Conductance (or) Conductivity of Electrolytes

CONDUCTANCE (OR) CONDUCTIVITY OF ELECTROLYTES

1. Ohm's law

The resistance of a conductor is directly proportional to its length and inversely proportional to its cross sectional area

 R ∝ l                  ……….. (1)

R ∝ l/a            ……….. (2)

Combining (1) & (2)

R = ρ l/a   

Where, R= Resistance in ohms;

 ρ = specific resistance;

 l= length in centimeter;

 a= area of cross‒section in cm²

Thus, if l = 1 cm and a = 1 cm²

2. Conductance (c)

The conductance of an electrolyte is the reciprocal of its resistance

 c = 1/R

Unit of conductance:

 c = 1/ohm = ohm^‒1 (or) mho.

3. Specific resistance (ρ)

According to ohm's law R ∝ l/a

 R = ρ l/a (or) ρ = R × a/l

Where, ρ = specific resistance

If l = 1 cm and a = 1 cm², then ρ = R

Thus, specific resistance is defined as the resistance of a conductor, if its length is 1 cm and area is 1 cm².

Unit of specific resistance:

ρ = [ ohm × cm² ] / cm = ohm.cm

4. Specific Conductance (κ)

The reciprocal of specific resistance is called specific conductance. (or) It is the conductance of 1 cm³ of a material.

κ = 1/ρ

= 1/ [R × a/l]

κ = 1/R × l /a

κ = c  × l /a

Where, I/R=c

Unit of Specific Conductance

 κ= cm / [ohm × cm²]

κ= 1 / [ohm × cm] = ohm^‒1 × cm^‒1 or mho.cm^‒1

5. Equivalent conductance (˄_eq)

It is defined as the conducting power of all the ions produced by dissolving 1 gram equivalent of an electrolyte in the solution.

 ˄_eq = 1000κ / C

Where, C = concentration of the solution in gm equivalent weight.

Unit of equivalent conductance

˄_eq = [ cm³ / gm.equivalent ] × mho.cm^‒1

= mho.cm² • gm • equ^‒1

6. Molar conductance (˄_m)

It is defined as "the conducting power of all the ions produced by dissolving 1 mole of an electrolyte in a given solution."

 ˄_m = 1000κ / C

Where, C= molar concentration

Unit of molar concentration

˄_eq =  cm³/mole × mho.cm^‒1

= mho.cm² • mole^‒1

7. Cell constant (x):

It is the ratio of distance between two electrodes (l) and area of the electrodes (a).     

 x = l/a

Where, l = length in cm; a = area in cm²

This cell constant is multiplied with observed conductance (c) or (1/R) to get specific conductance (κ)

 κ = 1/R × l/a

Unit of cell constant

 x = cm / cm² = cm^‒1

1. Relationship between specific conductance (κ) and equivalent conductance (˄_eq)

Imagine 1 cc (1 cm³) of a solution of an electrolyte placed between two electrodes of 1 cm apart and the cross‒sectional area of the electrodes is 1 cm².

The conductance (C) of the above solution will be its specific conductance (κ), because we having 1 cc (1 cm³) of the electrolyte. Now,

Conductance (C) = κ (Specific conductance).

Suppose 1 cc of the solution contains 1 gm equivalent of the electrolyte, then the conductance of the solution will be equal to its equivalent conductance (˄_eq).

Conductance (C) = κ (specific conductance)

 = ˄eq (equivalent conductance).

Suppose the solution is diluted to 1000 cc. Now, we have 1000 cc of the electrolyte. The conductance of the solution is 1000 times of its specific conductance. But, even after the dilution, the solution contains 1 gm equivalent of the electrolyte, so the conductance measured will be its equivalent conductance.

Thus, the equivalent conductance (˄eq) = 1000 × specific conductance

 Λeq = 1000 × κ

If the solution is diluted to V times, then

 ˄eq = V × κ

Where, V is the volume of the solution in cc containing 1 gm equivalent of the electrolyte. If the concentration is C gm equivalent per litre, then

˄eg = [1000 / C] × κ

2. Variation of specific and equivalent conductance on dilution

Specific conductance (κ) of an electrolyte decreases on dilution. As the dilution increases, the conducting power of 1 cc of the solution decreases because number of ions per cc decreases due to diffusion.

Equivalent conductance (˄eg) of an electrolyte increases on dilution. The conducting power of an electrolyte depends on the number of ions and this increases with increasing dilution, since the degree of ionisation of an electrolyte increases with dilution.

Thus, the equivalent conductance increases with increasing dilution whereas the specific conductance decreases with increasing dilution.

3. Variation of equivalent conductance on dilution for strong and weak electrolytes

Equivalent conductance of strong electrolytes like HCl, NaCl, etc., are always high and it slightly increases with dilution. Strong electrolytes are completely ionized at infinite dilution. The relationship between ˄ and concentration is linear for strong electrolytes. So the equivalent conductance (˄⁰) for strong electrolytes are obtained by extrapolating the line to zero concentration (Fig 3.1)

Equivalent conductance of weak electrolytes like CH₃COOH, NH₄OH, etc., are very low and it increases steadily with dilution. Even at infinite dilution weak electrolytes are not completely ionised. The relationship between ˄ and concentration is not linear for weak electrolytes. So the equivalent conductance cannot be obtained by extrapolation.

4. Measurement of specific and equivalent conductance

Aim

The measurement of electrical conductance of an electrolytic solution involves, the determination of electrical resistance since the conductance is the reciprocal of electrical resistance.

Procedure

The determination of electrical resistance is carried out by using wheatstone bridge (Fig. 3.2.)

AB is a uniform wire and a sliding contact x moves over it. Alternate current is fed into the circuit through the source S. C is the conductivity cell containing the solution of an electrolyte whose resistance is to be measured. R is the resistance box and D is the head phone to detect the current.

When current flows, a known resistance R is introduced through the resistance box. The sliding contact x is then moved along the wire AB until a point of minimum sound (called null point) in the head phone is detected. The lengths xA and xB can be measured from the scale fixed below the wire AB.

The distance xA is directly proportional to the resistance of the solution.

The distance xB is directly proportional to the resistance of the resistance box (R).

Using the standard resistance (R), the resistance of the solution is calculated as follows.

Calculation:

Resistance of the solution α length xA

Standard resistance (R) α length xB

Resistance of the solution / Standard resistance (R) = Length xA / Length xB

Resistance of the solution = [ Length xA / Length xA ] × R

(i) Reciprocal of this resistance gives the conductance of the solution.

(ii) The value of conductance is multiplied by cell constant to get the specific conductance (κ)

 Specific conductance (κ) = conductance × cell constant

 = conductance × l/a

(iii) From the normality of the solution and its specific conductance, equivalent conductance can be calculated as follows

 ˄eq = (1000 / C) × κ