62
PIERRE V.\X
RYSSELBERGHE
REFERESCES
(1) ADAM,il.K.: The Physics and Chemistry of Surfaces, 2nd Edition, pp. 113,115. Oxford Gniversity Press, London (1938). (2) ALEXANDER, A. E.: ilature 148, 752 (1941); Trans. Faraday Soc. 38,54 (1942). (3) CASSEL,1%.M.: 105th Meeting of the American Chemical Society, held in Detroit, Michigan, April, 1943. (4) CLAYTON, W.: The Theory of Emulsions and their Technical Treatment, 4th Edition, pp. 6-12, 53-55. The Blaliiston Co., Philadelphia (1943). (5) DREGER,E. E., KEIM,G. I., MILES,G. D., SHEDLOVSKY, L., ASD ROSS,J.: To be published. E. 0.: Advances i n Colloid Science, pp. 111, 395, 402-5. Interscience Pub(6) KRAEYER, lishers, Inc., Yew York (1942). (7) LOXG, F. A., KUTTISG,G. c . , A N D HARKISP, IT.D.: J. -4m. Chern. Soc. 69, 2197 (1937); 62, 1496 (1940). (8) LOTTERhTOSER, A , , A N D STOLL, F.: Kolloid-Z. 63, 49 (1933). (9) MCBAIN,J. W., . ~ S D DAVIES,G . P . : J. Ani. Cheni. Soc. 49, 2230 (1927). (10) MCBAIN,J. W., ASD MILLS,G. F.: Report on Progress in Physics 6,30 (1939). (11) MCBAIN,J. W., A N D WILSOX, D . A . : J. Am. Chem. Sac. 68, 379 (1936). (12) POWNEY, J., AND ADDISON,c. c.:Trans. Faraday soc. 33, 1243 (1937).
DISCUSSIOX h S D I N T E R P R E T A T I O S O F T H E MIGRATION DATA OF LAURYLSULFONC ACID IT\’ AQUEOUS SOLUTION PIERRE VAX RYSSELBERGHE Department of Chemistry, University of Oregon, Eugene, Oregon Received September 16, 1945
A few years ago, on the basis of the then available data, we gave (4) an interpretation of the osmotic coefficients, the conductivities, and the diffusion coeficients of the typical colloidal electrolyte laurylsulfonic acid in aqueous solution. An average negatively charged micelle H,L,, changing with concentration, was calculated. The values of z and z and the concentrations (H,L,) and (H+) ivere obtained b y solving, for each concentration, a system of four simultaneous equations : namely, two stoichiometric conditions, the freezing-point equation in which the experimental van’t Hoff i coefficients were introduced, and a conductivity equation based on the use of Stokes’ law according to the suggestions of J. W. McBain (3). The latter equation (equation 11 of our previous paper) is 350(H+)
(x - zy (H,L,) + 22 ___ 2113
=
AC
The values of x and x so obtained were then introduced into the Sernst formula for the diffusion coefficient, written for an unsymmetrical electrolyte whose molecule dissociateq into (z - z ) / x hydrogen ions and l/z micelles H,L,. The calculated diffusion roefficientq were found to be in satisfactory agreement with the experimental data of E. L. McBain ( I ) . I n particular, the interesting minimum in the diffusion cwve \\-a3 reproduced by the calculations haTed upon the average
63
MIGRATIOS DATA O F LAURYLSULFOXIC ACID
micelle. Furthermore, in the absence of transference data, x e made some predictions by means of the follon-ing formula (formula 22 of our previous paper) for the tranpference number of the laurylsulfonate radical:
We mentioned that these predictions would probably be considerably altered by viscosity corrections. It was, moreover, implicitly assumed in formula 2 that TBBLE 1 Measured and calculated transference numbers of laurylsulfonic acid i n aqueous solution CONCESTMTION
T
T
m
(UEASURED)
(C.4LCULATED)
‘DEGREE OF IOSIZATION” OF MICELLES
0 0.005 0.01 0.02 0.03 0.04 0.05 0.055 0.06 0.07 0.08 0.09 0.1 0.2 0.4
(0.059) 0.065 0.090 0.130 0.180 0.250 0.320 0.350 0.330 0.290 0.275 0.270 0.255 0.230 0.220 (extrapolated)
0.059 0.060 0.065 0.118 0.172 0.226 0.320 0.360 0.404 0.510 0.669 0.935 1.243 1.396 1.517
(1.0 1.o 1.0 1.o 1.o 1.o 1.0 1.O) 0.815 0.569 0.411 0.288 0.206 0.165 0.145
I
the averaging process which had led to the conductivity equation was also valid in the description of electrolytic migration. To what extent this is justified and what alterations should be introduced in the treatment are questions which can now be answered, thanks to the migration data recently published by E. L. McBain (2) 1 Dr. E. L. NcBain has asked us to indicate the following corrections in table 2 of her paper (2), the data below replacing the corresponding ones in the table:
s
I
EQUIVALENTS C H A N G E
’
11 S o change C 0.1164 0.3475
I
1
0.044
-0.00000362
(correct in paper) A $0.000485 11 -0.000011 C -0.000436
TRANSFERENCE NUMBER
~
0.239
0.223 I
TT-lien the meastired ti,::nsf’erence numbers :ire plotted agaiii.st conc~ntration, the values at roiind coiiccntrntions read from the c;tr~-eare tho.se in the second colunin of’ tnhle 1. 1-sing forniula 2 with the niliies of s and 2 in talde 1 of our previous paper \\-e find t h e transference niinihers given in the thii,d colunin of t hc present table. IT-e Rotice that up to the lll:lsi1ilti1ii in tlie esperimcnrn! t rmsference curve at coiiceiitrntion 0.055 771, the agreement betn-ecn calculntec! mid mea.uretl values is, all things con.siderec1, escellcnt. -1hove 0.035 n:, lioi\.eIw! our calciilated value: keep on increasing, tlie ratio Tc,,lcd.;’TIl?easd. rencliing tllz d u e 6.895 at the concentration 0.4 m. Oliviousl\., some efi’ect not taken into nccount in formula 2 i? appearing around the concentration 0.055 m and IJecomei increasingly more important as concentration rises. As pointed out above? formula 2 is based upon the same averaging process as the conductivity equation : namely,
in n-hich H,L, designates any particular niicellar species, poqitive or negatiw. and the summation is extended to all pairs of values of i and j present in the wlution. Actually, the transference number of the laurylsulfonate radical diould lie
and it is not necesaarily true thnt
The experimental data, lion-ever, sho~vthat this is true up to the mnsimuni in the transference curve. Son-. marked departure from equation 5 TI ould occur if, in the migration process, there i.q a certain compensation between the moI-enients in opposite directions of negatire and positive micelles. -411 micellec, regardlesh of sign, contribute a positive amount to the conductivity: namely,
for the species HjLi , while this same species contributes
t o the transference number of the radical, and thi3 contribution T\ ill be po-itive or negative according to the sign of i - j. The conipensating effect of opposite migrations is particularly likely to occur 11ith poqitive and negative micelles of similar size and mobility, i.e , when their net charge; are small nunibers like & l , 1 2 , etc. and the i values 01 oppositely charged micelles are exactly or nearly equal to each other. The maw action eKect, ~\-oulclcause such micelle; to be preqent in fairly equal amounts. When i - 1 = j l and 2’ - 2’ = -1. n i t h
XIGR.\TiOS
D l T l O F L I C R I L C T L F O S I C .ICID
65
(13L , i t 1 id1 t o tH ,L i and i equal t o I ’ , the contril)ution; of these t n o bliecies t o thc tran-ferpiice nLimber of the indica1 15 oulcl cancel each othei.. The rather lnige ~ n - l ~ of e =:he ratio- ?IcTlcdTme,.d nhove the ma\iniuni wggest that thi. type of compenwtion is important, and hence that an appieciable amount of micelle. are nenrl?- neutral. Belon the mnxinium the micelle. 11-ould be preponcleiantly negntive ,ind their compoqition would be fsomevhat concentrated aroiuiid the average niiwlle E&. TI-e h a w
aiicl this r:itio iz. in a i u y , a nieasure of the “degree of ionization” of t,he micelles. The smaller this ratio, the greater is the compensating effect of the opposite migration. (2micelles much closer t o neutrality than the a-,-ewge niicelle H,L,. The numerical values of this r:at’io are given in the fowth coliinin of table 1. -4 possible alternative t o the foregoing explanation of the transference data is a consideration of the efYect of the hydration of the micelles. In determining our H,L, awrnge micelle it has heen implicitly assumed that the size of the micelles and the application of Stokes’ laiv t o the calculation of their mobilities and conductivitiea are only negligibly nfYected 11-: hydration. If, hoxerer, we make a hydration correction in the transference number, :as.suniing that the migration i3 due t o the single species H,L,, n.e arrive a t the conclusion that all the \i-ater in the solution. and a t the higher concentrations even more than the total amount of n-ater. \~-ouldlie wtter of hydration of the micelles. I t may he that the true picture ~ o u l c he l n compromise lietn-een hydration ant1 nearly neutral micelles with compensating migrations. The latter effect: hon-ever, is no doubt present and this is a nioit important piece of information fmnislied by E. L. IIcBain’s migration data. SUMXARY
E. L.SIcBain‘s recent migration data for laurylsulfonic acid in aqueous solution are sho\m t o indicate the probable presence of rather large amounts of nearly neutral micelles v-ith compensating migrations a t concentrations above the masimuni in the transference curve. Below the masinium the transference nunibers are in excellent agreement with the values calculated on the basis of a previously calculated aT-erage micelle whose composition and size change continuously with concentration. (1) (2) (3) (4)
REFEREKCES ~ I C B A I E. S , L . : Proc. Roy. SOC. (London) A170, 415 (1939). I l c B a ~ sE. , L . : J. Phys. Chem. 47, 196 (1943). MCBAIN,J. W.:Trans. Faraday Soc. 9, 99 (1913). VAS RTSSELBERGRE, P.: J. Phys. Chem. 43, 1049 (1939).
