Measurement of Transport Number by Hittorf's Method

Measurement of Transport Number by Hittorf's Method (Analytical Method)

Hittorf's method is based on the fact that during electrolysis the amount of electrolyte lost around any electrode is proportional to the speed of the ions moving away from it, this is called Hittorf's rule.

The transport number of an ion is calculated from the changes in concentration found experimentally around the electrodes. The apparatus used in this method consists of two vertical glass tubes joined together through a U-tube in the middle. All the three tubes are provided with stopcocks at the bottom. The U-tube is also provided with stopcocks at the tops of the two limbs. By closing these stopcocks, the communication between the solutions in the cathode and anode limbs can be stopped. The silver anode is sealed in a glass-tube and the cathode is a piece of freshly silvered foil. The apparatus is filled with a solution of silver nitrate and a steady current of about 0.01 ampere is passed for two to three hours. It is an important precaution that the current is passed only for a short time so that too large a change in concentrating does not take place. The apparatus is connected with a silver or copper coulometer as shown in figure, which shows the circuit for the experiment.
When the current has been passed for about three hours, the stopcocks at the top of the U-tube are closed. The whole of the liquid in the anode compartment is carefully drained into a weighed flask and its weight determined. Its silver content is determined by titrating against a standard solution of potassium thiocyanate. The weight of silver deposited in the silver coulometer is also noted. If a copper coulometer is used in place of silver coulometer, the weight of silver equivalent to the copper deposited is calculated by multiplying it with 108/31.5. There should be no change in the concentration of the solution in the U-tube if the experiment has been successfully performed. If the above experiment has been performed by using silver electrodes, in this case nitrate ions attack the silver anode. Consequently, there is an increase in concentration of Ag⁺ ions rather than decrease. The same experiment can also be performed by using platinum electrodes to avoid the attack of anions on the anode.

Calculation of Transport Number by Hittorf’s Method

There are two different cases may arise. One case is for an unattackable electrode and another for an attackable electrode.

Case 1: When electrodes are unattackable

Pt electrodes are used.
After passing electric current-
Let the weight of anodic solution taken out = a gm
weight of AgNO₃ present in it by titration = bg weight of water = (a – b) gm
Before passing electric current
Let weight of AgNO₃ in (a – b) gm of water before passing electric current be = c gm
∴ Fall in concentration = (c – b) gm of AgNO₃
or, Fall in concentration = (c – b) / 170 gm eqvt. of AgNO₃
or, Fall in concentration = (c – b) / 170 gm eqvt. of Ag = d(Let)

Let the weight of silver deposited in silver coulometer
= w₁gm
= w₁/108 gm eqvt. of Ag
= w gm eqvt. of Ag
Transport number of Ag⁺ = (t_Ag⁺) = [Fall in concentration around anode in g eqvt/ Amount of Ag deposited in gm eqvt.] = d/W
and Transport number of NO₃⁻ (t_NO3⁻) = 1 − (d/W)

Case 2. When electrodes are attackable

Ag electrodes are used.
Increase in conc. of anodic solution = (b – c) gm of AgNO₃
= [(b – c)/170] x 108 gm of Ag
= [(b – c)/170] gm of Ag = e (Let)
If no Ag⁺ ions had migrated from the anode, the increase in concentration of Ag⁺ ions would have been equal to W.
∴ Fall in concentration due to migration of Ag⁺ ion = W – e
Hence, transport number of Ag⁺ ion (t_Ag⁺) = (W – e)/W
and Transport number of NO₃⁻ (t_NO3⁻) = 1 − [(W – e)/W]
[Source:Essentials of Physical Chemistry; Arun Bahl, B. S. Bahl & G. D. Tuli]

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