Conductance of Electrolytes:

We are familiar that electrolyte solutions conduct electric currents via them by movement of the ions to the electrodes. The power of electrolytes to conduct electric currents is known as conductivity or conductance. Similar to metallic conductors, electrolytes follow Ohm's law. According to this law, the current 'I' flowing via a metallic conductor is represented by the relation.

I = E/R

Here, 'E' is the potential difference at two ends (in volts); and 'R' is the resistance measured in ohms (or Ω). The resistance 'R' of a conductor is directly proportional to length, 'l' and inversely proportional to the area of its cross-section 'A'. That is,

R α l/A

Or R = ρ x (l/A)

Here 'ρ' (rho) is a constant of proportionality and is termed as resistivity or specific resistance. Its value based on the material of the conductor. From the above, we can write:

ρ = R x A/l

When l = 1 cm and A = 1 sq cm, then

ρ = R

Therefore, it follows that the Specific resistance of a conductor is the resistance in ohms that one centimeter cube of it offers to the passage of electricity.

Specific Conductance:

This is obvious that a substance that offers very little resistance to the flow of current allows more current to pass via it. Therefore, the power of a substance to conduct electricity or conductivity is the converse of the resistance. The reciprocal of specific resistance is known as Specific conductance or Specific conductivity.

It is stated as: The conductance of one centimeter cube (cc) of a solution of an electrolyte.

The specific conductance is represented by the symbol κ (kappa). Therefore,

κ = 1/ρ = (1/R) x (l/A)

Units of Specific conductance:

The specific conductance is usually represented in reciprocal ohms (r.o.) or mhos or ohm^-1. The unit can be derived as follows:

κ = (1/A) x (l/R) = (1/ohm) x (cm/cm²) = ohm^-1 cm^-1

The internationally suggested unit for ohm^-1 (or mho) is Siemens 'S'. If 'S' is used, the conductance is represented as S cm^-1. It might be noted that Siemens is not a plural; the unit is named after Sir William Siemens - a renowned electrical engineer.

The specific conductance increases with: (a) Ionic concentration and (b) Speeds of the ions concerned.

In assessing the specific conductance of the aqueous solution of an electrolyte, the volume of water in which a certain amount of the electrolyte is dissolved is for all time measured in the cubic centimeters (cc) and this is termed as dilution. If the volume of a solution is V_cc, the specific conductance of the solution is represented as κ.

Equivalent Conductance:

This is stated as the conductance of an electrolyte obtained via dissolving one gram-equivalent of it in V_cc of water.

The equivalent conductance is represented by Λ. It is equivalent to the product of the specific conductance, κ and the volume 'V' in cc having one gram-equivalent of the electrolyte at the dilution 'V'.

Therefore,

Λ = κ × V

A solution containing one gram-equivalent of the electrolyte dissolved in, state, 9cc water be positioned between the two electrodes 1 cm apart. The solution could be considered as comprising of nine cubes, each of which consists of a conductance k (that is, specific conductance).

Therefore, the total conductance of the solution will be 9 × κ. Likewise, V_cc of solution will form 'V' cubes and the total conductance will be κ × V.

In common, if an electrolyte solution consists of N gram-equivalents in 1000 cc of the solution, the volume of the solution having 1 gram-equivalent will be 1000/N. Therefore,

Λ = (κ × 1000)/N

Unit of Equivalent conductance:

The unit of equivalent conductance might be represented as follows:

Λ = κ × V

   = (1/R) x (l/A) x V

   = (1/ohm) x (cm/cm²) x (cm³/eqvt.)

   = ohm^-1 cm² eqvt^-1

Variation of Equivalent conductance having Concentration (or Dilution):

The equivalent conductance of a solution doesn't differ linearly with concentration. The effect of concentration on equivalent conductance can be studied through plotting Λ values against the square root of the concentration. This has been found that variation of the equivalent conductance with √C based on the nature of electrolyte.

Fig: Variation of equivalent conductivity

Strong electrolytes are fully ionized at all concentrations (or dilutions). The increase in equivalent conductance is not due to the rise in the number of current carrying species. This is, however, due to the decrease in forces of attraction between the ions of opposite charges having the decrease in concentration (or increase in dilution). At higher concentration, the forces of attraction between the opposite ions increase (F α q₁q₂/r²). As a result, it influences the speed of the ions by which they move towards oppositely charged electrodes. This phenomenon is termed as ionic interference. As the solution becomes more and more dilute, the equivalent conductance rises, till it reaches a limitary value. This value is termed as equivalent conductance at infinite dilution (or zero concentration) and is represented by 'A'.

Weak electrolytes encompass low ionic concentrations and therefore interionic forces are negligible. The Ionic speeds are not influenced by decrease in concentration (or increase in the dilution). The increase in equivalent conductance by increasing the dilution is due to the increase in the number of current carrier species. In another words, the degree of ionization (α) increases. Therefore, increase in equivalent conductance (Λ) in case of a weak electrolyte is due to the the increase in the number of ions.

In case of a weak electrolyte Λ_α is the equivalent conductance whenever ionization is complete. Therefore, the conductance ratio Λ/Λ_α is the degree of ionization. That is,

α = Λ/Λ_α

Molar Concentration:

This is the other quantity that assists in comparing the conductivities of electrolytes. It is stated as: the conductance of all ions generated by one mole (that is, one gram-molecular weight) of an electrolyte whenever dissolved in a certain volume V_cc.

Molar conductance is represented by 'μ'. Its value is obtained via multiplying the specific conductance, 'κ', by the volume in 'cc' having one mole of the electrolyte.

Therefore, Molar conductance, μ = k × V here 'V' is the volume of the solution in cc having one mole of the electrolyte.

Units of Molar Concentration:

As,

κ = (1/R) x (l/A)

μ = (1/R) x (l/A) x V

   = (1/ohm) x (cm/cm²) x (cm³/mol)

   = ohm^-1 cm² mol^-1

Computation of Molar conductance:

Molar conductance can be computed by employing the relation:

μ = (k x 1000)/M

Here 'M' is the number of moles of the electrolyte present in 1000 cc of solution.

As dilution specific conductance decreases, at the same time as, Equivalent conductance and Molar conductance increases.

This is significant to note that the specific conductance decreases by dilution. It is the conductance of one cc of the solution. On diluting the solution, the concentration of ions per cc reduces. Therefore, the specific conductance falls. On other hand, the equivalent and molar conductance exhibit an increase as these are the products of specific conductance and the volume of the solution having one gram-equivalent or one mole of the electrolyte respectively. By dilution, the first factor decreases, as the other increases. The increase in the second factor is much more than the decrease in the first factor.

Variation of Conductance with Temperature:

The conductance of a solution of an electrolyte usually rises with the increase in temperature. It has been found via experiment that the conductance of a given solution raises by 2-3 per cent for one degree rise in temperature. For illustration, the conductances of 0.1 M KCl at two different temperatures are:

1.12 × 10^-2 ohm^-1 cm^-1 at 18ºC

1.29 × 10^-2 ohm^-1 cm^-1 at 25ºC

The conductance of a particular electrolyte based on two factors:

a) The number of ions present in the unit volume of solution.

b) The speed at which ions move towards the electrodes

At a specific temperature, the first factor remains similar for a specific electrolyte. Therefore the increase in conductance with increase in temperature is due to the affect of second factor. With the increase in temperature the viscosity of the solvent (that is, water) decreases that makes the ions to move freely toward the electrodes.

For weak electrolytes, the affect of temperature on conductance based on the value of ΔH accompanying the procedure of ionization. If the ionization is exothermic (- ΔH), the degree of ionization is less at higher temperature (that is, Le Chatelier's principle) and conductance decreases.

On the contrary, if the ionization is endothermic (+ΔH), the degree of ionization is more at higher temperature and the conductance increases.

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