Chapter 7 Electrolyte solution

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Chapter 7 Electrolyte solution
Chemical energy
Electrical energy
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7 Electrolyte solution
Main content

• Concepts in electrochemistry and Faradays Law
• Ions transference and its number
• Electric conductance
• Theory about Strong electrolyte solution

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7.1 Concepts in electrochemistry

(1)basic concept
(2)Faradays 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

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

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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 isnt 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
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Two kinds of conductor
? 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.
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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.
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Cathode ?Anode
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Galvanic cell
Cu electrode
Cu22e-? Cu(S) Reduction occurred, this
electrode is cathode, current electrode Cu to
electrode Zn, Cu electric potential is higher,
and it is positive electrode.
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Electrolytic cell
Electrode?
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 Cu22e-?Cu(S)
Electrode?
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)? Cu22e-
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Efficiency of current
Formula(1)
Efficiency of current
Formula(2)
Efficiency of current
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Faraday Law
? The quantity of substance, which occurred
chemical reaction in the surface of the
electrode, is in direct ratio with the given
quantity of electricity.
? 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.
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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
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Faraday constant
Faraday constant is equal to the quantity of
electricity of 1mol electric charge.
FLe
6.0221023 mol-11.602210-19 C
96484.6 Cmol-1
96500 Cmol-1
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7.2 Ion 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

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The phenomenon of the ions electromigration
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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.
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The phenomenon of the ions electromigration
1. If rr-, 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.
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The phenomenon of the ions electromigration
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The phenomenon of the ions electromigration
2. If r3r-, 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.
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The phenomenon of the ions electromigration
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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.
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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-1V-1.
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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 different proportion of
quantity of electricity when they transfer.
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Transference number definition
If the solution has only one electrolyte
If the solution has many electrolytes,
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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 a, c unit molm-3.
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Transference number definition
The speed of positive ion is r, in unit time
there is (cxaAr) mol substance passing through
any cross section, the quantity of electricity
transferred is (cxaAr)zF, because it is in the
unit time, so
The same reason
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Transference number definition
Because the solution is electric neutral, so
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Measuring methods of transference number

• Hittorf method
• Interface motion method
• Electromotive force method

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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.

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The method of measuring the transference number
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7.3 Electric conductance

• Electric conductance, electrolytic conductivity,
  molar, electrolytic conductivity
• Relationship of electrolytic conductivity and
  molar
• electrolytic conductivity with concentration
• Independent motion law of ions
• Some useful relation formula
• Application of the measurement of the electric
  conductance

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7.3.1 electric condutance
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7.3 Electric conductance
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7.3.2 Electric 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
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7.3.3 Molar conductivity
molar electrolytic conductivity ?m the electric
conductance of the solution, unit length, 1 mole
electrolyte solution,unit is Sm2mol-1.
?mk Vm k/c Vm is the volume of the 1mole
electrolytic solution, unit is m3mol-1, c
is the concentration, unit is molm3.
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7.3.3 Molar conductivity
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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.
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The measurement of electric conductance
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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,
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Cell constant
Cell constant unit is

• The distance L and the area A of Pt electrode
  cant be measured accurately.
• Measuring Kcell in known electrolytic
  conductivity
• Measuring the electrolytic conductivity of
  unknown solution.

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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.

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Relationship of electrolytic conductivity with
concentration
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Relationship of ?m 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 ?m must rise.
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Relationship of ?m of strong electrolyte with c
?m increase with decreasing of concentration.
when concentration descend below 0.001moldm-3,
the relationship of Lm (?m) and is linearity,
Put the line outside to , we can get
molar electrolytic conductivity of
infinitely diluted solution.
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Relationship of ?m of strong electrolyte with c
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Relationship of ?m 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.
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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.
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some useful relation formula
To the strong electrolyte, when the concentration
is not so large, we can approximately use this
formula.
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some useful relation formula
4.
To the strong electrolyte we can approximately
use this formula
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Application of the electric conductance
(1) measurement of the water purity
In fact, if the the water of electric
conductance less than , 1x10-4 S m-1 is thought
as pure water
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(2) Calculate dissociation constant of weak
electrolyte
AB A-
B- Start c 0
0 Eq c(1-a) ca ca
or
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(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.
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7.4 Theory 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
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Mean activity of ions and mean activity
coefficient of ions
Chemical potential of non-electrolyte
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Chemical potential of electrolyte
1-1valence electrolytes (HCl).
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Mean activity of ions and mean activity
coefficient of ions
To the electrolyte of random valence
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Mean activity of ions and mean activity
coefficient of ions
Definition
mean activity of ions
mean activity coefficient of ions
mean molality of ions
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Mean activity of ions and mean activity
coefficient of ions
Calculate From mB of electrolyte
To the 1-1 valence electrolyte
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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.
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The inter-attraction theory of the strong
electrolyte ions
vant Hoff factor
The colligative of the electrolyte is larger
than non-electrolyte of the same concentration.
Vant Hoff use a factor to express their
deflection, which is called Vant Hoff factor or
coefficient.
Non-electrolyte
Electrolyte
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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.
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Picture of Ionic atmosphere
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Debye-Huckels limiting law
Accord to the concept of ionic atmosphere,
Debye Huckel deduced the formula (Debye Huckels
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.
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Debye-Huckels limiting law
Debye Huckels 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.
The mean activity coefficient of ions
calculated from this formula is theoretical, use
the electromotive force method we can get the
actual value.
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Debye-Huckels limiting law
If the radius of the ion is very big and it
cant be regarded as a system of particle
electric charge, we can ameliorate Debye Huckels
limiting law as below
a is the average available diameter of the ion,
it is about 3.510-10m, B is the constant related
to temperature and solvent, in the water solution
at 298 K,
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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.
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Debye-Huckel-Onsager electric conductance theory
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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.
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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
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Example-1

• 3936
• ????,?????????????????????????????????????25????
  ????????????? Lm(H)349.8210-4 , Lm(OH-)
  198.010-4 Sm2mol-1,?????Kw(25?)1.00810-14(c?
  1moldm-3)?

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Answer-1

• ? ????Kw1.00810-14??
• cc(H)c(OH-)Kw1/21.00410-4 molm-3
• Lm(H2O)Lm (H) Lm(OH-)
• (349.2810-4198.010-4) 547.8210-4
• k (H2O) Lm(H2O)c 547.8210-4 1.00410-4
  moldm-3
• 5.50010-6

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Exercises

• P572/2, 3
• P 573/2
• P574/12, 13
• P575/14, 15, 18
• P576/27