Chapter 7 electrolyte solution
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Electrolysis. Cell . Chapter 7 Electrolyte solution. Chemical energy. Electrical energy. 7 Electrolyte solution. Main content:. Concepts in electrochemistry and Faraday’s Law Ions transference and its number Electric conductance Theory about Strong electrolyte solution.

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Chapter 7 Electrolyte solution

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Chapter 7 electrolyte solution

Electrolysis

Cell

Chapter 7 Electrolyte solution

Chemical

energy

Electrical

energy


7 electrolyte solution

7 Electrolyte solution

Main content:

  • Concepts in electrochemistry and Faraday’s Law

  • Ions transference and its number

  • Electric conductance

  • Theory about Strong electrolyte solution


7 1 concepts in electrochemistry

7.1Concepts in electrochemistry

(1)basic concept

(2)Faraday’s Law

  • Research areas

  • Faraday’ Law

  • Two kinds of conductor

  • Faraday constant

  • Anode and cathode

  • Math expression of Faraday’ Law

  • Positive electrode and Negative electrode

  • Primary cell

  • Example

  • Electrolytic cell

  • Efficiency of current


Research areas

Electrolysis

Electrical energychemical energy

Cell

Research areas

Electrochemistry principally researches the conversion of chemical energy into electrical energy and the relevant rules in this conversion.


Two kinds of conductor

Two kinds of conductor

1. The first kind of conductor

Electron conductor (such as metals and graphite)

A.Conduct by the moving of the free electron

B.The conductor isn’t changed in the process of

electronic conduction

C.Resistance is raised with the raising of the temperature

D.All the amount of the electricity conducted is

undertook by electron


Two kinds of conductor1

Two kinds of conductor

⒉ The second kind of conductor

Ion conductor

(such as electrolyte solution and melt electrolyte)

A.Conduct by the inversely moving of the positive and

negative ions.

B.There are chemical reactions in the process of

electronic conduction.

C.Resistance is descended with the raising of the

temperature

D.All the amount of the electricity conducted is

undertook by positive and negative ions

* Solid electrolyte such as AgBr and PbI2 belong to ion conductor, but because its conduction mechanism is very complicated and the ability of its conduction is not high, so in this chapter we mainly talk about electrolyte solution.


Positive electrode negative electrode

Positive electrode、Negative electrode

Positive electrode :

The electrode which electric potential is higher is called anode, current flows from anode to cathode. Among primary cells the positive electrode is cathode and among electrolytic cells the positive electrode is anode.

Negative electrode:

The electrode which electric potential is lower is called cathode, current flows from cathode to anode. Among primary cells the negative electrode is anode and among electrolytic cells the negative electrode is cathode.


Cathode anode

The cathode where the reduction occurred is called cathode, among primary cells cathode is positive electrode and among electrolytic cells cathode is negative electrode.

Cathode:

The cathode where the oxidation occurred is called Anode, among primary cells Anode is negative electrode and among electrolytic cells Anode is positive electrode.

Anode:

Cathode、Anode


Galvanic cell

Zn electrode:

Zn(S)→Zn2++2e-

Oxidation occurred, this electrode is anode, electrons flow from electrode Zn to electrode Cu, Zn electric potential is lower, and it is negative electrode.

Galvanic cell

Cu electrode:

Cu2++2e-→ Cu(S)

Reduction occurred, this electrode is cathode, current electrode Cu to electrode Zn, Cu electric potential is higher, and it is positive electrode.


Electrolytic cell

Electrolytic cell

Electrode①:

The electrode that is connected with the positive electrode of external electrical power is negative electrode and it occurred reduction reaction, so it is cathode

Cu2++2e-→Cu(S)

Electrode②:

The electrode (2) that is connected with the negative electrode of external electrical power is positive electrode and it occurred oxidation reaction, so it is anode.

Cu(S)→ Cu2++2e-


Efficiency of current

Efficiency of current

Formula(1)

Efficiency of current =

Formula(2)

Efficiency of current =


Faraday law

Faraday Law

⒈ The quantity of substance, which occurred chemical reaction in the surface of the electrode, is in direct ratio with the given quantity of electricity.

⒉ Pass the electricity through the series connection circuit of some electrolytic cells, when electric charge of the particle gotten is the same, the substances occurred chemical reactions in the entire electrode have the same mole, the quantity of the substances separated out is in direct ratio with its mole quantity.


Math expression of faraday law

or

Math expression of Faraday Law

Select the gains or losses electrons as z, quantity of electricity as Q, and the moles n of the substance that occurs chemical reaction in the electrode are:

The mass m of the substance that occurs chemical reaction in the electrode is:


Faraday constant

Faraday constant

Faraday constant is equal to the quantity of electricity of 1mol electric charge.

F=L·e

=6.022×1023mol-1×1.6022×10-19 C

=96484.6 C·mol-1

≈96500 C·mol-1


7 2 ion transference and its number

7.2Ion transference and its number

  • The phenomenon of the ions electromigration

  • The electric transference ratio and number of ions

  • The method of measuring the transference number


The phenomenon of the ions electromigration

The phenomenon of the ions electromigration


The phenomenon of the ions electromigration1

The phenomenon of the ions electromigration

Three solution parts: anode, middle and cathode.

Before passing through electricity, there are 5mol positive ions (+) and 5 negative irons (–) in every part.

All ions are 1 valence, when passing through quantity of electricity of 4 mole electrons, 4 moles negative ions in the anode are oxidized, 4 moles positive irons in the cathode are reduced.


The phenomenon of the ions electromigration2

The phenomenon of the ions electromigration

1.Ifr+=r-, the task of conduction are both 2 moles, on the surface of the imaginable planes AA and BB, there are both 2 moles negative and positive ions passing through.

When the electricity is over, the concentration of the solution in the anode and cathode parts are the same, but 2 moles less than the original solution, the concentration in the middle part is unchanged.


The phenomenon of the ions electromigration3

The phenomenon of the ions electromigration


The phenomenon of the ions electromigration4

The phenomenon of the ions electromigration

2. If r+=3r-, the task of conduction of positive ions are 3 moles, the negative ions is 1 mole. On the surface of AA and BB, there are 3 moles positive and 1mole negative ions passing through in inverse direction.

When the electricity is over, in the concentration in anode parts 3 moles positive and negative ions decrease, and in cathode 1 mole positive and negative ions decrease, the concentration in the middle part is unchanged.


The phenomenon of the ions electromigration5

The phenomenon of the ions electromigration


The rule of the transference of the ions

The rule of the transference of the ions

1. All the moles of the positive and negative ions that transfer to the cathode and anode are equal to the total quantity of the electricity passing through.

2.


The electric transference ratio of ions

The electric transference ratio of ions

The speed of ions in the electric field is expressed by formula:

dE/dl: electric potential gradient

U+electric transference rate of positive ions

U-electric transference rate of negative ions

Ionic mobility: the speed of the ions when the electric potential gradient is in 1 unit. Its unit is ㎡·s-1·V-1.


Transference number definition

Transference number definition

the transference number of ion B:

The ratio between the current of ion B carrying and the total current

Because the speeds of positive and negative ions are different, they carry different electric charge, so they undertake differentproportion of quantity of electricity when they transfer.


Transference number definition1

Transference number definition

If the solution has only one electrolyte:

If the solution has many electrolytes, :


Transference number definition2

Transference number definition

There are two parallel electrodes, the distance is l, the surface area A, and the external voltage is E. Put the electrolyte MxNy (concentration c) between two electrodes, the dissolve degree is α, c unit: mol·m-3.


Transference number definition3

Transference number definition

The speed of positive ion is r+, in unit time there is (cxαAr+) mol substance passing through any cross section, thequantity of electricity transferred is (cxαAr+)z+F, because it is in the unit time, so

The same reason


Transference number definition4

(,Electric potential gradient is the same)

Transference number definition

Because the solution is electric neutral, so


Measuring methods of transference number

Measuring methods of transference number

  • Hittorfmethod

  • Interface motion method

  • Electromotive force method


Hittorf method

Hittorf method

  • Put the electrolyte solution into the Hittorf tube, connect the stable voltage and direct current power, then the electrodes occur in chemical reaction, positive and negative ions transfer to cathode and anode.

  • The concentration near the electrode is changed.

  • Weigh solution in cathode (or anode), calculate the transference number according to the quantity of electricity inputted and the change of the concentration near the electrode.


The method of measuring the transference number

The method of measuring the transference number


7 3 electric conductance

7.3 Electric conductance

  • Electricconductance, electrolyticconductivity, molar, electrolyticconductivity

  • Relationship of electrolytic conductivity and molar

    electrolyticconductivitywith concentration

  • Independent motion law of ions

  • Some useful relation formula

  • Application of the measurement of the electric conductance


7 3 1 electric condutance

Electric conductance is the reciprocal

of the resistance, the unit is or s.

Electric conductance G is in direct proportion with the area A and is in reverse ratio with the length l of the conductor.

7.3.1 electric condutance


7 3 electric conductance1

7.3Electric conductance


7 3 2 electric conductivity

Because:

7.3.2Electric conductivity

k: electrolytic conductivity,

the electric conductance in unit length and unit area, the unit is

Electrolytic conductivity is the reciprocal of the resistance rate:


7 3 3 molar conductivity

7.3.3Molar conductivity

molar electrolytic conductivity Λm: the electric conductance of the solution, unit length, 1 mole electrolyte solution,unit is S·m2·mol-1.

Λm=k Vm =k/c

Vmis the volume of the 1mole electrolytic solution, unit is m3·mol-1,

c is the concentration, unit is mol·m3.


7 3 3 molar conductivity1

7.3.3Molar conductivity


The measurement of electric conductance

The measurement of electric conductance

Wiston electric bridge, measurement of resistance,

AB is even slippery string resistance; it is the changeable resistance, M is the electric conductance pool where the measuring solution is put. The resistance will be measured.

I is the high frequency intercourse electricity power. G is the earphone or the oscillograph.


The measurement of electric conductance1

The measurement of electric conductance


The measurement of electric conductance2

The measurement of electric conductance

Connect the electricity power, adjust C point, and make the circuitry DGC has no current, the drop of electric potential of point D and C is equal, the electric bridge is in equilibrium. According to the relationship of some resistance,


C ell constant

Cell constant

Cell constant:unit is

  • The distance L and the area A of Pt electrode can’t be measured accurately.

  • Measuring Kcell in known electrolytic conductivity

  • Measuring the electrolytic conductivity of unknown solution.


Relationship of electrolytic conductivity with concentration

Relationship of electrolytic conductivity with concentration

  • The electrolytic conductivity of strong electrolytic solution increases with increasing of the concentration. When the concentration is raised to a certain degree, the dissociation degree is descend, the speed of ion and electrolytic conductivity decrease. Such as H2SO4 and KOH solution.

  • The change of electrolytic conductivity of weak electrolytic solution is not so obvious, such as acetic acid.


Relationship of electrolytic conductivity with concentration1

Relationship of electrolytic conductivity with concentration


Relationship of m with concentration

Relationship of Λm with concentration

Material mass (1 mole) in the solution is given. When the concentration reduces, interaction between particles weakens, the speed of positive and negative ions quickens. So Λmmust rise.


Relationship of m of strong electrolyte with c

Relationship of Λm of strong electrolyte with c

Λm increase with decreasing of concentration. when concentration descend below 0.001mol·dm-3, the relationship of Lm (Λm) and is linearity,

Put the line outside to , we can get molar electrolytic conductivity of infinitely diluted solution.


Relationship of m of strong electrolyte with c1

Relationship of Λm of strong electrolyte with c


Relationship of m of weak electrolyte with c

Relationship of Λm of weak electrolyte with c

Lm slowly rises with decreasing of concentration, when the solution is very watery, the relationship of Lm and is linear. Below to a certain degree, Lm rapidly rises Such as CH3COOH.


Independent motion law of ions

Independent motion law of ions

Germany scientist, Kohlrausch discovered a law. In the infinitely diluted solution, every ion moves independently and it is not effected by other ions. The molar electrolytic conductivity of the infinitely diluted solution can be regarded as the sum of the two kinds of ions.


Some useful relation formula

some useful relation formula

To the strong electrolyte, when the concentration is not so large, we can approximately use this formula.


Some useful relation formula1

some useful relation formula

4.

To the strong electrolyte we can approximately use this formula:


Application of the electric conductance

Pure water itself has weak dissociation,the concentration of and both are k the table, we can get:

So, electric conductance of the pure water is

Application of the electric conductance

(1) measurement of the water purity

In fact, if thethe water of electric conductance less than , 1x10-4 S m-1 is thought as pure water


2 calculate dissociation constant of weak electrolyte

Use to draw a chart,from the intercept and slope,we can get and this is Ostwald’s dilution law.

(2) Calculate dissociation constant of weak electrolyte

AB = A- + B-

Start: c 0 0

Eq: c(1-a) ca ca

or


3 electric conductance titration

(3) electric conductance titration

In the process of titration,the concentration of ions change unceasingly, conductance titration changes all the time too, we can use the turning point of conductance titration to ensure the titration end point.

No indicator.


7 4 theory about strong electrolyte solution

limiting law

7.4Theory about Strong electrolyte solution

Mean activity of ions and mean activity coefficient of ions

Ionic strength

The inter-attraction theory of the strong electrolyte ions


Mean activity of ions and mean activity coefficient of ions

When the solution is very watery, it can be regarded as

ideal solution so,

Mean activity of ions and mean activity coefficient of ions

Chemical potential of non-electrolyte:


Chemical potential of electrolyte

Chemical potential of electrolyte

1-1valence electrolytes (HCl).


Mean activity of ions and mean activity coefficient of ions1

Mean activity of ions and mean activity coefficient of ions

To the electrolyte of

random valence:


Mean activity of ions and mean activity coefficient of ions2

Mean activity of ions and mean activity coefficient of ions

Definition:

mean activity of ions

mean activity coefficient of ions

mean molality of ions


Mean activity of ions and mean activity coefficient of ions3

Mean activity of ions and mean activity coefficient of ions

Calculate From mB of electrolyte:

To the 1-1 valence electrolyte:


Ionic strength

Ionic strength

In main factors of affecting activity coefficient of ions, the effect of the valence is more obvious. In 1921, Lewis put forward the concept of ionic strength.

mB is the real concentration of the ion B, If it is weak electrolyte, we must multiply the degree of ionization. The unit of I is the same to m.


The inter attraction theory of the strong electrolyte ions

The inter-attraction theory of the strong electrolyte ions

van’t Hoff factor

The colligative of the electrolyte is larger than non-electrolyte of the same concentration. Van’t Hoff use a factor to express their deflection, which is called Van’t Hoff factor or coefficient.

Non-electrolyte:

Electrolyte:


The inter attraction theory of the strong electrolyte ions1

The inter-attraction theory of the strong electrolyte ions

Ionic atmosphere

Debye-Huckel thought that every ion in the solution is embraced by the ions of different electricity. Because of the interaction of the positive and negative ions, the ions distribute not evenly.

If the central ion is positive ion, there are many negative ions around it, a part of electricity of charge is counteracted, but the left electricity of charge form a ball-shaped ionic atmosphere at r distance from the central ion.


Picture of ionic atmosphere

Picture of Ionic atmosphere


Debye huckel s limiting law

Debye-Huckel’s limiting law

Accord to the concept of ionic atmosphere, Debye Huckel deduced the formula (Debye Huckel’s limiting law), of the ion activity coefficient of the strong electrolyte dilutive solution.

Zi is the electric charge of ion i, I is ionic strength, A is a constant related to temperature and solvent, the A of the water can be checked in the certain table.


Debye huckel s limiting law1

Debye-Huckel’s limiting law

Debye Huckel’s limiting law usually use this formula:

This formula is suitable for the diluted strong electrolyte system and the system in which ions can be regarded as particle electric charge. Themean activity coefficient of ions calculated from this formula is theoretical, use the electromotive force method we can get the actual value.


Debye huckel s limiting law2

So

Debye-Huckel’s limiting law

If the radius of the ion is very big and it can’t be regarded as a system of particle electric charge, we can ameliorate Debye Huckel’s limiting law as below:

a is the average available diameter of the ion, it is about 3.5×10-10m, B is the constant related to temperature and solvent, in the water solution at 298 K,


Debye huckel onsager electric conductance theory

Debye-Huckel-Onsager electric conductance theory

Relaxation effect

Because every ion has a ionic atmosphere around it, at the impact of the external electric field, the positive and negative ions transfer at contrary direction, the original ionic atmosphere breaks, the new ionic atmosphere builds, there is a time interval, we call it Relaxation effect.

At the relaxation time, the ionic atmosphere is not symmetrical, it generate resistance to the motion of the central ion. This strength make the ion speed descend and it make the molar conductivity descend.The picture is in the next page.


Debye huckel onsager electric conductance theory1

Debye-Huckel-Onsager electric conductance theory


Debye huckel onsager electric conductance theory2

Debye-Huckel-Onsager electric conductance theory

Electrophoretic effect

In solution, ions are always solvent, at the impact of the external electric field, the solvent central ion and the solvent ionic atmosphere transfer at contrary direction, which adds the adherence and prevent the motion of the ions, so it make the ion transference speed and molar conductivity descend, this is called electrophoretic effect.


Debye huckel onsager electric conductance theory3

Conductance formula:

Debye-Huckel-Onsager electric conductance theory

Consider the relaxation effect and electrophoretic effect; we can deduce a formula that is used to calculate the discrepance of the molar conductivity between the electrolyte at one certain concentration and at the infinitely diluted solution, it is called

conductance formula:

p and q are the descendent amount of Lm caused by relaxation effect and electrophoretic effect, this theory well explain the following experience formula


Example 1

Example-1

  • 3936

  • 在工业上,习惯把经过离子交换剂处理过的水称为“去离子水”。常用水的电导率来鉴别水的纯度。25℃时纯水电导率的理论值为多少?已知Lm(H+)=349.82×10-4 , Lm(OH-)= 198.0×10-4 S·m2·mol-1,水的离子积Kw(25℃)=1.008×10-14(c=1mol·dm-3)。


Answer 1

Answer-1

  • [答] 由离子积Kw=1.008×10-14可得:

  • c=c(H+)=c(OH-)=Kw1/2=1.004×10-4 mol·m-3

  • Lm(H2O)=Lm (H+)+ Lm(OH-)

  • =(349.28×10-4+198.0×10-4) =547.82×10-4

  • k (H2O) = Lm(H2O)c= 547.82×10-4 ×1.004×10-4mol·dm-3

  • =5.500×10-6


Chapter 7 electrolyte solution

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Exercises

Exercises

  • P572/2, 3

  • P 573/2

  • P574/12, 13

  • P575/14, 15, 18

  • P576/27


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