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R. M. Kallo and 5. Bluestone Fresno State College Fresno, California
Graphical Integration Technique for Obtaining Transference Numbers by the ~ o v i nBoundary ~ Method
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Conventional measurements of transference numbers by the moving boundary method require that the direct current delivered to the transference cell be kept constant.' This is usually done either by constant manual adjustment or by regulating the current with a suitable power s ~ p p l y . ~ JThe alternate procedure presented below eliminates this requirement by graphical integration of the current delivered to the cell as a function of time. The integration technique is useful in numerous situations in physical chemistry. The cell used to determine the transference number of H + ion is similar in construction to those previously d e ~ c r i b e d . ' ~0.1N , ~ HCI, containing enough methyl violet. indicator, added as a powder, to be visible is used
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DANIELS, F., WILLIAMS, J . W., etal., "Experimental Physical Chemistry," 6th ed., McGraw-Hill Book Co., h e . , New York, 1962, p. 165. %BENDER, P., AND LEWIS,D. H., J. CHEM.EDUC.,24, 454 (1947). TO BEY, S. W., J. CHEM. EUUC.,38,516 (1961). G. A,, AND PEPPER,D. C., J. CHEM.EDUC.,42, 'LONEGRAN, 82 (1965).
FF 4 HCI
solution
wire
as the solution. A voltage of 140 v dc is applied to the cell so that the initial current is about 3 ma. The milliamp readings, determined in the usual manner by using a student potentiometer to measure the voltage drop, E , across a calibrated resistor, R, as shown in Figure 1 are recorded as a function of time. The time it takes the boundary to move between two graduations on the pipet is noted. Measurements can be made with a recording poteution~eter,such as a Varian Associates G-10 graphic recorder, which gives the voltage as a function of time directly. Figure 2 shows the curve obtained with key 1 of Figure 1 closed. The volume AV swept out by the moving boundary in time interval 1 1 4 is indicated by the line made by momentarily closing key 2. Figure 2 shows that it takes a longer time for the boundary to sweep out a volume of 0.01 ml as the experiment progresses, since the current is continually decreasing. The resistance R is set so that the potential is within the rangeof the (recording) potentiometer for each run of the experiment with different concentrations of HC1. The time scale recording potentiometer must he calibrated. I,the cell current in amps, equals E / R . The number of Faradays, f,is obtained from the graph of I in amps versus 1 in seconds. The number of coulombs, q, passed in the time interval 11-tz is
milliarnmeter
and f = q/96,500. A planimeter may be used to integrate the area under the curve in Figure 2 to obtain q in ecruation (1). Tn+,the transference number of H+, is caiculatedfiom the'relation I
Recording Potentiometer
-rubber
Figure 1.
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tubing
Moving boundary circuit.
Journol o f Chemical Education
Figure 2. Current in milliampr as a function of time, I. Each mark represents 0.01 ml swept out by the moving boundary in time interval t z to 1%. The curve is for 0.01 1 3 N HCI ot 25% The area under the curve between 0 and 4 3 0 seconds is 0.0845 amp seconds.
NAV TE+ = -
looof
where N is the concentration of HC1 in equivalents per liter, and the integrated area in equation (1) corresponds to the change in volume AV, swept out by the moving boundary. The results of student mns shown in Table 1 compare favorably with the literature value of 0.823 for 0.1N HCI at 25°C.5 SMITH,E. R., A N D MACINNES, D. A,, J. Am. C h m . SOC., 47, 1012 (1925).
Table 1 .
Resultsof Typical Student Runs with HCI at 25.0°C Area . ..
Concentration Eqlliter
Resistance R (Ohms)
integration of Figure 2 AV (cc) q (Amp Sea)
Tat
made with a recording potentiometer. 'Measurements Measurements made with a student potentiometer.
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Volume 43, Number 4, April 1966
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