficient

Question-1: Compare the solubility of AgCl(s) in NaCl solution, pure water, and concentrated KNO 3 solution using that in pure water as standard. AgCl(s) = Ag + (aq) + Cl ¯ (aq) On solubility equilibrium (1)The effect of co-ion; (2)The effect of additional electrolyte: salt effect

Effect of ionic strength on the rate of reaction between two ions. +4: Co(NH 3 ) 5 Br 2+ + Hg 2+ +2: S 2 O I  +1: [NO 2 NCO 2 C 2 H 5 ]  + OH  0: CH 3 COOC 2 H 5 + OH  -1: H 2 O 2 + H + + Br  -2: Co(NH 3 ) 5 Br 2+ + OH  When a substantial amount of inert salt (supporting electrolyte) was added to keep the ionic strength, the activity coefficient of the solution essentially keeps constant. Effect of ionic strength-primary/kinetics salt effect

For ionic reactions in solution, activity coefficients must be taken into consideration. The apparent rate constant depends on the ionic strength of the solution. +2: S 2 O I 