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Chapter 7 Solutions of Electrolytes. 7.1 transference of ion 7.2 conductance of electrolyte solution 7.3 Application of conductance 7.4 Strong Electrolytes. New Words and Expressions. galvanic cell 原电池 electrolytic cell 电解池 Cathode 阴极

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chapter 7 solutions of electrolytes
Chapter 7 Solutions of Electrolytes
  • 7.1 transference of ion
  • 7.2 conductance of electrolyte solution
  • 7.3 Application of conductance
  • 7.4 Strong Electrolytes
new words and expressions
New Words and Expressions
  • galvanic cell 原电池
  • electrolytic cell 电解池
  • Cathode 阴极
  • Anode 阳极
  • Electronic conductive 电子导体
  • Ionic conductive 离子导体
  • Electrolyte 电解质
Electric mobility 电迁移率
  • Transference number of ion 离子迁移数
  • Conductance 电导
  • Electrolytic conductivity 电导率
  • Molar conductivity 摩尔电导率
  • Ionization 电离
  • Degree ionization 电离度
Electrolytic equilibrium 电离平衡
  • Strong electrolytes 强电解质
  • Weak electrolytes 弱电解质
  • Ionic mean activity 离子平均活度
  • Ionic mean activity factor 离子平均活度系数
  • Ionic strength 离子强度
  • Debye-Huckel limiting law 德拜-格尔极限公式
galvanic cell





Cu2++2e-→ Cu(S)


原电池(galvanic cell)
7 1 transference of ion
7.1 transference of ion
  • ionic conductive
  • valence type of electrolyte

Consider an electrolyte of formula AaBb, which ionizes as follows:

AaBb == aAz+ + bBz-

a-b type of electrolyte

7 1 transference of ion1
7.1 transference of ion
  • Faraday’s Laws of Electrolysis
  • 1. The mass of an element produced at an electrode is proportional to the quantity of electricity Q passed through the liquid;
  • Q=It (7.1)
  • Q= nZF

7.1 transference of ion

  • Q= nZF
  • m= nM = Q/ ZF M
  • F = Le
  • =6.022×1023mol-1×1.6022×10-19 C
  • =96484.6 C·mol-1
  • ≈96500 C·mol-1
transport numbers


Transport Numbers
  • the transference number, or the migretion number is the fraction of the total current carried by each ion present in solution.
  • t+ + t- =1 (7.2)
Ionic Mobilities U

The speed with which the ion moves under a unit potential gradient.

The SI unit of it is m2·V-1· S-1.

Together with: az+=bz-
  • If both ions are moving at the same speeds, r+=r- , after some motion has occurred, the situation will be as represented in Figure bellow.
At each electrode two ions remain unpaired and are discharged, two electrons at the same time traveling from the anode to the cathode, equivalent amounts have been discharged at the two electrodes.
If both ions are moving but at different speeds, r+=3r- , after some motion has occurred, the situation will be as represented in Figure below.
At each electrode four ions remain unpaired and are discharged, four electrons at the same time traveling in the outer circuit from the anode to the cathode, equivalent amounts have been discharged at the two electrodes.
The methods to determine the transport numbers

1. Hittorf Method

2. Moving Boundary Method

7 2 conductance of electrolyte solution
7.2 conductance of electrolyte solution
  • Conductance:conductive ability of conductor
  • G=1/R =A/l (7.4) SI unit: S
  • Electrolytic Conductivity
  •  =1/ =G(l/A ) (7.5) SI unit:S m-1

cell constantK cell =l/A (7.6) SI unit:m-1,

  • Molar Conductivity
  • m=  Vm = /c (7.7) SI unit: S m2 mol-1
classify of electrolyte
Classify of electrolyte
  • Electrolytes: the substances which form ions in the solution and has a much higher conductivity.
  • Nonelectrolytes: the substances that don’t dissociate into ions in the solution and has the same electric conductivity as water itself.
  • Strong electrolytes: the substances which occur almost entirely as ions when they are in aqueous solution.
  • Weak electrolytes: the substances which are present only partially as ions in the solution.
conductance of electrolyte solution
conductance of electrolyte solution
  • For strong electrolytes, the electric conductivity increase with the concentration, but the larger electrostatic force between ions will decrease the conductivity value at more condensed concentration.
  • For weak electrolytes, the electric conductivity change little because of the stable particle numbers.
In all cases, the molar conductivity diminishes as the concentration is raised.
  • For strong electrolytes the molar conductivity falls only slightly as the concentration is raised.
  • The weak electrolytes produce fewer ions and exhibit a much more pronounced fall of  with increasing concentration.
molar conductivity at infinite dilution m
Molar conductivity at infinite dilution(m)
  • Molar conductivity at infinite dilution(m): the conductivity when the concentration of the solution is near to zero.
  • For strong electrolytes, we can extrapolate the curves back to zero concentration and obtain m.

m = m - Ac1/2 (7.8)

(dilute solution of strong electrolytes)

  • But with weak electrolyte, this extrapolate is unreliable.
law of the independent migration of ion
law of the independent migration of ion
  • Each ion is assumed to make its own contribution to the molar conductivity, irrespective of the nature of the other ion with which it is associated. In other words,
  •  =  + +  - (7.9)
  • Where  + and  - are the ion conductivities of cation and anion, respectively, at infinite dilution. This behavior was explained in terms of Kohlrausch’s law of independent migration of ions.
7 3 application of conductance
7.3 Application of conductance
  • The determination of the degree of dissociation and electrolytic equilibrium constant of weak electrolytes: There exists an equilibrium between undissociated molecules AB and the ions A+, B-.

AB === A+ + B-

At very low concentrations this equilibrium lies over to the right, and the molar conductivity is close to  m
  • As the concentration is increased, this equilibrium shifts to the left and the molar conductivity decreases from  m to a lower value  m.
Degree of Dissociation
  •  = m/ m (7.11)
  •  m is the molar conductivity at infinite dilution.
EXAMPLE 7.1 The  value of HAc solution at 25oC is 5.20110-4 S·m2·mol-1, what is the degree of dissociation  and the equilibrium constant Kc of HAc.
The determination of the solubility of insoluble salts

Because of the limit concentration, so


(Salt) = (Solution) - (Water)

EXAMPLE 7.2 The values of AgCl solution and solvent H2O at 25oC is 3.1410-4 and 1.6010-4 S·m-1respectively. what is the solubility and solubility products of AgCl.
7 4 strong electrolytes
7.4 Strong Electrolytes
  • Ironic mean activity and ironic activity factor
7 4 strong electrolytes1
7.4 Strong Electrolytes

Ironic mean activity and ironic activity factor

离子平均活度(mean activity of ions)

离子平均活度系数(mean activity coefficient of ions

离子平均质量摩尔浓度(mean molality of ions)

Ionic Strength
  • I=1/2 ciZ2i (7.13)

Where ci is the molar concentration of the ions of type i, zi is the valence of the ions.

EXAMPLE 7.3 Calculate the ionic strength of: (1) The solution of 1.0mol·kg-1KCl and 1.0mol·kg-1K2SO4respectively at 25oC; (2) The solution containing both of 0.001mol·kg-1CaCl2 and 0.002 mol·kg-1Na2SO4 at 25oC.
7 4 strong electrolytes2
7.4 Strong Electrolytes
  • Debye-Huckel Theory

1. The decrease in the molar conductivity of a strong electrolyte was attributed to the mutual interference of the ions, which becomes more pronounced as the concentration increases.

2. Because of the strong attractive forces between ions of opposite sighs, the arrangement of ions in solution is not completely random.

3. In the immediate neighborhood of any positive ion, there tend to be more negative than positive ions, whereas for a negative ion there are more positive than negative ions. This is called “ionic atmosphere”
Debye-Huckel limiting law
  • Constant B:A quantity that depends on properties such as T. when water is the solvent at 25°C, the value of B is 0.51mol-1/2dm3/2.


  • So for aqueous solutions at 25 ° C,


This is known as the Debye-Huckel limiting law

EXAMPLE 7.4 Applying the Debye-Huckel limiting law, (1) Calculate the activity coefficient of Zinc ion in the solution containing both of 0.002mol·kg-1CaCl2 and 0.002 mol·kg-1 ZnSO4 at 25oC (2) Calculate the mean activity coefficient of The solution of 0.001mol·kg-1 K3Fe(CN)6 at 25oC;.
Relaxation/asymmetry effect: if an electric potential is applied, a positive ion will move towards the negative electrode and must drag along with it an entourage of negative ions. The ionic atmosphere around a moving ion is therefore not symmetrical; this will result in a retardation in the motion of the ion.
Electrophoretic effect: The tendency of the applied potential to move the ion atmosphere itself. This is in turn will tend to drag the solvent molecules, because of the attractive forces between ions and solvent molecules. As a result, the ion at the center of the ionic atmosphere is required to move upstream.
1.Calculate the ionic strength of (a) solution that is 0.10 mol kg 1 in KCl(aq) and 0.20 mol kg 1 in CuSO4(aq).
2. Calculate the masses of (a) Ca(NO3)2 and, separately, (b) NaC1 to add to a 0.150 mol kg -1solution of KNO(aq) containing 500 g of solvent to raise its ionic strength to 0.250.
3. The mean activity coefficient in a 0.100 mol kg-1 CaC12(aq) solution is 0.524 at 250C. What is the percentage error in the value predicted by the Debye-Huckel limiting law\'?
4. At 250C, a cell contained 0.02mol/dm3 aqueous KCl, and it had a conductivity of 0.277Sm-1. The measured resistance was 82.4. When the same cell was filled with 0.005mol/dm3 K2SO4 aqueous solution, the resistance was 326.0 (Omit the conductivity of water).
  • Please find:(1) cell constant K(l/A).
  • (2)Conductivity K of K2SO4 solution.
  • (3) Molar conductivity m of K2SO4 solution.