UNIT 05 ELECTROCHEMISTRY

Syllabus
• Conductance of Electrolytic solutions
• Electrochemical cells
• Batteries
• Fuel Cells
• Corrosion

ELECTROCHEMISTRY
Electrochemistry is the study of the equilibrium and kinetic properties of ions in solution, production of electricity from energy released during spontaneous chemical reactions or its reverse when electrical energy is used to bring non-spontaneous chemical transformations.The subject is of importance both for theoretical and practical considerations. A large number of substances like sodium hydroxide , chlorine , fluorine and many other chemicals are produced by electrochemical methods. Batteries and fuel cells convert chemical energy into electrical energy and are used on a large scale in various instruments and devices. Many fast and convenient analytical techniques are based on electrochemical principles. The transmission of sensory signals through cells to brain and vice versa and communication between the cells are known to have electrochemical origin. Electrochemistry is therefore, is very vast interdisciplinary subject.
Electrochemical Changes
Chemical changes involving production or consumption of electrical energy are called electrochemical changes. These are of two types :
i) The changes in which passage of electricity through a solution bring about a redox reaction. The phenomenon is called electrolysis and the devise used to carry out electrolysis is called electrolytic cell. For example, when electricity is passed through molten sodium chloride, sodium is deposited at the cathode and chlorine is evolved at the anode.
ii) The changes in which electricity is produced as a result of a redox reaction. The device used to produce electricity from a spontaneous redox reaction is called an electrochemical cell or galvanic cell or voltaic cell.
Conductors
Substances which allow the passage of electricity through them are called conductors. On the other hand, the substances which do not allow the passage of electricity through them are called insulators or non-conductors. Conductors can be broadly classified into categories viz., metallic conductors and electrolytes.
Some Important Terms and Concepts
i. Ohm's Law
This law is obeyed by both metallic as well as electrolytic conductors. It states that the potential difference across the conductor is directly proportional to the current flowing through it. That is ,
Potential difference  Current
or Potential difference = Constant
Current
Thus the ratio of potential difference across the conductor to the current flowing through it is constant. This constant is called resistance of the conductor.
If I is the current strength and R is the resistance of the conductor , then according to Ohm's law :

Units
I is expressed in amperes, V in volts and R is expressed in ohms . It is also designated as  which in terms of SI base units is equal to ( kg m2 / s3 A2) which can be measured with the help of a wheatstone bridge.
ii. Resistance ( R )
Resistance of any conductor is the obstruction to the flow of current. It is directly proportional to the length (ℓ) of the conductor and inversely proportional to its area (A) of cross-section. Thus,

where  is the constant of proportionality and is also known as specific resistance or resistivity. IUPAC has recommended the use of the term resistivity over specific resistance. It is given by the expression :

If ℓ = 1 m ; A = 1 m2 ; then R = 
This leads us to define Specific resistance or resistivity as the resistance offered by the conductor of one metre long and its area of cross section one m2 . It may be defined as the resistance offered by a metre cube of a conductor. The units of specific resistance can be derived from the formula as :

Its SI units are ohm metre ( m) and quite often its submultiple , ohm centimetre ( cm) is also used. 1  m = 100  cm or 1  cm = 0.01  m
iii. Conductance
Conductance is a measure of the ease with which current flows through the conductor. It can be defined as the inverse of resistance ,R . It is denoted by G.

Unit
The SI unit of conductance is Siemens, represented by the symbol S and is equal to ohm1 (also known as mho) or 1
iv. Specific conductance (conductivity)
It is the reciprocal of specific resistance(resistivity) called conductivity (specific conductance). It is generally denoted by a Greek letter Kappa() . IUPAC has recommended the use of term conductivity over specific conductance.

Units
The units of conductivity as derived from the above formula are :

The SI units of conductivity are S m1 but quite often  is expressed in S cm1. Conductivity of a material in S m1 is its conductance when it is 1 m long and its area of cross section 1 m2. It may be noted that 1 S cm1 = 100 S m1.
Conductivities of some substances are given in the following Table.
TABLE
Conductivities of some substances at 298 K
Material  (S m1) Material  (S m1)
Conductors Aqueous solutions
Sodium 2.1 x 103 Pure water 3.5 x 105
Copper 5.9 x 103 0.10 M HCl 3.91
Silver 6.2 x 103 0.01 M KCl 0.14
Gold 4.5 x 103 0.01 M NaCl 0.12
Iron 1.0 x 103 0.1M HAc 0.047
Graphite 1.2 x 10 0.01M HAc 0.016
Insulators Semiconductors
Glass 1.0 x 1016 CuO 1 x 107
Teflon 1.0 x 1018 Si 1.5 x 102
Ge 2.0
CONDUCTANCE OF ELECTROLYTIC SOLUTIONS
It can be seen from the table that the magnitude of conductivity varies a great deal and depends on the nature of the material. It also depends on the temperature and pressure at which measurements are made. Materials are classified into conductors, insulators and semiconducors. Metals and their alloys have very large conductivity are known as conductors. Substances like glass, ceramics etc. having very low conductivity are known as insulators. Substances like, silicon, doped silicon, gallium arsenide, having conductivity between conductors and insulators are called semiconductors and are important electronic materials. Certain materials called superconductors by definition have zero resistivity or infinite conductivity. Earlier only metals and their alloys at low temperatures (0 to 15 K ) were known to behave as superconductors, but nowadays a number of ceramic materials and mixed oxides are also known to show superconductivity at temperatures as high as 150 K.
Metallic And Electrolytic conductance
1. Metallic Conductance
Electrical conductance through metals is called metallic or electronic conductance and is due to the movement of electrons. The electronic conductance depends on :
• Nature and structure of the metal.
• The number of valence electrons per atom.
• The density of the metal
• Temperture (it decreases with increase of temperature)
As electrons enter at one end and go out at the other end, the composition of the metallic conductor remains unchanged. Electronic conduction decreases with increase in temperature.
2. Electrolytic Conductance (ionic conductance)
Even the purest water has small amounts of hydrogen and hydroxyl ions ( 107 M) which lend it very low conductivity (3.5 x 105 S m1). When electrolytes are dissolved in water, they furnish their own ions in the solution and hence its conductivity also increases. The conductance of electricity by ions present in the solutions is called electrolytic or ionic conductance.
Types of electrolytes
Electrolytes are of two types :
i) Strong electrolyte.
ii) Weak electrolyte.
Strong Electrolytes
Electrolytes like mineral acids, alkalies and most salts which give solutions with high conductivities, are called strong electrolytes. This is because strong electrolytes are more or less completely ionised , when in solution, eg.,
HCl(aq)  H+ (aq) + Cl (aq)
NaCl(aq)  Na+(aq) + Cl (aq)
KOH(aq)  K+ (aq) + OH (aq)
In other words, their degree of ionisation is 1 or 100% or nearly so.
Weak Electrolytes
Electrolytes like most organic acids, bases, water and ammonium hydroxide which are poor conductors in solution are called weak electrolytes. This is due to the fact that only a small fraction of their molecules splits up into ions in solutions. Their solutions contain small number of ions in equilibrium with unionised molecules, e.g.,

The lack of complete ionisation accounts for their low conductivity. In other words, the degree of ionisation of weak electrolytes is small.
Factors affecting electrolytic conduction
The factors which affect the free movement of ions and hence electrolytic conduction are :
i) The ionic interaction.
ii) The solvation of ions.
iii) Nature of electrolyte and the solvent.
iv) Viscosity of the solvent.
v) Temperature.
i) The inter-ionic attractions
Every electrolyte consists of positive and negative ions. In a concentrated solution, the ions are closer to each other so that there exists strong inter-ionic attraction. Consequently, the mobility of the ions will be less so that the extent of conduction will be small. However, in a dilute solution, the ions are far apart so that the force of attraction between the oppositely charged ions is negligible. As a result, the ions can move freely so that the extent of conduction will be large.
To sum up
As the concentration decreases, the inter-ionic attraction decreases and extent of conduction increases.


ii) The Solvation of ions
The positive and negative ions of an electrolyte in an aqueous solution are surrounded by water molecules. This is called solvation or hydration. The greater the extent of solvation, the lower will be the conductance.
iii) Nature of the electrolyte and the solvent
Strong electrolytes dissociate almost completely in solutions and hence conduct electricity to a large extent. On the other hand , weak electrolytes dissociates only slightly and hence conduct electricity to a smaller extent. Electrolytes undergo greater dissociation in polar solvents. Thus , the greater the polarity of the solvent, greater is ionisation and hence greater the conduction.
iv) Viscosity of the solvent
The viscosity of the solvent affects the mobility of the ions and hence the extent of conduction. As the viscosity of the solvent decreases , the mobility of the ions increases and hence the extent of conduction increases.
v. Temperature
With increase in temperature, the conductance of an electrolyte in solution increases. This is because of the increase of the average kinetic energy of the ions with temperature. In addition to this, the viscosity of the solvent, inter-ionic interaction etc. also decrease with rise in temperature.
Measurement of resistance of electrolytic solutions
The resitivity of a solution of electrolyte kept between two parallel electrodes of cross section A cm2 and ℓ cm apart , then the resistivity  should be :

where R is the resistance of this column of the liquid. Hence electrolytic conductivity  , which is the reciprocal of  is given by :

where G is the conductance of the column of the above solution.
Knowing the values of R, ℓ and A value of  can be calculated. The solution of of electrolyte is taken in a suitable cell known as conductance cell and the resistance of the solution between the two parallel electrodes is determined by using the wheatstone bridge method. It is difficult to determine the values of ℓ and A of the conductance cell precisely. However, for any particular cell , the value of ℓ / A is constant. This is known as cell constant G* and is defined as the factor which when multiplied by obseved conductance of a solution gives its conductivity. It has the the dimensions of cm1 (or m1)
Hence ,  = observed conductance x cell constant
Kohlrausch determined accurately the conductance of KCl solutions of different concentrations at different temperatures. These values are taken as the standard values to determine the cell constant of the given cell. Conductance of a standard KCl solution (e.g., 0.1 M) is determined experimentally using the cell. Knowing the value of  (as determined by Kohlrausch)

Direct current source cannot be used in these determinations as it will give wrong results due to :
(i) alteration in concentrations of solution due to electrolysis and
(ii) change in resitance of electrolyte due to polarization at the electrodes.
The difficulties are overcome by using alternating current source (an induction coil, for example). An oscillator is also used as a convenient and suitable alternating current generator. Each electrode is alternately positive and negative and any small amount of chemical change which takes place during half cycle is reversed in the next. An earphone or magic eye is used to determine the null point.
Conductance cells (Fig) are usually made of resistance glass. Electrodes are invariably of platinum , usually coated with platinum black to dimnish polarization effects. Cells with long paths are used for concentrated solutions, and cells with short paths and large electrodes are used for dilute solutions so that resistances to be measured will be of a convenient magnitude.

Conductance cells

Once the cell constant is determined, we can use it for measuring the conductivity of any solution by filling the conductivity cell with it and measuring its resistance. The set up for the measurement is shown in Fig.

Arrangement for measurement of resistance of a solution of an electrolyte
It consists of two fixed resistances R3 and R4, a variable resistance R1 and conductivity cell having unknown resistance R2. The Wheatstone bridge is fed by an oscillator O (a source of a.c. power in audio frequency range 550 to 5000 cycles per second). P is a suitable detector (a headphone or other electronic device) and bridge is balanced when no current passes through the detector.
The unknown resistance R2 equals :

These days, inexpensive conductivity metres are available which can directly read the conductance or resistance of the solution in the conductivity cell. Once the cell constant and resistance of the solution in the cell is determined, the conductivity of the solution is given by the equation:

Thus the whole operation consists of two steps :
• Determination of cell constant using a standard KCl solution of known concentration in the conductance cell.
• Determination of resistance of the given electrolyte.
Determination of cell constant
The cell constant is not generally calculated from the values of ℓ and ‘A’ because these are difficult to be measured for a given cell. It is therefore more convenient to obtain its value by measuring the conductance of a standard solution whose conductivity is known. For this purpose, a standard solution of KCl is used whose conductivity is known at different concentrations and temperatures. For example, for 0.1 M KCl solution at 298 K , the conductivity is 0.012886 ohm1cm1. Suppose the conductance of this solution in the given cell is measured to be X. Then,

Once , the cell constant is known, the conductivity can be calculated from the measured conductance or measured resistance of the electrolytic solution.
Calculation of specific conductance ()
The specific conductance  is related to the resistance R or conductance (G ) as :

Here, ℓ is the distance of separation of the two electrodes and A is the area of cross section of the electrodes.
The quantity (ℓ/ A) is called cell constant (G*).


Equivalent Conductivity Of Electrolytic Solutions
The conductivity of metallic conductor has a definite value at a given temperature. However, in the case of electrolytic solution the conductivity not only depends on temperature but also varies with the concentration of the solution. It is due to the fact that conductivity of a solution is attributed to the presence of ions. The number of ions in one centimetre cube of the solution changes with the variation in concentration. In order to compare the conductivity of different electrolytes, it is necessary to consider the solutions of equivalent concentrations, i.e., solutions which are capable of furnishing ions carrying the same total charge of electricity. For example, one gram equivalent of different electrolytes in the solutions produce ions carrying the same total charge of electricity. (Let us consider the same volume of two solutions containing one mole each of NaCl and Na2SO4 respectively. One mole of NaCl produces one mole Na+ ions and 1 mole of Cl ions. On the other hand , one mole of Na2SO4 produces 2 moles of Na+ and one mole of SO42 ions. It is evident , therefore , that 1 mole of NaCl yields ions carrying 2 faradays of electricity while 1 mole of Na2SO4 yields ions carrying 4 faradays of electricity. But if we take 1 gram equivalent of NaCl and 1 gram equivalent of Na2SO4 (=1/2 mole), then each one produce ions carrying 2 faradays of electricity). Thus, the most convenient method used to compare the conductivities of electrolytes is to express them as equivalent conductivity.
Equivalent Conductivity is defined as the conductance of a solution containing 1 gram equivalent of the electrolyte such that the entire solution is placed between two electrodes one centimetre apart. It is denoted by the symbol eq..
Relationship between Conductivity () and Equivalent Conductivity (eq)
In order to derive relationship between  and eq , let V cm3 of the solution containing 1 gram-equivalent of the electrolyte be placed between two large electrodes 1 cm apart.
Let the measured conductance of the solution = x
As the solution contains 1 gram-equivalent of electrolyte, the measured conductance also represents the equivalent conductance.
Hence , eq= x
As the volume of the solution is V cm3,
The number of centimetre cube in V cm3 = V
The conductivity () is the conductance of 1 centimetre cube of solution.
  = x / V
or  = eq
V
or eq =  V
where, V refers to volume containing 1 gm-equivalent of electrolyte.
If C is the concentration of solution in gram-equivalent per litre, i.e., normality of the solution, then the volume of solution containing one gram-equivalent of electrolyte can be calculated as :
C gram-equivalents of electrolyte are present in = 1000 cm3 of solution.
1 gram equivalent of electrolyte is present in = (1000/C) cm3 of solution.
Thus ,

where , N is the normality of the solution.


Units

In SI system the units are S m2 equivalent1
1 S m2 equivalent1 = 104 S cm2 equivalent1
1 S cm2 equivalent1 = 104 S m2 equivalent1
Molar conductivity
Molar conductivity is defined as the conductance of the solution containing one gram-mole of the electrolyte such that entire solution is placed between two parallel electrodes one centimetre apart. It is denoted by m. Molar conductivity is related to conductivity() by the relation:

where M is the molarity of the solution.
Units

In SI system the units are S m2 mol1
1 S m2 mol1 = 104 S cm2 mol1
1 S cm2 mol1 = 104 S m2 mol1
Problems
1. Resistance of a conductivity cell filled with 0.1 M KCl solution is 100 . If the resistance of the same cell when filled with 0.02 M KCl solution is 520 . Calculate the conductivity and molar conductivity of 0.02 M KCl solution.
2. The electrical resistance of a column of 0.05 M NaOH solution of diameter 1 cm and length 50 cm is 5.55 x 103 ohm. Calculate its resistivity, conductivity and molar conductivity.
3. A 0.05 M NaOH solution offered a resistance of 31.6 ohm in a conductivity cell at 298 K. If the cell constant of the conductivity cell is 0.367 cm1, find out the molar conductance of the sodium hydroxide solution.
4. Calculate the equivalent conductivity of 1 M H2SO4 solution whose conductivity is 26 x 102 ohm1cm1.
5. Electrolytic conductivity of 0.02 mol L1solution of KCl at 298 K is 2.48 x 102 ohm1cm1. Calculate its m ?
6. The resistance of 0.5 N solution of an electrolyte in a conductivity cell was found to be 45 ohms. Calculate the equivalent conductivity of the solution, if the electrodes in the cell are 2.2 cm apart and have an area of 3.8 cm2.
7. The specific conductivity of N/10 KCl solution at 180C is 0.112 S cm1. The resistance of the cell containing this solution at 180C was found to be 55 ohms. What is the cell constant ?
8. A conductivity cell filled with 0.01 M solution of KCN offered a resistance of 11,210 ohms at 00C. Calculate the specific conductance of the electrolyte if the cell constant be 8.76 cm1 .
9. A conductance cell has two parallel electrodes of 1.25 cm2 area and 10.5 cm apart. When filled with 0.1 N solution of an electrolyte at 250C, the resistance was found to be 2,000 ohms. Calculate :
i) Cell constant
ii) Equivalent conductance of the solution of the electrolyte.
10. The resistance of a conductivity cell when filled with 0.02 N KCl solution is 164 ohms at 250C and when filled with 0.05 N AgNO3 is 78.5 ohms. The specific conductivity of 0.02 N KCl is 2.768 x 103 ohm1cm1. Calculate :
i) the specific conductance of 0.05 N AgNO3 solution.
ii) the equivalent conductance of this solution.
11. Specific conductance of two electrolytes of 0.1 M concentration of the substance A and B are 9.2 x 103 and 4.7 x 104 ohm1cm1 respectively. Which of them offers less resistance for the flow of current and which is the stronger electrolyte ?
12. The resistance of a conductivity cell containing 0.001 M KCl solution at 298 K , is 1500 . What is the cell constant if conductivity of 0.001 M KCl solution at 298 K is 1.46 x 103 S cm1.
Variation Of Molar Conductivity
In general the conductance of an electrolytic solution depends up on the following factors:
i) Nature of electrolyte.
ii) Concentration.
iii) Temperature.
i) Nature of electrolyte
The conductance of the solution depends upon the nature of electrolyte. All electrolytes do not ionise in their aqueous solutions to the same extent. They can be divided into two categories depending upon their extent of ionisation.
a) Strong electrolytes
An electrolyte which is completely ionised in aqueous solution is called strong electrolyte.
Some examples of strong electrolytes are : mineral acids like HCl, H2SO4 etc. bases like NaOH, KOH etc. and salts like KCl, NH4Cl, CH3COONH4, etc. Such electrolytes have high values of m.
b. Weak Electrolytes
An electrolyte which is not completely ionised in aqueous solution is called weak electrolyte. The aqueous solution of weak electrolytes contains ions in equilibrium with undissociated molecules. Some examples of weak electrolytes are CH3COOH, NH4OH etc. Such electrolytes possesses low values of molar conductivities.
ii) Variation of molar conductivity with Concentration
In order to understand this, let us examine the values of m for some electrolytes at different concentrations as given in the following Table.
TABLE
Molar Conductance m of Electrolytes (S cm2 mol1) at 298K
Concen
( M) HCl NaOH NaCl CH3COOH NH4OH
0.1 391.3 - 106.7 5.2 3
0.05 399.1 - 111.1 7.4 11.3
0.02 407.2 - 115.8 11.6 34.0
0.01 412.0 238.0 118.5 16.2 46.9
0.005 415.8 240.8 120.7 22.8 -
0.001 421.4 244.7 123.7 48.6 -
0.0005 422.7 245.6 124.5 - -

From the above table, it is clear that the molar conductivity of electrolytes generally increases with increase with dilution. The relative increase in the molar conductivity in case of strong electrolytes is not so large as that in the case of weak electrolytes. The variation of m versus C for KCl , a strong electrolyte and CH3COOH , a weak electrolyte has been shown in Fig 2.

Fig 2. Variation of Molar Conductivity for KCl and
CH3COOH with concentration.

From the figure , it is evident that in the case of strong electrolytes there is a tendency for molar conductivity to approach a certain limiting value when concentration approaches zero, i.e., when dilution is infinite. The value of molar conductivity when the concentration approaches zero is known as molar conductivity at zero concentration or at infinite dilution. It is denoted by mo and is determined by extrapolating the graph to zero concentration (Fig 2 ).
In the case of weak electrolytes such as acetic acid, there is no indication that the limiting value can be attained when the concentration approaches zero. Thus, for weak electrolytes the value of molar conductivity at infinite dilution cannot be obtained by extrapolating the graph. It may , however, be obtained indirectly by Kohlrausch's law.
Explanation for the variation of Molar conductivity
a) For weak electrolytes, the variation in the value of m with dilution can be explained on the basis of number of ions furnished by it in the solution. The number of ions furnished by the electrolytes in solution depends upon the degree of ionisation of the electrolyte. On dilution, the degree of ionisation of the weak electrolyte increases, thereby increasing the value of m. Therefore , it is evident that when the limiting value of molar conductivity is reached, the degree of dissociation of the electrolytes approaches unity i.e., whole of solute dissociates into ions. Therefore, at any other concentrations, the degree of dissociation,  is given by the expression :

b) For strong electrolytes , the number of ions in the solution do not increase because, these are almost completely ionised in solution at all concentrations. However, in concentrated solutions of strong electrolytes the density of the ions is relatively high which results in the significant inter-ionic interactions. Such inter-ionic attractions effectively reduce the speed of the ions and are responsible for the lower value of m. On increasing dilution the ions move apart and inter-ionic attractions are decreased. As a result the value of m increases. In general, m and mo for strong electrolytes are related as :

where m is molar conductivity,
mo is molar conductivity at infinite dilution.
b is a constant which depends upon the viscosity and dielectric constant of the solvent, C is the concentration of solution. It is quite evident that as C approaches zero :

V

QUESTIONS

Atoms and Molecules
1.

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