B. Sc. S. Y. ELECTROCHEMISTRY

Dr. S. M. Reddy

Associate Prof.

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Physical Chemistry

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Conductivity cell

Cell constant and its determination

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The exact value of the cell constant (l/A) can be determined by measuring the distance between the electrodes (l) and their area of cross-section (A).

Actual measurement of these dimensions is very difficult.

Therefore an indirect method is employed to determine the value of cell constant. We know that

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To determine cell constant, a standard solution of KCl whose specific conductance at a given temperature is known is used.

Then a solution of KCl of the same strength is prepared and its conductance determined experimentally at the same temperature.

Substituting the two values in the above expression the cell constant can be calculated.

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Arrhenius theory of electrolytic dissociation

According to Arrhenius the conductance of solution was due to the presence of ions.

In 1884, he put forward the theory of ionisation.

• When electrolytes are dissolved in water, then the neutral electrolyte molecules split up into two types of charged particles called ions.
• The positively charged ions are called as cations while negatively charged particles are called as anions.

AB → A⁺ + B^‾ (Old view)

In its modern form, the theory assumes that the ions are already present in the solid electrolyte and these are held together by electrostatic force.

When electrolytes are placed in water, these neutral molecules dissociate to form separate anions and cations.

A⁺B‾ → A⁺ + B‾ (Modern view)

Therefore, this theory is also called as theory of electrolytic dissociation.

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• The ions present in the solution constantly reunite to form neutral molecules.
• Thus there is a state of equilibrium between the undissociated molecules and the ions.

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Applying the law of mass action

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K – is called as dissociation constant

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• The charged ions are free to move through the solution to the oppositely charged electrodes.
• This movement of the ions constitutes the electric current through electrolytes.
• This explains the conductivity of electrolytes as well as the phenomenon of electrolysis.

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• The electrical conductivity of an electrolyte solution depends on the number of ions present in the solution.
• Thus the degree of dissociation of an electrolyte determines whether it is a strong electrolytes or weak electrolytes.

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Limitations of Arrhenius theory of electrolytic dissociation

• Arrehenius suggested that ionization of the electrolyte takes place when dissolved in water.
• However, from X-ray analysis it is observed that many such electrolytes are already present in the ionised state ( eg Na⁺Clˉ).
• As an electrolyte can conduct electricity even in the molten state, it shows that the dissociation of the electrolyte takes place even in the molten state.
• As such the function of water could not be explained by Arrhenius theory.

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• This theory fails when applied to strong electrolytes:
• Ostwald’s dilution law which is derived on the basis of Arrhenius theory, using the concept of ionic equilibrium, fails for the strong electrolytes ie a constant value of the dissociation constant K is not obtained.

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• The degree of dissociation (α) of strong electrolytes calculated from conductance measurement (α = λc/λ∞) was found to be different from that calculated from colligative properties.

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• Strong electrolytes are almost completely dissociated even at moderate concentrations, ie α = 1 or 100 % at all concentrations.

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• Hence Arrhenius view that conductance increases with dilution because the dissociation increases is not valid in case of strong electrolytes.
• The increase in conductance with dilution is therefore, due to some other factors.

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Debye-Huckel theory of strong electrolytes

In case of weak electrolytes, the increase in the equivalent conductance with dilution can be explained on the basis of Arrhenius theory which suggests that the conductance increases because the dissociation of weak electrolyte increases with dilution.

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However, in case of strong electrolytes, as they are almost completely dissociated even at moderate concentration, the increase in equivalent conductance with dilution must be due to some additional factors.

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Debye-Huckel theory explains the increase in the equivalent conductance of strong electrolytes with dilution is based on following factors.

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Relaxation effect or asymmetric effect

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• Each ion in a solution is surrounded by an ionic atmosphere of opposite charge. As long as no electric field is applied, the ionic atmosphere remains symmetrical around the central ion (Fig.a).

• However, when a current is passed through the solution, the central ion moves towards the oppositely charged electrodes.

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As it is moving out of the ionic atmosphere, it has to rebuild an ionic atmosphere of apposite charge around it and the old ionic atmosphere is destroyed. However, the destruction of old ionic atmosphere and the formation of new ionic atmosphere do not take place at the same time. There is some time lag called as time of relaxation between the destruction of old ionic atmosphere and the formation of new ionic atmosphere.

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During this time, the old ionic atmosphere pulls the moving ion backward and hence retards its motion (Fig. b). Hence this effect is known as relaxation effect. Alternatively, it may be argued that as the central ion moves, the symmetry of the atmosphere is lost, more ions of the ionic atmosphere are left behind than are present in the front (Fig. b). The excess ions of the ionic atmosphere present behind the moving ion drag the ion backward and retard its motion. Thus the effect arises because of the asymmetry of the ionic atmosphere of the moving ions and hence is also known as asymmetric affect.

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Electrophoretic effect

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Fig. c

When EMF is applied, the central ion moves in one direction and the oppositely charged ionic atmosphere moves in the opposite direction. As this ionic atmosphere moves, the solvent molecules associated with it also moves. Thus the flow of the ionic atmosphere and that of the solvent molecules attached to it takes place in a direction opposite to that of the movement of the central ion. In other words, the central ion is moving against the stream. Thus motion of the ions is retarded. This effect is called as electrophoretic effect (Fig. c).

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Debye- Huckel Onsager’s equation and its verification

Besides these two effects, the third retarding force is the normal frictional resistance offered by the medium which depends on the viscosity of the medium, its dielectric constant etc.

Bases upon the above facts, Debye and Huckel (1923) derived a mathematical expression for the variation of equivalent conductance with concentration. This equation was further improved by Onsagar (1926-27). Therefore this equation is known as Debye-Huckel –Onsagar equation or simply Onsagar equation. For uni-univalent electrolyte, it is written in the form :

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Where, Λ_c – is equivalent conductance at concentration c

Λ_o – is equivalent conductance at infinite dilution

D – Dielectric constant of the medium

η – Viscosity of medium

T – Temperature of the solution in degrees absolute

C – concentration of the solution in moles/lit

As D and η are constants for a particular solvent, therefore at constant temperature, the above equation can be written as :

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Where, A and B are constants for a particular solvent at a particular temperature.

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Verification of Onsager’s equation

Validity of the Onsagar equation is established by the following two observations:

• The plot of Λ_c vs √C is linear
• The slope of the line obtained is equal to A + B Λ_o after putting the values of A and B.

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Migration of ions

AgNO₃ → Ag⁺ + NO₃^–

CuSO₄ → Cu⁺⁺ + SO₄^{– –}

H₂SO₄ → 2H⁺ + SO₄^{– –}

The electrolytes dissociate in solution to form positive ions (cations) and negative ions (anions). As the current is passed between the electrodes of the electrolytes, the cations will move towards cathode and anion will move towards anode. Usually the different ions move with different rates.

Migration of ions through electrolytic solution to opposite electrodes

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• Lodge’s moving boundary experiment:

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The apparatus used consists of a U tube having long horizontal portion. It is fitted with side limbs. The horizontal portion is filled with a jelly of agar – agar treated with a trace of alkali. This is then made red by adding few drops of phenolphthalein.

When jelly is set, dil H₂SO₄ is added in the anodic limb of the tube. Sodium sulphate solution is added in the cathodic limb. On passing the current H⁺ ions in the left limb solution eventually move into the agar – agar jelly. Their passage is marked by the gradually discharge of the red colour due to the neutralization of the alkali by H⁺ ions. The movement of the red boundary through the agar – agar jelly shows that H⁺ ions migrates to the cathodic limb.

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• Movement of coloured ions:

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The lower part of the U – tube is filled with a 5 % water solution of agar – agar with a small amount of copper dichromate (CuSO₄ + K₂Cr₂O₇). The surface of the green solution in the two limbs of the U – tube is marked by a small amount of charcoal. In both the limbs, a layer of solution of potassium nitrate and agar – agar is placed. This is allowed to set. Over this second layer of potassium nitrate solution in this water is placed and two electrodes are inserted in it.

As the current is turned on, the blue colour of Cu⁺⁺ ions rises into the jelly under the cathode and reddish yellow dichromate ions (Cr₂ O₇^{– –} ) move up under the anode. After some times the two types of ions are seen rising with well defined boundaries. The use of jelly is to prevent the mixing of the solutions by diffusion.

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Transport number

During electrolysis the anions and cations carry current.

The fraction of the total current carried by the cation or the anion is called as transport number. It is also known as Hittorf number.

Let, v₊ - be the speed of migration of cation.

v_ be the speed of migration of anion.

t₊ and t_ are the transport numbers of cations and anions respectively.

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r – r t₊ = t₊

r = t₊ + r t₊

r = t₊ ( 1 + r)

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t _ = 1 – t₊

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Kohlrausch law

In 1875, Kohlrausch studied the equivalent conductance of different electrolytes at infinite dilution ( λ_∞) and he observed that each ion contributes to the conductance of the solution. He stated the general equation known as Kohlrausch law. It states that:

The equivalent conductance of an electrolyte at infinite dilution is equal to the sum of the equivalent conductance of the component ions. Mathematically, it states as :

λ_∞ = λ_a + λ_c

where, λ_a is equivalent conductance of anion

λ_c is equivalent conductance of cation

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Applications of Kohlrausch’s law:

Each ion has the same constant ionic conductance at a fixed temperature, no matter of which electrolyte it forms a part. It is expressed in ohm^-1 cm² and is directly proportional to the speeds of the ions.

λ_a α v_ or λ_a = k x v_

λ_c α v₊ or λ_c = k x v₊

where k is constant of proportionality

also

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Dividing eq 1 by 2

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From the equation 3 we can determine the ionic conductance from the experimental values of the transport number of the ions.

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• Determination of equivalent conductance at infinite dilution of weak electrolytes

Weak electrolytes do not ionize to a sufficient extent in solution and are far from being completely ionized even at very great dilution. The practical determination of ( λ_∞) in such cases is, therefore, not possible. However, it can be calculated with the help of Kohlrausch’s law.

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Thus the ionic conductance of an ion is obtained by multiplying the equivalent conductance at infinite dilution of any strong electrolyte containing that ion by its transport number.

In this manner, the ionic mobilities of the two ions present in the weak electrolyte can be calculated. Thus we can get the equivalent conductance of the electrolyte at infinite dilution by adding up these two values.

• Determination of degree of dissociation or conductance ratio:

The apparent degree of dissociation (α ) of an electrolyte at infinite dilution V is given by α = λ_v/λ_∞, where λ_v is the equivalent conductance of the electrolyte at the dilution V and λ_∞ is its equivalent conductance at infinite dilution. This according to Kohlrausch’s law and is equal to the sum of λ_a and λ_c .

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• Determination of solubility of sparingly soluble salts.

Substances like AgCl or PbSO₄ which are ordinarily called as insoluble do possess a definite value of solubility in water. This can be determined from conductance measurements of their saturated solutions. Since a very small amount of solute is present it must be completely dissociated into ions even in a saturated solution so that the equivalent conductance k V is equal to equivalent conductance at infinite dilution. This according to Kohlrausch law is the sum of the ionic mobilities.

k V = λ_∞ = λ_a + λ_c

Knowing k and λ_∞ , V can be calculated which is the volume in ml containing 1 gm-eqvt of the electrolyte.

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• Determination of absolute ionic mobility

The absolute ionic mobility of an ion is defined as the velocity of an ion in centimeters per second under a potential gradient of one volt per centimeter. It is expressed in cm/s.

Potential gradient = Applied EMF / Distance between the electrodes.

For example, let the velocity of the ion at infinite dilution be U cm per sec. when the distance between the electrodes is 20 cm and the voltage 100 V. then the potential difference is 100/20 ie volts per cm and the ionic mobility is U/5 cm/sec.

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It has been found that the ionic conductance is directly proportional to the ionic mobility ie

λ_a α U _a and λ_c α U_c

λ_a = k U _a and λ_c = k U_c

Where, k is the proportionality constant. Its value is equal to the charge on one gram-equivalent of the ion under the potential gradient of 1 volt per cm ie k = 96500 coulomb (1 Faraday). Therefore, the ionic mobility is obtained by dividing the ionic conductance by96500 coulombs.

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• Determination of ionic product of water

The observed specific conductance of the purest water at 25 °C is 5.54 x 10^-8 mhos. The conductance of one litre of water containing 1 gm eqvt of it would be:

λ_H2O = 5.54 x 10^-8 x 1000 = 5.54 x 10^-5 mhos

At the temperature the conductance of H⁺ ions and OHˉ ions are :

λ_H⁺ = 349.8 mhos and λ_OH^- = 198.5 mhos

according to Kohlrausch law

λ_H2O = λ_H⁺ + λ_OH^-

= 349.8 + 198.5

= 548.3 mhos

One molecule of water gives one H⁺ ion and one OHˉ

H₂O = H⁺ + OHˉ

Assuming that ionic concentration is proportional to conductance, we have

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K_w = [H⁺] [OHˉ] = 1.02 x 10^-14 at 25 °C

For most purposes, the value of K_w is taken to be 10^-14

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Conductometric titrations:

Conductometric methods help us to reach accurate end points in titrations. The basic principle in conductometric titration is that when one solution from the burette is added to the other solution in the titration flask, conductance value changes. This helps us to arrive at the end point.

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• Conductometric titrations of a Strong acid against strong base

Suppose a solution of HCl is to be titrated against NaOH solution. The acid solution is taken in a beaker in which conductivity cell is deepened and the NaOH solution in the burette. The conductivity of the acid solution is noted initially as well as after successive addition of small amount of NaOH solution. Evidently, the conductance of the acid solution in the beginning is very high as it contains highly mobile H⁺ ions ( HCl → H⁺ + Cl ˉ ). On adding NaOH solution to the HCl solution, the H⁺ ions are replaced by slow moving Na⁺ ions and hence the conductance of the solution keeps on falling till the end point is reached (ie. all the H⁺ are replaced by Na⁺ ions).

H⁺ + Cl ˉ + Na⁺ OH ˉ → Na⁺ + Cl ˉ + H₂O

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Beyond the end point, further addition of NaOH solution brings in fast moving OH ˉ ions and hence the conductance of the solution again starts increasing. If conductance values are plotted against the volume of the alkali added, a curve of the type ABC is obtained as shown in fig a. Point of intersection B corresponds to the end point.

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• Conductometric titrations of a Strong acid against weak base

Consider a titration of strong acid such as HCl against weak base NH₄OH solution. The conductance of HCl solution is initially high because of the presence of fast moving H⁺ ions. As NOH⁴OH solution is added, the fast moving H⁺ ions are replaced by the slower NH₄⁺ ions and hence the conductance falls along the line AB.

H⁺ + Cl ˉ + NH₄OH → NH⁺ + Cl ˉ + H₂O

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When the end point is reached, further addition of NH₄OH does not cause much change in the conductance because NH₄OH is weakly ionized substance. Therefore the line BC is almost horizontal.

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• Conductometric titrations of a Weak acid against strong base

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Consider a titration of weak acid such as CH₃COOH against strong base NaOH solution. The conductance of the acid initially is very low because of low ionization of the acid. However on adding NaOH solution to the acid solution, the salt produced CH₃COONa is highly ionized and hence the conductance keeps on increasing along the line AB as shown in fig .When the whole of acetic acid is neutralized, further addition of NaOH solution causes the conductance to increase sharply along the line BC because the NaOH added introduces the fast moving OH‾ ion. Intersection of the two lines AB abd BC at the point B gives the equivalent point.

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• Conductometric titrations of a weak acid against weak base.

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Consider the titration of weak acid acetic acid against weak base NH₄OH. Initially the conductance of the solution is low due poor dissociation of acetic acid. As the base is added to it, the conductance starts picking up due to the formation of ionizable ammonium acetate. After the neutralization point, conductance remains almost constant, because the free base NH₄OH is a weak electrolyte. The end point is quite sharp as shown in the fig.

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• Precipitation titration.

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Consider the titration of silver nitrate solution against KCl solution. AgNO₃ solution has some definite value of conductance in the beginning. As KCl solution is added to the AgNO₃ solution, the following reaction takes place.

Ag⁺ + NO₃ˉ + K⁺ + Cl ˉ → K⁺ + NO₃ˉ + AgCl

Thus the net result is the replacement of the Ag⁺ ions of AgNO₃ solution by K⁺ ions. Since both these ions have nearly equal ionic mobility, the conductance remains almost constant till the end point is reached as shown in fig. After the end point, further addition of KCl brings in K⁺ and Cl ‾ ions. Thus the conductance begins to increase along the line BC. Point of intersection B corresponds to the equivalence point.

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Advantages of conductometric titrations.

Conductometric titrations have number of advantages over ordinary titrations:

• These titrations can be used for coloured solutions where ordinary indicators fails.
• As the end point in these titrations is the intersection of two lines, no extra care is needed near the end point.
• These can be used for the titration of mixture of weak and strong acids.
• These can be used for the titration of even very dilute solutions.

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Thank you