1. The apparatus is shown as a simple U-tube with a stopcock in the middle. This type of arrangement was rejected years ago as unworkable since on electrolysis there are large changes in concentration and density that can cause both mixing and siphoning, which defeat the entire experiment. This is the reason that Hittorf included a central buffer compartment (2). Table 1 shows a 65% change of concentration of the HCl and NaOH solutions, which supports this conclusion.
2. The basic premise of the Hittorf method is that the water does not migrate (whether this is true or not, it still is the premise). Consequently all concentrations should be either weight percent or molal since the weight of water in the compartment must be obtained. Molarity (a volume measure) should never be used for serious work (2).
3. The electrode system is critical for determining the exact changes in concentration. In Table 1 the authors neglect to tell us what the electrode system is and which compartment is being analyzed, and suggest that one equation serves for all systems.

The following example will disprove that assumption. Consider a solution of CuCl₂ in the anode compartment electrolyzed with (A) a Cu metal electrode and (B) a Ag/AgCl electrode. At the anode the electrode reactions are:

(A) Cu → Cu²⁺ + 2e^- and

(B) Ag + Cl^- → AgCl + e^-

The balance sheet for the changes in concentration in (A) is as follows:

+ N_e eq. of Cu²⁺ (electrolysis) - t₊ N_e (migration) = N_f - N_i

There is a gain of Cu²⁺ due to electrolysis and a loss due to migration, where N_e is the total charge transferred in chemical equivalents (i × t/F), N_i and N_f are the equivalents of Cu²⁺ before and after as determined by some analytic method. Then:

N_f - N_i = N_e - t₊ N_e = (1 - t₊) N_e = t_- N_e

or:

In (B) the changes are the same as (A) but no Cu²⁺ is formed by electrolysis and there is only a loss of Cu²⁺ by migration. Then:

N_f - N_i = - t₊ N_e

or:

Note that equations 1 and 2 are different and the transport numbers switch from the negative to the positive ion. Also, in (A) the solution becomes more concentrated, and in (B) more dilute. To those teachers who want to confound students, all that is needed is to stabilize the solution with some inert KCl. The transport numbers may turn out negative or greater than one since CuCl₄^2- complex is formed and the Cu ion will migrate in the wrong direction.

Literature Cited

1. Jinqing, K; Qin, X; Ke, C. J. Chem. Educ, 2001, 78, 937–938.
2. Glasstone, S. Textbook of Physical Chemistry, 2nd ed.; D. Van Nostrand Co.: New York, 1946; pp 910–921.

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