Washburn number

In the literature, several different notations for tj and Tj have been used. Today, the terms transport number and transference number are used for q side by side Staverman introduced the terms reduced electrical transport number for Ti and electrical transport number for tj. Scatchard called Ti a transference number and ti a transport number, while Agar " introduced the notation Washburn number if Ti is referred to one of the uncharged components. The solvent transference number A, which was introduced by C. Wagner is a reduced transference number with the reference system fixed to the sum of moles of all solvent components. Elektrische Losungsmitteliiberfuhrung , (electrolytic solvent transport) originates in the proposal of Nernst to discriminate between solvent molecules in the solvation shell of the ions and the free solvent. is a reduced transference number referred to the motion of the free solvent. Inspection of Eqs. (54) and (57) shows that Ti depends on the reference system used. This will be shown in the following section in more detail. 

The reduced transference numbers and are the Washburn numbers W2 and Wi introduced by Agar In his discussion the movement of a neutral solute is treated with respect to the solvent. Later on, Feakins used Washburn numbers to explain the solvent transport in mixtures of two solvent components when the solvent mole fraction is varied between 0 and 1. 

A relation between Washburn number W, e.g. and solvation numbers follows from Eqs. (91), (92) and (68)... 

Two methods have been used to obtain Washburn numbers W2, wj or solvent transference numbers A. 

Washburn numbers of hydrochloric acid and of alkali-metal halides have been determined in mixtures of water with methanol ethanol ... 

XMeOH- Additionally, the Washburn number w mso been calculated using Eq. (97) and is also plotted versus xu go. With x mso 1 the Washburn number wdmso tends versus 4 and, though w mso is quite different from the coordination number of Ag from nmr chemical shift measurements the agreement of the results indicates that the contribution of the sulphate ion is of minor importance. 

Fig. 3. Solvent transport number, A, and Washburn number, wjjMgo, for Ag2S04 in methanol-DMSO mixtures at 25 °C...

Nernst suggested in 1900 that could be found by adding to the solution a small known amount of a nonelectrolyte which was assumed to remain stationary in the electric field. The movement of solvent and of the various ion-constituents, relative to the inert nonelectrolyte, would then give co and r respectively. Early work on this principle was confined to aqueous systems but within the last decade it has also been applied to water-ethanoP and water-dioxan " mixtures. Unfortunately, however, the results are devoid of any simple physical mean-ingM58 because experimental evidence has accumulated to show that the basic assumption of the method is invalid. On reflection we can see why. The reference substances employed—rafflnose, fructose and the like—are polar, partially solvate the ions, and so are no more stationary or inert than the solvent itself. The Washburn numbers obtained are therefore not solvent transference numbers but simply convenient parameters for expressing certain experimental results. 

Washburn numbers or a quantity involving them can, however, be determined in mixed solvents without the use of a reference substance because the composition of the solvent itself changes in the electrode compartments. Take, for example, a 1 1 electrolyte in a medium of mole fraction in component 1 and X2 in component 2. Equation 5.11.1 tells us that, when f faradays have passed, A i moles of solvent 1 and A 2 moles of solvent 2 are carried out of the anode and into the cathode compartment, where... 

The above treatment has glossed over the reference state on which the experimental Washburn numbers are based. The data of Strehlow et al. seem to refer to the final and initial contents of the cathode compartment of their cell so that their Washburn numbers have been determined relative to the glass walls of the apparatus, with no correction for any increase or decrease of electrode volume. Composition changes should have been calculated with respect to the total mass of solvent in the cathode section. Two extreme but interesting cases arise when one or other of the two solvent components is regarded as fixed. If this is component 1,... 

As dissociated ions are always solvated, electrolysis entails transport of solvate with the ions. This phenomenon has been known for a long time in 1900, Nernst determined the transport of water in, for example, sulfuric acid [447]. Washburn quantified it in the so-called Washburn number [440], which simply expresses the net number of moles of solvent carried by the electrolyte. 

Inert polymer matrices, studied for use in possible controlled release applications, have used porosimetry to investigate a number of properties [54-56]. The kinetics of liquid capillary penetration into these matrices was explored using a modified Washburn equation [54]. It was shown that water... 

References to the literature. References to the original data are given in the text, as Washburn.2 The exact citation can then be found in the list of references, which are given in alphabetical (and numerical) order, as Washburn,2 Bur. Standards J. Research 10, 525 (1933), where the numerals indicate, respectively, the volume, page, and year. The abbreviations used for the titles of the periodicals are those adopted as standard by the International Union of Chemistry (See, for example, Chemical Abstracts List of Periodicals Abstracted ). When the citation is that of a book, it is written as Washburn, Introduction to the Principles of Physical Chemistry, McGraw-Hill Book Co., New York (1921), where the title is in quotation marks, and then in order follow the name of the publisher, the place of publication, and, in parentheses, the year of publication. If the book citation includes volume and page numbers, these follow immediately after the title. 

There are a number of formulae which are relevant for modelling the infiltration kinetics of a liquid into preforms. The first equation to calculate the height of infiltration against time was formulated by Washburn (1921) ... 

Other aspects of transport phenomena including activation energies for viscosity parameters and Washburn transport numbers (Feakins, 1974a Feakins and Lorimer, 1974) have also been measured to probe ion-solvent interactions in mixed solvent systems. 

Following Haase s treatment ° the transference numbers q of the ions (i = +, -) of a binary electrolyte in a single solvent 1 (e.g. water) shall be discussed with respect to the Hittorf reference system and the Washburn reference system. 

These are solutions m which the vapour pressure of the solute cannot be regarded as negligible compared to that of the solvent—-in fact the terms solute and solvent are not very applicable, as both liquids may be present in large amount Such systems have been examined theoretically and practically by Dolezalek [Zeitsch physik Chem, 64, 727, 1908, tbid,TL, 198, 1910), see also Stern, loc at, and Washburn [Journ Amer Chem Soc, 32,670, 1910) The following simple relation has been put forward by Dolezalek as being of fundamental importance in these cases The partial vapour pressure pa. of a component a present in the liqmd state is proportional to the molecular concentration of the component a in the liquid state when such concentration is expressed as a fraction of the total number of moles present If xa is the fractional molar concentration of a in the liquid state at a given temperature, and p0 is the vapour pressure which the liquid a alone would exert, then the partial pressure of a m the mixed vapour is given by pa where—... 

Transference numbers obtained by a method which is uninfluenced by the movement of water of hydration have been called true 41 transference numbers. The first attempt to obtain such numbers was made by Nernst and associates.42 Successful measurements in this field have been carried out by Buchbock43 and much more extensively by Washburn.44 The procedure employed was essentially that of a Hittorf measurement. However, a second solute (usually a carbohydrate, such as sucrose or raffinose) is added to the aqueous solution, and, instead of referring the changes of salt concentration to the water, as in the computations for Hittorf transference numbers, the changes, both of salt and of water, are referred to the added solute. The apparatus used by Washburn has already been described. It is evident that if the added "reference substance is uninfluenced by the passage of the... 

The transport of water by the ions was first measured by Washburn. Using the Hittorf method, a reference substance such as sugar or urea is added to the solution. Presumably the reference substance does not move in the field, and the transport of the solvent can be calculated from the analysis of the solution in the three compartments. If a value is assumed f or the number of water molecules attached to one ion, a value f or the number attached to the other ion can be calculated. Presently other methods for evaluation of hydration numbers are preferred—from measurements of the partial molar volume of the salt in the solution, for example. The different methods are internally consistent but often do not agree well with each other. It is generally assumed that the negative ions are not hydrated. Then the hydration numbers are, approximately Li", 6 Na", 4 K", 2 Rb", 1. 

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