A n EXPERIMENT for the DETERMINATION of TRANSFERENCE
NUMBERS by ELECTROMOTIVE FORCE METHODS CHARLES M. MASON AND EDWARD F. MELLON The University of New Hampshire, Durham, New Hampshire
F
OR some time electromotive force measurements have been used for the determination of transference numbers where suitable reversible electrodes could be found for the ions concerned (1). An examination of some seven or more of the standard laboratory texts in physical chemistry reveals that of those examined only two (2) mention this method. In all the texts examined the preferred method given for student use is the Hittorf analytical method which even with the best of students gives indifferent results. Recently, Longsworth (3) has published an excellent procedure for the determination of transference numhers in the elementary physical chemistry laboratory by the moving boundary method. Although this procedure gives excellent results, it requires some special apparatus not always easily available. Since simple apparatus is available for the measurement of electromotive force in nearly every physical chemistry laboratory, it seems as though the measurement of transference numbers by this means would be advantageous for several reasons. (1) Excellent results are easily obtained in a short time. (2) The experiment may be used to illustrate the principles of electromotive force as well as transference. (3) The experiment illustrates to students the ever-present need to consider the liquid junction potentials in electromotive force measurements. (4) The experiment also illustrates the more advanced theory and material which is now included in every treatment of both transference and electromotive force. ( 5 ) The high mobility of hydrogen ion is demonstrated. THEORY INVOLVED
For the cell without transference
.
nF
at
(1)
. When the same cell is written with transference we obtain
(11)
where T. is the transference number of the anion which in this case is the chloride ion. The cell always gives the transference number of the ion to which the electrodes in (11) are not reversible. Dividing equation (2) by (1) we obtain
Ta = EIIIE,
(3)
from which the value of T. is readily obtained. Returning to cell I we find that it can he rewritten in the form Ag, AgCI, HCI (a,), H2 (1 atm.). . .Hn (1 atm.). Ag HCI (a), AgCl (111)
for which we may write for the electromotive force
Rewriting this cell with transference we have Ag, AgC1. HC1 (at), HCI (a2),AgCI, Ag
(IV)
for which the electromotive force is given by
Dividing (5) by (4) we obtain the expression from which T,,the transference number of the cation, is easily calculated. EXPERIMENTAL DETAILS
HS (1 atm.), HCI (ad,A ~ C I . A ~.Ag, . AgCI, HCl (ad, HZ(1 ~ m . ) (1)
we may write for the electromotive force (4) RT a, E,+2-In-
Hq (1 atm.), HCI (a,), HCI (a*), HZ(1 stm.)
and for the electromotive force of this cell we write
The galvanic cell described above is easily measured in the elementary physical chemistry laboratory. The apparatus used is shown in the figure. A and D are the standard Ostwald hydrogen electrode assemblies which are available in most laboratories. B and C are silver-silver chloride electrodes. These are most easily prepared by the method described by Harned (5) as Type (11). A platinum spiral about four millimeters in diameter is made by coiling about ten centimeters
of medium-weight platinum wire around a glass tube of that diameter. One end of this is then'sealed into the end of a four-millimeter soda glass tube ten centimeters long. The spiral is filled with silver oxide paste and heated to 450° in a small vertical electrical crucible furnace. The silver oxide paste is prepared by precipitation of the oxide from the nitrate with boiling sodium hydroxide solution. This oxide is then care-
CELL TRANSFERENCE
fully washed free of alkali by decantation and dried in the oven to a paste. The oxide decomposes to give a globule of unstrained amorphous silver on the wire. This is built up in layers to a diameter of about six millimeters. The silver electrode thus formed is then electrolyzed as the anode in one-normal hydrochloric acid for two hours with a current of ten milliamperes. The electrodes are best kept in the dark immersed in the solution in which they are to be used. The setup shown in the figure consists of two Ostwald hydrogen assemblies dipping into separate 150-ml. beakers, which are close enough together to be connected by the glass bridge. For student work temperature control is not essential and the setup may be placed
on ihe desk top. The bridge is most conveniently made as shown so that it can be filled by suction. It is essential that the solutions all be a t the same level to prevent siphoning; 0.1 normal or 0.1 mold hydrochloric acid is placed in one cell and 0.2 in the other. If the potentiometer is not sensitive enough for these concentrations, 0.1 and 0.5 may be used without seriously affecting the accuracy of the results. Tank hydrogen passed through distilled water gives good results. The measurement is carried out as follows. After a sufficienttime has elapsed for equilibrium to be established (one to two hours), Cell I is measured by connecting B and C with a copper wire and measuring the potential across A and D. Cell 111 is then measured by connecting A and D with a copper wire and measuring the potential across B and C. The same result may be accomplished in either case by measuring the potential across A and B and across C and D and adding the two together algebraically. Cells I and I11 will, of course, have the same potential. The bridge is now dipped into the two beakers, filled by suction, and the stopcock closed. The potential is measured between A and D giving the potential of Cell I1 and between B and C giving the potential of Cell IV. The values of T , and T, are then calculated from the potentials. Since the sum of T, and T, is one, this serves as a test of the validity of the data. Table 1shows the result of a typical experiment. TABLE 1 THB
Trial
AVERADE TRANSP&PSNCB N ~ B B OP X 0.30 NORMAL HYDROCHLORTC ACID
El
EII
E m
EIV
Tn
TI
Te
+
Tc
1
0.07009
2 0,07028 Average -
0.01152 0.01156
-
0.07009 0.07028
-
0.05857 0.05855
-
0.837 0.833 0.835
0.164 0.165 0.165
1.001 0.998 1.000
The theoretical value may be taken from the data of Longsworth (6) who found for T , the value 0.831. This gives an error of 0.48 per cent. as compared to the three to five per cent. usually obtained by the Hittorf method.
LITERATURE CITED
(1) (a) F~nGuso~, I.Pkyr. C h . ,20, 326 (1916). (6) MACINNES AND PARKER, 1. Am. Chcm. Soc., 37, 1445 (1915). (6) MACINNES AND BEATTIE, ibid., 42, 1117 (1920). (d) Lucass~.ibid., 47, 743 (1925).
(3) (4)
(2) (a) D A N ~ E LMATHEWS, ~. AND WILLIAMS."Experimental physical chemistry," 2nd ed., McGraw-Hill Book Co., New York City, 1934, p. 233.
(5) (6)
(b)
FINDLAY, "Practical physical chemistry," 6th ed.,
Longmans, Green and Co., New York City, 1935, p. 243. LONGSWORTH, J. CHEM.Enuc., 11, 420 (1934). GERMN Am DAN~ELS, "Outlines of theoretical chemistry," 5th ed., John Wiley and Sons, Inc., New York City, 1931, p. 456. HARNED. J. Am. Chem. Soc., 51, 416 (1929). LONGSWORTH, did., 54, 2758 (1932).
SEVENTEENTH EXPOSITION OF CHEMICAL INDUSTRIES The Seventeenth Exposition of Chemical Industries will be held the week of December 4th, a t Grand Central Palace, New York City. The Exposition opens a t 11 A.M.daily. The morning hours will be used for lectures in industrial chemistry, involving new processes, products, methods of analyses, and professional probbe lectures and confer. lems. D ~ the" afternoon, ~ ~ there ences devoted to unit chemical engineering operations and equipment, especially the newer developments shown a t the Exposi-
tion. I t ~ m v i d e sfacilities for college juniors and seniors who are in charee - of instructors. Graduate students are welcome. Arrangements must be made to obtain special students' tickets in advance of the Exposition. Faculty members who wish further write directly to Dr. W. T. Read, care of Seventeenth Exposition of Chemical Industries, Grand Central Palace. New York City. The program will be complete about November 15th.
