Hittorf number

If the cation is more hydrated, then W is a positive number if the anion is more hydrated, then W is a negative number and water is transported to the anode. Transport numbers calculated from measured concentration changes involving transport of water by solvated ions are sometimes called Hittorf (/, ) numbers those corrected for the transport of water are called true transport numbers (f,). These two types of transport numbers are related by... 

The probable error in Tc is estimated by Tolman to be o oro It is of interest to compare these values with the transport number obtained by other methods Very few data are available in the case of iodides with the exception of the measurements of Dennison (Trans Fataday Sac, 5j 165 (1909)) The Hittorf number may also be calculated from conductivity results at infinite dilution The following table contains these comparative results —... 

If, for instance, the positive ions carry more water into a solution surrounding a cathode than the negative ions carry out of it, the effect of the resulting movement of water will be a dilution of the solution around the cathode, and the measured Hittorf transference number of the cation will be smaller than would be the case if the ions were unhydrated, and moved at the same relative velocities. Similarly if the negative ions carry more water away from the cathode than the positive ions carry to it the effect on the Hittorf number will be in the opposite direction. 

The ratio of the total current i in the solute to a partial current i of species a is referred to as the transport number or the Hittorf number ... 

We express the altered concentration in terms of the adsorption excess. If all the adsorbed substance were contained to the extent of k gr. per cm.2 on a superficial layer of zero thickness and surface total mass present in the volume Y would be m = V + kto. The layer of altered concentration must, however, have a certain thickness. We will therefore imagine a plate 2 placed in front of the surface and parallel to it, and define the adsorption excess as the concentration in the included layer minus the concentration in the free liquid. That this result is independent of the arbitrarily chosen thickness is easily proved when we remember that the problem is exactly the same as that of finding the change of concentration around an electrode in the determination of the transport number of an ion by Hittorf s method. 

For obtaining internal or external mobilities, the corresponding transport numbers are usually measured. There are several methods for determining transport numbers in molten salts that is, the Kleimn method (countercurrent electromigration method or column method), the Hittorf method (disk method), the zone electromigration method (layer method), the emf method, and the moving boundary method. These are described in a comprehensive review. ... 

There is difficulty in defining the absolute mobilities of the constituent ions in a molten salt, since it does not contain fixed particles that could serve as a coordinate reference. Experimental means for measuring external transport numbers or external mobilities are scarce, although the zone electromigration method (layer method) and the improved Hittorf method may be used. In addition, external mobilities in molten salts cannot be easily calculated, even from molecular dynamics simulation. 

Based on the general scenario provided above, the analytical method to determine transference or transport numbers has been devised and is carried out in an apparatus which can essentially be regarded as an improvement over the Hittorf apparatus. This consists of two vertical tubes connected together with a U-tube in the middle all three tubes are provided with stop-cocks at the bottom. The U-tube is also provided with stop-cocks at the top by closing these, the solutions in the cathode and anode limbs can be isolated. The silver anode is sealed in a glass tube as shown, and the cathode is a piece of freshly silvered silver foil. The apparatus is filled up with a standard solution of silver nitrate and a steady current of about 0.01 ampere is passed for 2-3 hours. In order to avoid the occurrence of too large a change in concentration it is necessary to pass the current only for a short duration. The... 

Fig. 2.10 Schematic design of a cell for the determination of transport numbers from measurements of the concentration decrease in electrode compartments (Hittorf s method)...

The methods for determination of transport numbers include the Hittorf method and the concentration cell method (p. 121). 

To date there have been few reliable measurements of Hittorf transference numbers in solid polymer electrolytes because of experimental difficulties in applying the technique. Leveque, Le Nest, Gandini and Cheradame (1983) have, however, applied it to highly cross-linked networks where cells could be formed using a series of non-adherent thin... 

Hittorf method phys chem A procedure for determining transference numbers in which one measures changes in the composition of the solution near the cathode and near the anode of an electrolytic cell, due to passage of a known amount of electricity. hi-dorf, meth-od ... 

With high dilutions P. Walden found the increase with dilution is very small and finally decreases, showing that the salt is completely hydrolyzed. W. Hittorf measured the transport numbers of the ions of the sodium salt. 

Bismuth may be used in place of lead, but it dissolves only one-fifth as much phosphorus, and the crystals obtained are less pure. The metals appear to be held in solid soln. Only very minute quantities of Hittorf s phosphorus are obtained by sublimation. According to L. Troost and P. Hautefeuille, the same variety is formed when red phosphorus is heated under press, to 580°. The work of A. Pedler, J. W. Retgers, and D. L. Chapman shows that this variety differs from ordinary red phosphorus only in the size and development of the crystals. Fine-grained red phosphorus is scarlet phosphorus, while coarse-grained red phosphorus is metallic or violet phosphorus. A number of other allotropes have been reported, but many of them are the result of a misinterpretation of facts, or of an incomplete knowledge of facts. 

A review of the alleged allotropes of phosphorus reduces their number to four, namely, the a- and/3-forms of yellow phosphorus, red or violet phosphorus, and black phosphorus. Most of the work of various investigators has been directed towards elucidating the nature of red phosphorus, and of the transformation of yellow to red phosphorus and conversely. Red phosphorus was formerly considered to be amorphous, and it was often called amorphous phosphorus. The term amorphous, however, here referred more to the general appearance of the powder rather than to its minute structure. J. W. Retgers 5 showed that the particles of ordinary red phosphorus are rhombohedral crystals, which are well developed in those of W. Hittorf s violet phosphorus. All four varieties are therefore crystalline. J. W. Terwen has reviewed this subject in a general way and M. Copisarow discussed the theory of allotropy,... 

W. Plotnikoff found the mol. conductivity of ethereal soln. diminishes with dilution, and increases with rise of temp. W. Hittorf attempted to determine the transport number of the anion in aq. soln. of normal sodium phosphate, but the salt was so much hydrolyzed that most of the current was carried by the alkali. With aq. soln. of sodium hydrophosphate, the transport number of the HP0"4-anion was 0-516 and with sodium dihydrophosphate for the H2PO 4-anion, 0-383. J. F. Daniell and W. A. Miller also made some observations with this salt. W. Hittorf found with soln. of potassium dihydrophosphate, the transport number of the H2P0,4-amon was 0-277. O. Wosnessensky measured the potential difference at the boundary of phosphoric acid and a non-aqueous solvent. P. Pascal studied the magnetic properties. J. Murray tried if he could decompose a soln. of the acid by magnetized iron. 

Transport numbers can be measured by different methods. The small mono- and divalent inorganic ions have been used to demonstrate skin permselectivity, and have been determined from membrane potential measurements, or by the Hittorf method [10,25,77,79]. The latter method has been frequently used for drugs alternatively, the transport number can be estimated from the slope of a plot of drug flux as a function of current intensity (Figure 14.4) [18,66]. 

The quantity [ zlLkf izfLJ is the transference number of the fcth ion as determined by the Hittorf method and, therefore, Equation (12.105) may be written as... 

The transport number of an ion varies with the ionic constitution of the solution, and is another way of expressing conductivities or mobilities. There are two important methods for measuring transport numbers the Hittorf method and the moving boundary method5. 

Fig. 2.6. The Hittorf method for determining transport numbers. In the diagram the passage of a current I for time t is shown. It is assumed that t+ +1 = 1. The electrolytic cell is divided into three compartments.

Unequal velocities of ions cause changes in concentrations in the proximity of electrodes. From these changes the transference numbers can be calculated provided the quantity of electricity passed through the electrolyte is known (Hittorf s method). 

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