Chapter 6 Solutions of Electrolytes

CONTENTS Properties of Solutions of Electrolytes Arrhenius Theory of Electrolytic Dissociation Theory of Strong Electrolytes Coefficients for Expressing Colligative Properties

PROPERTIES OF SOLUTIONS OF ELECTROLYTES

1. Electrolysis When under a potential of several volts, a direct electric current flow through an electrolytic cell, a chemical reaction occurs. The process is known as electrolysis.

음극(cathode) : 전자가 음극으로 들어가 양이온이 환원 Fe3++e Fe2+ 양극(anode) : 음이온이 전자를 내어놓아 산화 OH- 1/4O2+1/2H2O+e 용액 중에서의 전류 : 전극으로 향하는 양이온과 음이온의 흐름 금속도체에서 전류 : 양이온으로 고정되어 있는 결정격자를 통하여 이동하는 자유전자흐름

2. Transference number Transference(transport) number : 운반율 : The fraction of total current carried by the cations or anions is known as the transport or transference number. 양이온이나 음이온에 의해서 운반된 전류의 총전류에 대한 분율. 이온의 속도와 관계가 있으며 빨리 움직이는 이온일수록 많은 몫의 전류를 운반 t+ = current carried by cations/total current t- = current carried by anions/total current t++t-=1

3. Electrical units I : 전류세기 ampere E : 전위차, 전압 volt R : 저항 ohm I=E/R 전류흐름의 속도, 즉 단위시간에 흐르는 columb으로 표시되는 전기(전하)량 Q이다. I=Q/t (Quantity of eletric charge : 1 coulmb = 3*109esu) Electric energy = E * Q

4. Faraday’s law The passage of 96,500coulombs of electricity through a conductivity cell produces a chemical change of 1 gram equivalent weight of any substance F=9.648456*104

5. Electrolytic Conductance  : specific resistance 비저항 l : length 길이 A : cross-sectional area 단면적 C= = : conductance 전도도 = = = : specific conductance 비전도도 l A R 1 l A  1 * l A * C  1 R 1 l A *

6. Measuring the Conductance of Solutions Rx=Rs*R1/R2  =1/ =c*l/A=1/R*l/A l/A=K  =K/R  =K*C

7. Equivalent Conductance c=V= V=(1000cm3/liter)/c Eq/liter =1000/c (cm3/Eq) c=V= mhos cm2/Eq  1 * V  1000 c

Equivalent Conductance (c) Conductance of a solution of sufficient volume to contain 1 gram equivalent of the solute when measured in a cell in which the electrodes are spaced 1 cm apart 1 그램당량의 용질을 함유하기에 충분한 용적의 용액을 전극이 1 cm 떨어진 용기중에서 측정하였을 때의 전도도

전해질의 농도와는 관계없이 분자가 이온으로 해리되는 현상을 연구하기 위해서는 specific conductance를 사용하는 것보다 equivalent conductance를 사용하는 것이 편리 Equivalent conductance : the conductance of a solution of sufficient volume to contain 1gram equivalent of the solute when measured in a cell in which the electrodes are spaced 1cm apart.

8. Equivalent Conductance of Strong and Weak Electrolytes Strong electrolyte가 희석되어 감에 따라 용액의 단위용적당 이온수가 감소하므로 -> Specific conductance는 감소 -> Equivalent conductance는 꾸준히 증가 (이온간의 간섭이 줄어들기 때문에 운동성이 향상)

Kohlrausch c= o-bc (강전해질 용액) 모든 전해질의 ion은 용액이 희박해짐에 따라 독립적으로 이동시작 o=lcº+laº (약전해질 용액)

9. Colligative Properties of Electrolytic Solutions and Concentrated Solutions of Nonelectrolytes In solutions of nonelectrolyte Van’t Hoff :  = RTc in solutions of electrolyte  = iRTc

ARRHENIUS THEORY OF ELECTROLYTIC DISSOCIATION

Strong electrolyte : HCl, HNO3, HI, NaOH, H2SO4, KOH, Ba(OH)2, Ca(OH)2 Weak electrolyte : H3BO3,H2CO3, NH4OH, HgCl2, complex ion

1. Drugs and Ionization 1) some drugs are more active when in ionic state 2) other compounds are active when in nonelectrolyte 3) other compounds are active when both in ions or neutral molecules.

2. Degree of Dissociation  = c / o : conductance ratio i = 1+ (v-1)  = (i -1)/(v-1)

THEORTY OF STRONG ELECTROLYTES

1. Activity and Activity coefficients a / m = m : practical activity coefficient on the molal scale a / c = c : practical activity coefficient on the on the mole scale a / x = x : rational activity coefficient on the mole fraction scale -> in dilute solutions the difference among three activity coefficients may be disregarded in which c=m < 0.01

a+ : activity of a cation a- : activity of a anion mean ionic activity a=[(+c+)m(-c-)n]1/(m+n) NaCl a=(aNa+aCl- )1/2 FeCl3 a=(a Fe+3 a Cl-3 )1/4 a=[(+c+)m(-c-)n]1/(m+n) a=(+m - n)1/(m+n) (c+mc-n)1/(m+n) a=  (c+mc-n)1/(m+n)

mean ionic activity coefficient : ±= (+m -n)1/(m+n) ±= +m -n

a / m = m

2. Activity of the Solvent When a solution is made infinitely dilute, it can be considered to consist essentially of pure solvent. Therefore, X1 = 1, and the solvent behaves ideally in conformity with Raoult’s law. Under this condition, the mole fraction can be set equal to the activity of the solvent, or a = X1 = 1 As the solution becomes more concentrated in solute the activity of the solvent ordinarily becomes less than the mole fraction concentration, or a = x X1

activity = concentration I = activity / concentration 3. Reference State 4. Standard State Reference State : the solution in which the concentration of the component is equal to the activity activity = concentration I = activity / concentration Standard State : state of the component at unit activity

(ci : molar concentration, zi : valence) 5. Ionic Strength Ionic strength : 모든 형태의 ion이 정전기적 힘에 어느 정도 기여하는가를 나타내는 것  = 1/2(c1z12+c2z22+c3z32+•••+cjzj2) = 1/2cizi2 (ci : molar concentration, zi : valence) ex) 0.01M KCl  =1/2(0.01*12+0.01*12)=0.01 0.01M BaSO4  =1/2(0.01*22+0.01*22)=0.04

6. The Debye-Huckel Theory  < 0.02 : log i = -AZi2  0.02<  < 0.1 : log i = -AZi2  / (1+   ) 0.1 <  < 1 : log i = -AZi2  / (1+ aiB )+c i : activity coefficient ai : mean effective ionic distance aiB=  : constants related to ionic radius of the electrolyte A,B : constants influenced only by the nature of for several electrolytes at 25ºC

COEFFICIENTS FOR EXPRESSING COLLIGATIVE PROPERIES

1. L value Van’t Hoff equation : Tf = iKfm in dilute solutions, m=c, L=iKf  Tf = Lc At a concentration of drug that is isotonic with body fluids, L=iKf is designated here as Liso Liso 비전해질 1.86-1.9 약전해질 2.0 1가-1가 전해질 3.4 높은원자가 전해질 >3.4

Liso values Fig. 6-7. Liso values of various ionic classes

2. Osmotic Coefficient The solution becomes more dilute, i approaches v, the number of ions into which an electrolyte dissociates, and at infinite dilution i = v, or i / v=1. The ratio i / v is designated as g and is known as the practical osmotic coefficient when expressed on a molal basis. i / v=g , Tf = iKfm = gvKfm

3. Osmolality 1-osmolal solution : A solution containing 1 mole ( 1 gram molecular weight) of a nonionizable substance in 1 kg of water (a 1-m solution). It contains 1 osmol (Osm) or 1000 miliosmols (mOsm) of solute per kilogram of solvent. mOsm/kg = imm (i : number of ions formed per molecule, mm : milimolal concentration) Osmolarity = (measured osmolality)*(solution density in g/ml-anhydrous solute concentration in g/ml)