Hittorf's Method (also known as the Analytical Method) is founded on a fundamental electrochemical principle: during electrolysis, the amount of electrolyte concentration lost around any given electrode space is directly proportional to the relative speed of the target ions moving away from it. This foundational principle is universally recognized as Hittorf's Rule.
The transport number of a specific ionic species is derived by analyzing the post-electrolysis changes in concentration within localized electrode compartments. The specialized experimental apparatus comprises two primary vertical glass tubes interconnected by a central U-tube bridge. All three segments are equipped with isolation stopcocks at their lowest points.
Additionally, the U-tube features terminal stopcocks at the peaks of both limbs. By closing these specific valves at the conclusion of the process, fluid exchange between the cathode and anode chambers is instantly halted. In this configuration, a silver anode is sealed within an insulation sleeve while the corresponding cathode is constructed from highly purified, freshly silvered foil metallic sheets.
The system is filled completely with an active silver nitrate (AgNO3) solution, and a highly stable, low-amperage direct current of approximately 0.01 A is passed through the system for a duration of two to three hours. Restricting both current and duration is a vital operational safeguard; it prevents extreme, turbulent concentration gradients that would induce unwanted thermal diffusion errors across the chambers.
To record aggregate charge, the cell is placed in series with a silver or copper voltammetric coulometer. Following the run, the upper U-tube stopcocks are tightly sealed. The entire liquid volume of the anode compartment is carefully drained into a tared flask to determine its exact mass, and its residual silver ion concentration is evaluated via volumetric titration against a standardized potassium thiocyanate (KSCN) solution.
Concurrently, the absolute mass of silver deposited onto the coulometer electrode is recorded (W). If a copper coulometer is substituted instead, the corresponding silver equivalent weight is computed directly by multiplying the copper mass gain by the electrochemical ratio factor of 108/31.5 (108 over 31.5). If the procedure is executed flawlessly, the middle U-tube solution concentration must show absolutely zero analytical change. When using reactive silver electrodes, the nitrate anions attack the silver anode structure. This chemical side-reaction causes a net increase rather than a decrease in anode-chamber Ag+ concentration. To avoid this, inert platinum plates can be used as unattackable electrodes.
Calculation of Transport Number by Hittorf's Method
Quantitative analysis depends on whether the chosen analytical electrode materials participate directly in the secondary oxidation/reduction phases.
Case 1: When Electrodes are Inert / Unattackable (Platinum Electrodes)
When inert platinum (Pt) elements are used, the chemical composition of the terminal plates remains completely unchanged throughout the process. The post-electrolysis (after passing electric current), calculation proceeds as follows:
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+ = (tAg+) = [Fall in concentration around anode in g eqvt/
Amount of Ag deposited in gm eqvt.] = d/W
and Transport number of NO3− (tNO3−) = 1 − (d/W)
Case 2: When Electrodes are Chemically Active / Attackable (Silver Electrodes)
When active silver (Ag) electrodes are used, migrating nitrate anions strike the anode plate, forming fresh silver nitrate. This produces a net increase in local concentrations rather than an expected depletion zone:
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 (tAg+) = (W – e)/W
and Transport number of NO3− (tNO3−) = 1 − [(W – e)/W]
[Reference: Essentials of Physical Chemistry; Arun Bahl, B. S. Bahl & G. D. Tuli]