ELECTROLYTES

• An electrolyte is a substance which conducts electricity when

in the liquid or in the dissolved state, owing to movement of
ions.

• An example is sodium chloride, either in the fused (molten)

state, or dissolved in water.
• The force of attraction (F) between two opposite charges, q1 and q2, separated by
a distance r in a medium of permittivity ε, is given by Coulomb’s inverse square law

• When an ionic substance is melted, heat energy is supplied to overcome

coulombic attraction and the ions undergo a dissociation, that is, acquire the ability
to move independently.

• Similarly ionic dissociation occurs when the substance is dissolved in a solvent of

high permittivity, such as water, because the force of attraction between the ions is
lowered considerably during the dissolution process
 ELECTROLYSIS

• When an electric current is passed through an electrolyte melt or

solution, the positive ions (cations) migrate to the negative electrode
(cathode), where they are reduced, and the negative ions (anions) migrate
to the positive electrode (anode) where they undergo oxidation.

• The products of electrolysis are deposited or liberated at the electrodes.

• The mass (W) of an element discharged in this manner is governed by Faraday’s
laws of electrolysis, which may be summarised as follows:

• Where I is the constant current passing for a time t, A is the relative atomic mass
of the element, z the valency of the ion discharged, and F the Faraday constant.

• This constant, approximately 96500 coulombs per mole of a univalent element, is

the charge associated with one mole (i.e., an avogadro number) of electrons.
 IONISATION AND DISSOCIATION

• Many compounds (e.g., hydrogen chloride, ethanoic acid) are largely covalent
when in the pure state, but an ionisation takes place in solution because of a
reaction with the solvent.

• For example, a non-ionic compound of the type HA, dissolved in water, might
react as follows:

• The extent of such an ionisation reaction is dependent upon the nature of the
compound and the solvent.
• Even for compounds which are fully ionised (e.g., salts) the ionic dissociation may
be incomplete.

• At any instant a certain proportion of the ions may be associated with one
another as ion-pairs (e.g. Mg++SO4 -- , or Ca++Cl- ), and sometimes as even more
complicated ionic groupings.

• Such ionic association becomes more probable in concentrated solutions, more so

for highly charged ions, and is expected to affect the electrical conductivity of the
system.

• The degree of dissociation , which is the fraction of each mole electrolyte

existing as completely free ions.
 Measurement of Electrolytic Conductance
• Electrical conductance is the reciprocal of the resistance.

• An electrolyte placed between two inert parallel electrodes, a distance d apart, and
each of area A, will have the following conductance:
• The electrolytic conductivity κ (units: Ω -1 m -1 ) depends on the temperature, the
nature of the electrolyte and its concentration.

• Another important quantity is the molar electrolytic conductivity , with units Ω-1
m 2 mol-1 :

• where c is the electrolyte concentration (in mol m-3 ). When, however, c is in mol dm-3 ,
then it is possible to write that
• To prevent polarisation at the electrodes while measuring conductance, an
alternating current must be used, and consequently the balance point must be
obtained using earphones, or else an “electron beam” detector, such as a cathode
ray oscilloscope.

Wheatstone bridge
• The Wheatstone bridge works on the principle of null deflection, i.e. the ratio of their
resistances are equal and no current flows through the circuit.

• Under normal conditions, the bridge is in the unbalanced condition where current flows
through the galvanometer.

• The bridge is said to be in a balanced condition when no current flows through the
galvanometer.

• This condition can be achieved by adjusting the known resistance and variable resistance.
• The ratio for the conductivity cell is known as the cell constant

• Therefore from the conductivity of the solution in the cell is obtained

as follows:

• The cell constant is usually obtained by calibration using a solution of independently

known conductivity.

• Since even very pure water conducts electricity to some extent, for accurate conductance
measurement it is usually necessary to apply a solvent correction.
 The Ionic Atmosphere

• Owing to coulombic attraction an ion in solution tends to be surrounded

by a shell or “atmosphere of ions of opposite charge.

• When ions move in an electric field, the ionic atmosphere is distorted and
the speed of migration of each ion is reduced.

• This effect is especially strong in solutions where the concentration of

ions is high; such solutions therefore behave in a non-ideal manner.
• However when an electrolyte is progressively diluted, its behaviour becomes less
imperfect because the ions are placed farther apart and exert less influence on one
another.

• An electrolyte “at infinite dilution” is expected to behave ideally, in the same way as a gas
at “zero” pressure becomes an ideal gas.
 Dependence of Molar Conductivity on Concentration
• Since κ depends on the number of ions present in the solution, we might reasonably
expect that the molar conductivity, being the ratio , should be independent of the
electrolyte concentration, c.

• In practice, this is not so; we generally find that decreases as c increases.

• From the extent of this variation it is possible to distinguish between two limiting types
of electrolyte: the “weak” and the “strong”.
• Strong electrolytes

• has relatively high values at all concentrations.

• According to Kohlrausch, the change of molar conductivity with concentration may

be represented by the following equation:

• where m is a constant characteristic of the electrolyte, and is the molar

conductivity at infinite dilution, obtainable by extrapolation of the above graph to c
= 0.
• Weak electrolytes

• For electrolytes of this type (e.g., the weak acids and bases), ionisation and
dissociation are low in concentrated solutions.

• For this reason the molar conductivity is also low.

• However, when the system is progressively diluted, ionisation and dissociation

increase, and may be assumed to become 100% at infinite dilution.

• Arrhenius suggested that the degree of dissociation (α) of a weak electrolyte

should be obtainable from conductivity measurements:
• This relation is now known to be good approximation, but not be used for strong
electrolytes because they are excessively affected by the ionic atmosphere.

• In the case of weak electrolyte solutions the concentration of ions is always relatively low,
so the effect of the ionic atmosphere can usually be neglected.

• The use of equation requires a knowledge of .

• For weak electrolytes this cannot be obtained by extrapolation of the above, but an
indirect method like the Law of independent migration of ions can be used.
Law of Independent Migration of Ions

• Kohlrausch's law of independent migration of ions states that “at infinite dilution,
the dissociation of the electrolyte is complete and hence each ion makes definite
contribution to the equivalent conductivity of the electrolyte irrespective of the nature of
other ions associated with it”.

• Therefore the limiting molar conductivity of an electrolyte can be represented as

the sum individual contributions of its cations & anions.

• The conductivity of a solution decrease with dilution because less ions are
present for conduction.
• According to this Law, at infinite dilution each ionic species contributes a definite
amount towards the value of the molar conductivity.

• For any electrolyte MA we may therefore write:

• are the limiting molar conductivities of the ions M+ and A- ,

respectively.
• However the Kohlrausch law can also be stated in terms of molar conductivities as:

• The limiting molar conductivity of an electrolyte is the sum of individual

contributions of limiting molar conductivities of its constituent ions.
Experimental Basis And Theoretical Explanation Of Kohlrausch Law

• Kohlrausch observed that at infinite dilutions, the difference between the conductivities of
sodium and potassium salts is constant irrespective of the associated anions, as tabulated
below.
• Kohlrausch argued that the constant difference in the conductivities of above pairs
can be ascribed to the fact that the mobility of sodium and potassium ions at
infinite dilution is not influenced by the nature of counter ions.

• The ions at such a low concentration migrate in the electric field as they are
independent i.e., they show same ionic conductance irrespective of the nature of
counter ion.
 Applications of Kohlrausch Law

• These ionic contributions can be measured experimentally and a table of such

values enables to be obtained for any weak electrolyte.
• Alternatively we could obtain Λo for a weak electrolyte by suitable
addition and subtraction of Λo values for strong electrolytes, obtained by
extrapolation

EXAMPLE.

• At 25oC and at infinite dilution, the molar conductivities of the strong

electrolytes sodium benzoate, hydrochloric acid and sodium chloride, are 82, 426
and 126 Ω-1cm2 mol-1, respectively.

• Therefore for benzoic acid at the same temperature,

Λo = 82 + 426 – 126 = 382 Ω-1cm2 mol-1.

 Correction For Non-ideality of Electrolytes
• Ionic interaction causes a reduction in the speeds of migration of ions, and
consequently lowers the electrical conductance.

• Thus, the solution behaves as if fewer ions than there actually are were present to
carry the current. To correct for such imperfection, ionic concentration (c) is
replaced by ionic activity (a):

• The correction factor γ is known as the activity coefficient.

• At infinite dilution, ionic interactions are reduced to zero and therefore γ → 1 as a

→ c.
• However, as the concentration is increased γ becomes less than unity
 Calculation of Activity Coefficients
• The distribution of ions in an electrolyte solution, and to obtain a quantitative
relationship between the activity coefficient and the concentration was studied.

• For any ionic species i :

• where zi is the valency of the ion, A is a calculated constant ( = 0.51 kg½ mol-½, for
aqueous solutions at 25oC), and I is the ionic strength of the solution.

• The above equation is called the Debye-Huckel equation and is a “limiting law”, strictly
valid only for sufficiency dilute solutions (< 0.01M).
• Ionic strength is a measure of the intensity of the electric field existing
within the solution due to the presence of ions.

• If the solution contains several ionic species of valencies z1, z2, z3,.., and
concentrations c1, c2, c3, …, then
EXAMPLE. For a solution which is 0.01M in sodium chloride and 0.005M in calcium
chloride, calculate:

• (i) the total ionic strength, and

• (ii) the activity coefficient of the sodium ion.

• SOLUTION
(i) The concentration of Na+, Ca++ , and Cl-, are 0.01, 0.005 and 0.02M, respectively.

Therefore
 Conductimetric Titration

• Conductance measurements find an important analytical application in determining the

end-point of a titration.

• The experimental procedure is as follows.

• The solution to be titrated is placed in a beaker; a dip cell is inserted and connected to a
conductance bridge. The titrant is added in small quantities (e.g., 0.5 – 1.0 cm³).

• After each addition the solution is stirred and its conductance measured.

• A graph is plotted of conductance against total volume of titrant added, the endpoint being the
point at which the graph suddenly changes slope.
• The shape of a conductimetric titration graph depends upon the strength of the acid and
of the base used, and on the molar conductivities of the ions involved.

• For example when the weak base ammonium hydroxide is progressively added to the
weak ethanoic acid:

• The conductance initially rises because the sparingly ionised molecules of acid are
gradually replaced by ethanoate and ammonium ions.

• Beyond the endpoint the poor ionisation of excess ammonia is repressed by the already
present NH4+ ions, so the conductance becomes constant, as shown below
• When hydrochloric acid is titrated with sodium hydroxide, the titration graph is V-shaped.

• The initial decrease in conductance is due to a replacement of H3O+ by Na+ ions, which
have a lower molar conductivity.

• The increase in conductance beyond the endpoint is due to the presence of excess Na+
and OH- ions.

• To obtain linear conductance changes during titration it is necessary to prevent excessive dilution.

• For this reason the titrant must be at least five times more concentrated than the solution being
titrated (the titrand), and therefore has to be added using a microburette.

• The conductimetric technique is especially advantageous for titrating coloured or very dilute
solutions, very weak acids or bases, or mixtures of a weak and a strong acid or base.
 Measurement of The Solubility of a Sparingly Soluble Salt
• The concentration of a saturated solution of a sparingly soluble salt may be conveniently
obtained by measuring its conductivity (κ) and applying equation

• The value of Λ is calculated from equation and a table of

molar conductivities of ions by assuming that the solubility is so small that the saturated
solution behaves as if it were at infinite dilution.

•
• From equation