Transference Numbers of Colloidal "Ferric Hydroxide." - The Journal of

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TRANSFERENCE NUMBERS OF COLLOIDAL “FERRIC HYDROXIDE”’ JAMES W. McBAIN

AND

WINIFRED McCLATCHIE THOMAS

Department of Chemistry, Stanford U n i v e r s i t y , C a l i f o r n i a

Received J u n e 11, 1986 INTRODUCTION

It was demonstrated by Laing ( 2 ) , in her work with soap solutions, that colloidal electrolytes and ordinary electrolytes show the same type of electrokinetic behavior, and hence can be studied by comparable experimental methods. “Ferric hydroxide” sols are typical charged colloids differing only in degree from typical colloidal electrolytes. It is therefore to be expected that their transference numbers can be measured by the same methods that are used for simple electrolytes, namely, the analytical method of Hittorf and the method of moving boundaries. The identity of these two methods for measuring transference numbers was pointed out by Miller (8) and by Lewis (3), and was experimentally verified by MacInnes and his coworkers (4,5 ) . Pllany colloid chemists, however, have not recognized that this identity must also hold true for colloids. It was therefore desired to demonstrate this truth by experimental measurements on a typical charged colloid such as a “ferric hydroxide” sol. The requirements for reliable Hittorf determinations of colloids have been clearly stated by Laing ( 2 ) . The requirements for moving-boundary measurements of ordinary electrolytes have been established by MacInnes and his coworkers (5), but have been applied to colloidal solutions only by Robinson and Moilliet (9) in their study of dye solutions. The following are the most important conditions that should be observed in any moving-boundary determination: The slower ion, usually the indicator, should follow; only the receding boundary should be observed; the denser solution should be on the bottom; the concentrations of the two ions forming the boundary should be approximately in the ratio C/T = Cl/Tl, where C and C1 represent concentrations and T and T1 represent transference numbers; the concentration of the indicator should preferably be slightly less than that indicated by the equation; a tube of small bore should be used; one electrode compartment should be closed; the electrode 1 Presented a t the Thirteenth Colloid Symposium, held a t St. Louis, Missouri, June 11-13, 1936. 997


998

JAMES

w.

MCBAIN AND WINIFRED

MCCLATCHIE

THOMAS

in the closed compartment should be reversible; and volume changes on the closed side of the boundary should be known. Colloidal “ferric hydroxide” is a good material with which t o demonstrate the fact that accurate transference measurements can be made by both the Hittorf and the moving-boundary methods. Moderately concentrated sols can be prepared, and they exhibit a conductivity comparable to that of dilute solutions of ordinary electrolytes. I t is therefore possible to find an ion of lower mobility that the colloid to serve as an indicator. The only uncertain factor is the presence of small amounts of hydrogen ion in all “ferric hydroxide” sols It is, however, probable that there would be no appreciable disturbance of the boundary if the same concentration of hydrogen ion were present in the indicator as in the sol. EXPERIMENTAL

Hittorj determznatzons These experiments aere carried out on “sol 13,” the properties of which have been recorded in two previous communications (6, 7 ) . The method used for Hittorf determinations was similar to that described by Laing (2). Figure l shows the transference cell. It was of Pyrex glass, and had a capacity of about 100 cc. The usual silver coulometer was not sufficiently sensitive to determine the current passed through thp cell. The current density was therefore measured by means of a galvanometer that had been calibrated as a milliammeter. The total current TT as determined by plotting current density against time and taking the area under the curve. Four B-batteries in series (200 volts) supplied the current. 411 portions of the circuit were insulated from the ground. In these gravimetric Hittorf measurements the sol was placed so as t o a1 the middle portion (tubes 3 and 4) completely, and to extend half way up in tubes 2 and 5. Then with the cell in position, a known weight of 0.0001 N sodium nitrate solution was introduced from a separatory funnel with flaring, upturned tip, to serve as a guard solution. This prevents contact with the electrodes and also provides definite electrode reactions not interfering with the analysis employed. Before starting a run, the cell was allowed fifteen minutes to attain the temperature of the thermostat, 25” i 0.02”C. During a run the current density was measured every 5 minutes, and the zero point of the galvanometer was checked frequently. Three middle portions, “AM,” “AI,” and “CM,” and both electrode portions were analyzed for iron and chlorine according to the methods described in a previous communication ( 7 ) . The transference numbers of ferric oxide and of chlorine were calculated relative to water. The final weight of water in each electrode compartment was determined by subtracting the weight of guard solution and the


TRANSFERENCE NUMBERS OF COLLOIDAL “FERRIC HYDROXIDE”

999

weight of ferric oxide found by analysis from the total weight of solution. The weights of ferric oxide and chlorine originally present were calculated from the composition of the sol. The Hithorf migration results are given in table 1. The Hittorf number is defined as the number of chemical equivalents of the named constituent which pass from one electrode compartment to the other for each faraday (96,500 coulombs) of current passed through the solution. The middle portion remains unaltered in composition. For colloidal systems, as for electrolytes, the algebraic sum of the number of electrochemical equivalents or charges carried in the two directions must always add up to unity for each faraday of current passed. In the case of simple electrolytes carrying

FIQ.1. Migration apparatus

one charge per chemical equivalent, the same statement holds true for chemical equivalents. However, since a colloid may carry many chemical equivalents per electrical charge, the Hittorf numbers may be greater than unity, as in table 1. Here the migration numbers appear as 70.3 equivalents of iron and 2.50 of chlorine for each faraday, both moving towards the cathode. Thus, 2.50 more equivalents of un-ionized chlorine is carried in the positive colloidal particles towards the cathode than is simultaneously carried toward the anode by the corresponding free chloride ions.

Moving-boundary determinations The migration velocity of colloidal “ferric hydroxide” was measured in the same cell that was used for Hittorf determinations. The guard

1000

JAMES Pi. MCBAIN AND W’INIFRED MCCLATCHIE TITOMAS


solutions, now used as indicator solutions, were of lithium chloride, made to the same hydrogen-ion concentration as the sol with hydrochloric acid, and were equally conducting with the sol. TA4BLE1 Hittorf measurements of transference numbers expressed as chemical equivalents of zron and chlorine transported per f a r a d a y f o r “ferric hydroxide sol IS” TRAXBFERENCE OF PORTION

j

Change in equivalents

Fe(0H)s

T R A X ~ F E R E N C Eor

~

’

H,ttorf number

C1

Change in

Experiment 1: current passed, 4.66 X 10-j faradays

A ................ AM. . . . . . . . . . . . . . .

!

-0,00329

+o, 00001 70

31,. . . . . . . . . . . . . . . CM... . . . . . . . . . . . . C . .. . . . . . . . . . . . . . .

+ 0 , 00002’ +O. 00004) +0 ,00318,

69.6

Average. . . . . . . . . . . . . . . . . . . . . . . .

A ............... AM. . . . . . . . . . . . . . .

-0.00245

71 0

+o. 00001 +o. 00002

I :

$0 00238

0 0000873

-2.51

-2 56

0 0000000 -243

1

1

+70 8

-2 51

-X81

-0 0000007 3-0 0000028 4-0 0000810

69 9

Average. . , , , , , , , ,

: j

1

$70.1

+O. 00002

BI... . . . . . . . . . . . . . . CM.. . . . . . . . . . . . . . C. . . . . . . . . . . . . . . . .

-0 000001j -O 000116’ $0 000003’, $0,000002 1 + 0 , 000112,l

-2.50

__

TABLE 2 Moving-boundary measurements expressed a s transference numbers and as absolute velocities, showing i d e n t i t y w i t h results of Hittorf method f o r “ferric hydroxide sol 19” Indicator solution: 7.5 X 10-6 N hydrochloric acid $ 5.5 X 10-3 N lithium chloride TIME

i

MOTEMENTOF BOUNDARY

1

1

~~f$~&‘

cm./sec./rolt/cm.

min u !e s

90 From Hittorf number, table l . ,. . . . . . . . . . . . .

MOBILITY

.,I

4.48 x 10-4 4.58 X lo-‘ 4.45 X

1

HITIOBF N U M B E R

I~

1

7 0 72.4

3

70.3

(C = 0.933 equiv. per liter on basis of analysis in Hittorf experiments.)

The potential gradient was determined by measuring the difference in potential between two of the platinum terminals shown in figure 1. The measurements were made by means of a Leeds and Northrup student



1001

potentiometer and a high-sensitivity, high-resistance galvanometer. The method was checked by using a dilute potassium chloride solution in the cell, the potential gradients observed between different terminals checking within less than 1 per cent. The boundaries between sol and guard were formed in the manner that was described for Hittorf determinations. The cell was allowed fifteen minutes to attain the temperature of the thermostat. The boundaries were observed by means of a traveling microscope. Their position, when first formed, could be read to within 0.2 to 0.4 mm. After the current had been passed for about fifteen minutes, the anode boundaries were read to within 0.1 mm. Observations of potential gradient and of boundary position were made about every 5 minutes during each run. The transference numbers of iron obtained by this method for ‘‘sol 13” are summarized in table 2 for two independent experiments, involving twenty-seven readings. They were calculated from the equation

T I - UFC

lOOOK

where T is the Hittorf number, U is the absolute velocity in em. per second per volt per centimeter, F is Faraday’s constant (96,500 coulombs), C is the concentration in chemical equivalents per liter, and K is the specific conductivity. DISCUSSION OF RESULTS

These results definitely prove the possibility of measuring the transference numbers of charged colloids as well as colloidal electrolytes by both the analytical and the moving-boundary methods. The values obtained by the two methods agree within the experimental error of the moving-boundary measurements as made in these experiments. More accurate results could be obtained by more rigid adherence to the principles listed in the introduction. The chief source of inaccuracy was in the use of an apparatus with both electrode compartments open, making the application of exact volume corrections impossible without further study (3). However, since the total current passed was very small, about 5 X faradays, volume changes due to electrode reactions were practically negligible. The only appreciable errors were due, first, to the slight hydrostatic readjustment of the liquid boundary caused by the transference or displacement of the “ferric hydroxide” in density, and, secondly, to the slight volume changes accompanying the transference. This might make the results low by about 2 per cent. A third source of error was due to the use of an indicator solution that was more concentrated than the required value, 4.2 X calculated from

1002

JAMES W. MCBAIN AND WINIFRED MCCLATCHIE THOMAS


C/T = C1/T1. However, it has been found (1) that the range of adjustment is relatively great for solutions of this dilution, so that the error was probably very slight and would tend to cancel the error due to transference of “ferric hydroxide.’J COLLECTED PROPERTIES

A summary of the chemical and physical properties of “ferric hydroxide sol 13,” as presented in this and two previous cominunications (6, 7 ) , is given in table 3 . The second column gives properties of the actual sol, containing both colloid and small amounts of free hydrochloric acid. The third column represents an “ideal” sol containing only the positive colloidal particles and the corresponding chloride ions. These values are obtained by correcting the values in column two for the effect of the ultrafiltrate. TABLE 3 S u m m a r y o j properties of “ferric hydroxide sol 13‘’ at d6”C.*

Equivalents of Fe per.lOOO g. HzO., , . . . . . . . , Equivalents of C1 per 1000 g. HzO . . . . . . . , . . , CE+ . , . . , , . . , . . . . . . , . . , , , . . . , . , . , . . , , , , , , , , , Specific conductivity, in m h o s , , . . . . . . . . . . . . . Hittorf number of F e . , . . . . . . . . . . , . . , . . . . . , , Hittorf number of C1 (not C1- only). , , , . ,. , , Mobility of F e in cm./sec./volt/cm.. , . . . . . , . Mobility of C1- in cm./sec./volt/cm .. . . . . . . Equivalent of Fe per faraday of free charget. Concentration of free chloride i o n t . . , . . . . , . .

0.934 0.0449 6 . 3 X 10-6 8.70 x 10-4 70.3 -2.51 4.52 x 10-4 7.91 x 10-4 206 0.0064

0.934 0.0430 1 x 10-7 5.40 X 74.2 -2 65 4.52 X IO-& 7.91 x 10-4 206 0,0048

* The diffusion coefficient of “sol 20” a t 25°C. was found t o be 0.613 as compared with 0.46 for sucrose by McBain, Dawson, and Barker (J. Am. Chem. SOC.66,1021 (1934)). t Calculation as given below. The number of chemical equivalents of iron per faraday of free charge, calculated by means of the Laing equation (2),

W L F ~was ,

where TFe is the Hittorf number, 74.2, fFe is the conductivity contributed by one chemical equivalent, cFeis the concentration in chemical equivalents per 1000 g. of solvent, 0.934, and I.( is the conductivity of that amount of solution containing 1000 g. of solvent, approximately 1000 X 5.40 X = 0.540 mho. All the above quantities are experimentally determined except l l and ~ The. latter can be eliminated by means of the independent equation, f ~ ~

~

~


1003

+


j i = C FfFe ~ Ccl-v, where eel- is the concentration of free chloride ions and v their mobility. Solving for fFe and substituting = CFe/mFe gives

Substituting this in the Laing equation,

TFeis taken as the value for the “ideal” sol or 74.2, v is assumed to be the same as a t infinite dilution or 76.3, and p may be taken equal to K x 1000 or 0.540. This gives m F e = 206. The corresponding concentration of chloride ion due to dissociation is 0.934/206 = 0.0045 N . This free chloride ion, 0.0045 N C1-, is only 10.5 per cent of the total chloride, 0.0430 N , carried in the sol, the other 89.5 per cent being carried in the positive particle in undissociated unconducting form. As compared with the equivalent conductivity of the free chloride ion, 76.3 mhos, the conductivity of one equivalent of positive charges carried on the positive particles is 43.6 mhos; hence that of the amount of charge carried by one chemical equivalent of iron is 206 times less, or 0.212 mho. A positive charge on the colloidal particle thus conducts 43.6/76.3, or 57 per cent as well as an ordinary chloride ion. Finally the so-called zeta potentials, which, since they have never been measured directly are always calculated by multiplying the observed linear mobility by 4 q / D or 129,700, come out as +58.6 mv. for the positive colloidal particles and -102.6 mv. for the ordinary free chloride ions. SUMMARY

The transference numbers of iron and chlorine in a “ferric hydroxide” sol were measured by the Hittorf and moving-boundary methods, which were found to give identical results within the limits of experimental error.2 The importance of making such measurements in accordance with methods established for use with simple electrolytes was pointed out. The interesting and significant physicochemical properties of “sol 13,” as reported in this and two previous communications, are summarized. 2 Footnote added in prooj: Roberts and Carruthers (J. Phys. Chem. 40, 703 (1936)) have now shown t h a t the moving boundary and the observation of a single particle give identical results. This is inevitable, if electrode changes do not reach through the middle portion, since all movement is referred t o motionless solvent. On the whole, apart from slight density changes outside the middle portion, the solvent does not move in either a closed or an open U-tube.

1004

JAMES

w. MCBAIN

AND WINIFRED MCCLATCEIIE THOMAS


REFERENCES

(1) HARTLEY, G. S., AND MOILLIIT, J. L.: Proc. Roy. Soo. London lMA, 141 (1923). (2) LAINQ,M. E.: J. Phys. Chem. 28,673 (1924); and a later more systematic study, Trans. Faraday SOC.31, 153 (1935); of. MCBAIN,J. W.: Acta Physicochimica U. R. S. S. 4, 169 (1936). (3) LEWIS,G . N.: J. Am. Chem. SOC.32, 862 (1910). (4) LONQSWORTH, L. G.: J. Am. Chem. SOC.64, 2741 (1932). (5) MACINNES, D. A,, AND LONQSWORTH, L. G.: Chem. Rev. 11, 171 (1932). (6) MCBAIN,J. W., AND MCCLATCHIE, W. L.: J. Am. Chem. SOC.66, 1315 (1933). (7) MCCLATCHIE, W. L.: J. Phys. Chem. 36, 2087 (1932). (8) MILLER,LASH:2. physik. Chem. 69, 436 (1909). (9) ROBINSON AND MOILLIET:Proc. Roy. SOC.London 143A, 630 (1934).

Transference Numbers of Colloidal "Ferric Hydroxide." - The Journal of

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