Dec. 20, 1952
DIFFUSIONCOEFFICIENTS OF CERTAIN METALSIN MERCURY
as double molecules.12 From molecular weight determinations for acetic acid by the cryoscopic method with benzene as ~ o l v e n t ' ~and ~ ' ~the study of the Raman spectra of aqueous acetic acid solut i o n ~ , it ' ~is apparent that acetic acid a t concentrations higher than 20y0exists as dimers. Compound formation between solvent and solute is the only cause of negative deviation from ideality and since a positive deviation was observed, this evidence also favors the absence of compound formation. Recent studies of the polymorphism of stearic acid16 and palmitic acid" show a similarity of the (12) W. W. Lucasse, R. P. K o o b a n d J. G. Miller, J. Chcm. Educalion, 21, 454 (1944). (1.7) J. M. Peterson a n d W. H. Rodebush. J . P h y s . Chcm., 32, 709 (1928). (14) C. R. B u r y a n d H. 0 Jenkins,J . Chcm. SOL.,688 (1934). (15) S . I. Leitman a n d S. A. Ukholin, J . Chcm. P h y s . , 2 , 825 (1934). (16) W. S. Singleton, T. L. W a r d a n d F. G. Dollear, J . A m . Oil Chcmtsts' S O L . , 27, 14 I (1950) (17) T. L. W a r d and W. S . Siugleton, J. P h y s . Chem., 6 6 , 696 (1952).
[ C O N T R I B U T I U N PROM TIlE JJEPARTMENT O F
6
7
8
9
6183
6
"C.
7
8
9
OC.
Fig. 2.-Dilatometry with rising temperature.
Fig. 3.--L)ilatometry m ith falling temperature.
polymorphism of those acids to that revealed here for acetic acid. In fact, a plot of the dilatometric data of Ward and Singleton" for palmitic acid gives a curve similar to those of Figs. 2 and 3 for acetic acid, and shows a transition point in the neighborhood of 25.5". PHILADELPHIA, PENNA.
CHEMISTRY, UNIVERSITY O F \vISCONSlN
A N D THE ITRICK CHEMICAL 1,ABORATORY
O F PRINCETON UNIVERSITY]
The Diffusion Coefficients of Certain Metals in Mercury BY b'. CHARLES COOPER
AND
N. HOWELL FURXIAN
RECEIVED AUGUST4, 1952 A discussion of the electrochemical methods of determining the diffusion coefficients of individual metals through mercury is presented. Diffusion coefficient data for the metals zinc, cadmium, lead, copper, thallium, tin and bismuth are presented. and 0.99 X lo-& Diffusion coefficients for tin and bismuth, derived from polarographic data, were found to be 1.68 X cm.2 sec-1, respectively. The nature of dilute amalgams is examined, and evidence of compound formation in dilute mercurial solution between mercury and the metals copper and bismuth is presented.
Introduction One approach to a study of the diffusion of nietals in mercury is through the measurement of diffusion coefficients. According to Smith' the diffusion coefficient D can be defined by the formula dc d S = -Dp-dt dx
in which d S is the quantity of the diffusing substance which passes a given point in the time dt through a cross-section p of a diffusion cylinder under the influence of the concentration gradient dc/dx.2 '$11 experimental methods used to determine diffusion coefficients hinge on the various possibilities for the determination of concentration changes. In the case of amalgams the possibilities are not so numerous as they are with aqueous solutions, since all the optical methods which have been applied successfully to such solutions cannot be used. Although chemical analysis and density dcterininaiions can be used for amalgams, the principal methods are electrochemical in nature. The purpose of this paper is to discuss briefly these electrochemical methods with particular emphasis o n the polarographic method used by the authors ( 1 ) G. M c P . S m i t h , THIS JOURNAL, 36, 847 (1914). ( 2 ) A more critical definition of diffusion coefficient is given IJY
IInrtley and J. C r a n k , Trans. Faraday SOL, 46, 801 (1049).
G. S.
and to examine the nature of dilute anialgams i n the light of diffusion coefficient data. Methods of Measuring Diffusion Coefficients E.m.f. Methods.-The diffusion coefficients of cadmium, zinc and lead in mercury were determined by Meyer3 who made the amalgam the anode of a small cylindrical cell. By electrolysis the metal in the amalgam was put into solution from the under base of the amalgam. The rate of diffusion of the metal atoms to the under surface of the amalgam was determined by measuring the potential between the upper region of the amalgam and a constant amalgam reference electrode a t various time intervals. A disadvantage of Meyer's method is the fact that an accurate determination of the height of the small amalgam column is very di&cult. Here is a serious source of error, since in the equation used for the calculation of D the height of the column appears as hi. Lfeyer's student von Wogau4 determined the diffusion coefficients of a number of individual metals in mercury employing a method analogous to that of Graham.6 A cylindrical column of mercury was covered over by the amalgam of the metal being investigated whereupon the diffusioii (3) G. Meyer, A ~ Rphysik. . Chcm., 61, 225 (1897). (4) h l . von Wogau, A n n . physik, 23, 345 (1907). (5) T. G r a h a m , A n n . chcm. g h a i m , 121, 1 (1862).
618-2
bv.
CHARLES COOPER A4NDN.
HOWELL FURMAN
VOl. 74
commenced. After a certain time the column ping amalgam anodes. At 25" the anodic diffusion was separated into several layers through thc current i d = -607nD'/Cmz/atL/6. If the diffusion removal of sliding singly perforated glass plates, current constant ID = ('id/c?nx''t'/6) is determined, These plates comprised the column. The amalgam the diffusion coefficient for the particular metal in held in the perforation of each plate was analyzed mercury can be calculated, since, as the diffusion chemically or potentiometrically by measurement current equation indicates, I D = - 607nD1/2. against a constant amalgam electrode of the metal The variation in diffusion current constant with uiider consideration. This method has thc dis- suplwrting electrolyte which has been observed by advantage that the diffusion process is disrupted TABLE I before the actual measurements are made. Cohen and Bruins6 developed a method which DIFFUSIONCURRENT CONSTANT DATAFOR TIN AMALGAMS gave more accurate, reproducible data than did the IN VARIOUSSUPPORTING ELECTROLYTES methods of Meyer and von Wogau. The principle of their method was first described by des Coudres. h known quantity of the metal was brought into Supporting electrolyte 1 dl HCl the surface of a large mercury cathode by elec(1 00041 -- 3.56 1.53 1 55 -4.88 trolysis in an electrolytic cell. The rate of diffusion ,00042 -- 3.49 8.54 1.52 -4.88 of the metal in mercury was then determined po.00042 - 3.63 4.23 1 56 -4.85 tentiometrically by measuring the potential differ,00402 -32 26 2 68 1 44 -4.88 ence between the iriercury surface and a constant Supporting electrolyte 4 :li NH4C1-I JI €IC1 amalgam electrode a t various intervals of time after the electrolysis. Cohen and Bruins investigated 0.00041 - 3.59 4.58 1.53 -4.97 but one metal, vh., cadmium. ,00042 - 3.57 3.71 1.50 -3.00 Conductance Method.-The diffusion coefficients ,00043 - 3.64 4.40 1.56 -4.90 of cadmium and zinc in mercury were determined by 00402 - 34.00 3 .99 1 ,53 -4.80 \Veischede18 who followed the change in concentraSupporting electrolyte O..? JI H2SOa tion occasioned by diffusion directly- as a function O.lJOOS1 - 3.170 4 . 7 1 1.54 -,i, 11 of time and without disruption of the diffusion .00402 -34.97 4 ,1)8 1,52 --6 . i J 1 process. The amalgam and mercury were stratified in a cylindrical vessel and the electrical resistance Supporting clectrolytc I HNOr between wire probes iiitroduced into the diffusion i) 00041 - :3.35 4 56 1 52 -4 !)B iiiediurn a t even intervals was tneasurcd. For thc 00402 -:i4 3 1 .: 81) 1 49 - .j 03 calculation of the diffusion coefficient the relative Supporting electrolyte 2 Jf HCIO4 resistance values measured on the probes were IJOOO4L -3.68 457 151 -- ,>, 18 plotted against time. A plot of In w (where w = ,00402 -35 09 1 29 -5.24 :: 53 resistance between heights izl and h z after time t ) E'S. t yielded a straight line, the slope of which gave TABLE I1 U , the diffusion Coefficient. DIFFUSION CURRENT CONSTANT DATAFOR BISMUTHAMALPolarographic Methods.---Reboul and Bong used GAMS IN \.ARIOUS SUPPORTING ELECTROLYTES the cathode ray oscilloscope to study dropping amalgam electrodes and applied their technique to determine the rate of diffusion of metals in mercury. They investigated the variations in the instanSupporting electrolyte 1 lICl taneous current xiieasured during the formation of 0 lJ0:isI --%0.178 1 fit; 1.22 --
