svedberg equation

activity coefficient data that the observe: behavior agrees with that expected, the .... In the experiments reported here, the offset arrangement was ...
0 downloads 0 Views 907KB Size
Download PDF
J. M. CREETH

1228

Vol. 66

STUDIES OF THE TRANSPORT PROPERTIES OF THE SYSTEM THALLOUS SULFATE-WATER. 11. SEDIMENTATION COEFFICIENTS AT 25’ ; A TEST OF THE “SVEDBERG EQUATION” AT FINITE CONCEKTRATIOW BY J. M. CREETH~ Department of Chemistry of the University of Wisconsin,Madison 6, Wis. Received October ii, 1061

+

With the purpose of testing the extended form of the Svedberg molecular wei h t equation: M = Rl’s( 1 d In y/d In O p ) , measurements have been made of the sedimentation coefficient o! the solute in the strictly two-component system TlzSOd-HaOover the concentration range 0.f3-5.0 g. dl.-I. The Gutfreund-Ogston method was used, in a form ap ropriate to the Rayieigh interference optical system. It was found necessary to extend the expression relating the reiactive index changes in the cell to the sedimentation coefficient to take into account the non-linearity of the relation between refractive index and concentration, and also the effects of pressure. The sources of error in the experimental procedure have been examined, and ways of minimizing the errors are demonstrated. The sedimentation coefficients obtained range between 1.0 and 1.2 S., with a positive de endence upon concentration. It is shown from previous1 obtained diffusion and activity coefficient data that the observe: behavior agrees with that expected, the concentration-dpendenoe being due to incomplete dissociation of the electrolyte. The significance of the findings iB examined; it is concluded that a macroscopic mobility exists for the solute in a two-component system which is independent of the particular flow situation.

c)/D( 1 -

I n a two-component system, the relation between the experimentally-measurable sedimentation coefficient, s ~ diffusion , coefficient, D,solution density, p, and partial specific volume, t‘~~, may be expressed as Mi =

+

RTsl[l d In gl/d In e l ] D(l - OIP)

(1)

where MI is the molecular weight, el, the concentration, and yl, the activity coefficient of the “solute” (component 1) on: e.g., the molar scale, and R and T have their usual significance, All qumtities measured, with the exception of D and p, depend on the choice of components. I n the limit of zero concentration of component 1, the expression reduces to the Fell known “Svedberg equation.’lg Equation 1, which will be referred to as the extended Svedberg equation, may be derived by methods based either on the concept of frictional or explicitly in terms of the thermodynamics of irreversible processes*; the latter derivations are less restrictive and have special importance in that the flows of solute occurring in the separate sedimentation and diffusion experiments are formulated in terms of the same fundamental coefficient, which has the nature of a mobility, Thus the vexed question of whether or not the frictional coefficients are identical in the two processes’ is avoided completely,6~sthough specification of the reference frames remains important. (1) A preliminary report of this work was presented to the Faraday Society Informal Discus3ion on Ultracentrifugatlon of Biological Macromolecules held in Birmingham, England, Sept. 14-15, 1960, an account of which has been given by D. R. Stanworth, Nature, 188, 635 (1960).

(2) Lister Institute of Preventwe Medicine, London, S.W.1, England. (3) T. Svedberg and K. 0. Pedersen, “The Ultracentrifuge,” Oxford University Press, Oxford, 1940. (4) R. L. Baldwin and A. G. Ogston, Trans. Faraday Soc., 50, 749 (1954). (5) 0. Lamm, Trans. Roy. Inst. Tech. (Stockholm), 184, No. 3 (1959). (6) J.

W. Williams, K. E. Van Holde, R. L. Baldwin, and H. Fujita (Chem. Rev., 58, 715 (1958)) have summarized the work in this field. (7) G. Kegeles, 6 . M. Klainer, and W. J. Salem, J. Phys. Chem., 61, 1286 (1957). (8) L. Peller, J. Chem. Phus., 29, 415 (1958).

An experimental demonstration that {I) applies to a system where the thermodynamic factor varies significantly with concentration would therefore constitute (at least in principle) a direct check on the propriety of the formulation, since the interpretation would then be solely in terms of macroscopic measurable properties (cf. the case of diffusion alonegJO). No such test of (I) has yet been performed on a two-component system (the various tests of the limiting form of (1) are discussed below), the chief difficulty being that of finding a substance whose constitution is precisely known and which possesses a sufficiently high molecular weight for the sedimentation coefficient to be measurable with the desired accuracy, A further restriction on the choice of materials arises because of the need to have the thermodynamic factor change significantly over a relatively small concentration range. For the test of eq. 1 which forms the subject of this paper, the strictly two-component system thallous sulfate-water was studied. Although Tl2SO4has a relatively low molecular weight, the partial specific volume in aqueous solution is also low, so that maximum advantage is taken of the occurrence of the factor (1 - i i p ) in the formula. The thermodynamic factor11s12possesses the desired attributes, and the diffusion behavior has been established.12 Sedimentation coefficients have now been measured over the whole accessible concentration range; it has been found that even moderately accurate determinations depend critically upon the control of several sources of error, which are accordingly discussed. Experimental Materials, Solutions, Partial Specific Volume Determinations.-Solutions were prepared as in the previous investigations.”-12 Density measurements were made at 25.00” using a 25-ml. single-bulb pycnometer. Sedimentation Coefficient Determination.-The Spinco (9) H. S. Harned and B. E. Owen, ”The Physical Chemistry of Electrolytic Solutions, 3rd Ed., Reinhold Publ. Corp., New York, N. Y . , 1958. (10) R. A. Robinson and R. S. Stokes, “Electrolyte Solutions,” 2nd Ed., Aoademic Press, Ino., New York, N. Y . , 1959. (11) J. &I. Creeth, J. Phys. Chem., 64, 920 (1960). (12) J. M, Creeth and B. E. Peter, ibid., 64, 1502 (ISGO).

July, 1962

TRANSFER PROPERTIES OF THE SYSTEM THALLOUS SULFATE-WATER

Model E analytical ultracentrifuge was employed; it was fitted with the "RTIC" temperature resulating device, and all experiments were carried out a t 25.0 . 'rhallous sulfate solutions do not form boundaries which separate from the meniscus a t the maximum speed obtainable with the Spinco instrument. Reliable reuults could not be obtained with a boundary-forming cell, as diffusion was too rapid. Measurements therefore were made following: the Gutfreund-OgstonIa procedure, employing Rayleigh opti~s.1~J6This method has been applied16 to the determination of the sedimentation coefficient of a high molecular weight protein, but no application to low molecular weight syEtems has appeared; in principle, several advantages over schlieren optics may be anticipated. The essential result obtained by Gutfreund and Ogston (eq. 6a of ref. 13) may be written (after the second integration has been performed) In

-/

1

- 2 $:,X[c(rx) - c(r)!rdr/corm2i = - 2 s ~ Z t

where s is the sedimentation coefficient (assumed here to be independent of concentration; see below), w , the angular velocity, assumed constant over the whole time, t , in which sedlimentation occurs. The concentration (in g . dl. -1) co is that of the original solution (at t = O), c ( T ) , the value at a point distance r from the center of rotation, and rmand T X are similar radial distances to the meniscus and a point in the plateau region, respectively; rm < r < rx. While co is thus operationally defined, neither of the other concentrations can be directly observed, although their difference is proportional to the refractive index difference between the two points r and rxtle if certain com licating factors can be ignored. The most important o f these factors1' are (i) pressure effects on the refractive index, n, and (ii) nonlinear dependence of n upon c. The following treatment takes account of these factors. We assume that the refractive index of a solution at constant temperature is adequately represented by the equation

+ +

so that the expression for the fringe number becomes j(Tk) = (d/x)(R[C(rk)- C(rX)]-!- a[C(7"k)a/z C(Tx)'i2] b [ C ( T k ) * C(Tx)'] f

-

+ +

n = no Rc U C ~ ' ~ bc2 kpP (3) where P is the pressure and c is the concentration of the solute coniponent whose sedimentation coefficient is sought. The coefficients R , a , b, and the limiting value no are assumed identical with those measured a t 1 atm. (The term in (cab may be expected t o vanish for non-electrolytes.) Fringes, denoted j , are counted from zero at the plateau regjon toward the meniscus. Since the fringes represent unit increments in the refractive index di@rence between the two compartments as a function of r,l* we have j(Tk) = - ( d / k ) {nII(Tk) - nI(?-kk)[ n ~ d r x-) n d r d l l (4) where d it3 the length of the cell along the optic axis, k, the wave length of the light, and the subscripts I and TI refer to solvent and solution compartments, respectively. We note the relations between the solution density, the concentration, and the excess pressure at Tk, P(rk)

(5)

+

P = PO LC (6) It is assumed that higher order terms in the density expression are not required, and that the solution is incompressible. The values of n required in (4)are then given by

+

kpkCuz

-

[-:c(r)r d7 - l/zc(rx)(rxz- r m 2 ) ]1

(8)

Because the experiment will generally be conducted so that c ( r ) - C ( T X ) is small, the terms in ca/r and c2 may be expanded, and only the first term in each series retained. We then have, after some simplification (k/d)j(Tk)= [C(Tx) - C(Tk)][R-k 3(U/z)C(Tx)'/Z f

+

2bc(rx)]

(2)

1229

kpkcd

[-I

c(r)r dr

- I/~c(rx)(rx~-

The second bracketed term in (9) is identical with the differential refraction increment, n' (cf. eq. 3 )

The concentration function required in (2) is therefore given by C ( T X ) - c(Tk) = kj(rk)/n'd - kPkcW2C(rX)(rX2 - rk2)/2n' [ k ~ k , u ~ / ( n 'l) "~ jd(] r ) ~dr Tm

+ .. ,

+

(11)

Three important conclusions implicit in this result may be summarized: (i) The differential refraction increment a t the original concentration is a better approximation than the integral value, and its use is consistent with the other limitations on the validity of (11). (ii) The main effect of pressure, the second term on the right of (11), is due to the different densities of solution and solvent, since effects due to the differing values of the meniscus positions in the two compartments cancel. In some experiments in this series, this effect was quite large, j(rm) being reduced by 0.5 or more. However, insofar as C ( T X ) is independent of time, so also is this effect independent of time, and thus it may be ignored when interest lies solely in the determination of s values-that is to say, the apparent, uncorrected, j values may be used in the integration procedure. (iii) Because of the progressive loss of solute from the part of the cell centripetal to the plateau region, the density at T k , and hence the pressure correction at this point, varies with time. This produces a time-dependent error in the apparent value of j ( r ) . When s values are to be calculated, appreciable errors may result, if the effect, given by the third term on the right of (ll),is ignored. However, a correction of adequate precision may be applied quite easily. The basis of the method is that the measurements of j(r) are made a t the same values of r in each exposure: thus while j(r) is a function of time, T itself is not. The correction is formulated as follows. Expanding (2) for the case of a sufficiently small, differentiating with respect to time, and substituting from (11) for the concentration-difference function, we obtain

---

(13) H. Gutfreund and A. G. Ogston, Niochern. J . , 44, 163 (1949). (14) J. S. Johnson, G. Scatchard, and K. A. Kraus, J . Phus. Chem., 63, 787 (1959). (15) E. G . Richards and H. K. Schachman, ibid., 68, 1578 (1959). (16) W. F. H. M. Mommaerts and B. B. Aldrich, Bioehinz. Biophya. Acta, 28, 627 (1958). (17) Svensson (Optic5 Acta, 1, 25 (1954)), and Forsberg and Svensson (ibid., I., 90 (1954)) have examined anomalies inherent in the Rayleigh method, which might also lead to error in the interpretation of experimenhl records. No attempt to correct for these effects will be made here, as the values of the refractive index gradient in the cell were always small. (18) The two possible arrangements of the light-limiting diaphragm have been discussed b y Richards and Schachmanls and Johnson, st at." I n the experiments reported here, the offset arrangement was used.

where K = X / w 2 c ~ ~ m 2 n ' dThus . the correctJion term is separated from the main term and is expressed in terms of measurable quantities. The full derivation of (13) has been omitted, but it may be verified readily by writing down, from (11), the concentrations at the same point, Tk, a t two different times, and then subtracting, it being realized that the sedimentation coefficient depends essenTX

tially on the quantity

Tk rm

(dj/dt),,

,k.

Vol. 66

1230 Cell Filling and Velocity Experiments.4tandard pmcedures,14J6including the recording of a “blank” experiment, were followed; 0.43 ml. of solution and 0.46 ml. of solvent were used, to ensure that both menisci were visible. The cell was not dismantled during a series of experiments, the solution compartment only being washed, rinsed with distilled acetone, and dried between times. Speeds ranged from 29,500 r.p.m. for the more concentrated solutions, to 39,460 r.p.m. for the dilute range. Six photographs at 6-8 min. intervals were taken, using Kodak “Kodaline C.T.C.” plates, after an initial period of 5-10 min. at s eed; before and after this series, an exposure using the schieren optical system (with bar atngle 90’) was recorded. Measurement of Records and Evaluation of the Integrals, -Established methodsX4J6were foflowed, and the following description deals only with points of detail. CapiCah will be used to denote planes as recorded on the photographic plate, and lonrer case for the corresponding planes after conversion to true radial distances. The cell fringe-patterns obtained were about 2.85 cm. long, and the plane Rx was taken as being 1.400 cm. from the solution meniscus; for this purpose, the position of the meniscus wa9 assumed to be the point where the fringes ended ((Rm)II). After precise alignment on the stage of the toolmaker’s microscope, measurements were made of the lateral displacement y (normal to the radius vector) of an intensity minimum near the center of the pattern, at the R x plane. For this value of R, four measurements of y were obtained, reading to 0.0002 cm., while single measurements of the fringe nearest to the original sufficed for the other R values: these were taken at 0.1000 cm. intervals. In this way, values of y for a total of 15 R values were obtained. The blank experiment having been measured in the same way, values of [v(R ) - y( Rx)loorwere obtained by subtraction, some being positive and others negative due to the choice of a fringe nearest to the original. Division by the fringe separation resulted in conversion to fractions of a fringe, Since Aj/AR did not exceed 1.5 mm.-lin these experiments, the precise j(r)-r relationship can readily be constructed from these data. This procedure of recording at constant r values, rather than locating r values for predetermined j ’ s , was adopted because the blank correction can be applied very easily and accurately, and because the subsequent calculations are greatly simplified; moreover, the error in j arising from an error in the fringe separation is minimal and non-cumulative. The integrals required in (13) were approximated by Simpson’s Rule, in the form of sums of j(rk).rk products, where k: is an integer running between 0 and 14; this procedure was demonstrated to be very reliable and more accurate than one employing r2 as a variable. For the first ta-o exposures in some experiments, it was found more accurate to make measurements of y a t intervals of 0.05 em. in R . The integrals so obtained are subject to significant errors arising from meniscus and base line locations, which will now be discussed. Sources of Error and Corrections. (ij Meniscus Errors. -It is well known that considerable difficulty may be experienced in locating the true position of the meniscus in a centrifuge experiment”Js20and indeed there is some uncertainty as to the precise meaning of the term.21 Defining (&)I. as the position of the outer end of the air-fringes and (R,)II as the position of the inner end of the main fringe pattern, it is found that these planes may be located with a reproducibility approaahing 0.001 cm. The same reproducibility has been found for the centers of the ima es of the menisci in a schlieren exposure taken at 90” bar an$e, at the speeds used in this work; these images each constitute a “central shadow” as defined by Trautman.’g If the latter meniscus images may be taken as being blurred symmetrically on the r axis (i.e., that each infinitely thin meniscus records as a line where the intensity minimum is symmetrically situated) then it is clear that the planes R, in the Rayleigh image cannot correspond to the true rm. However, the difference ARRayleigh = (Rm)ll - (&)I compared with the corresponding quantity from a schlieren exposure mdl give a precise estimate of the error attaching to the location of the meniscus in the Rayleigh exposure. Defining y = (ARRayieiph - ARsohtleren)/2M, where M is the magnifica(19) R. Trautman, Bzochim. B i o p h y s . Acta, 28, 417 (1958). (20) S. R. Erlander and G. E. Babcock, ?bid.,60, 205 (1961). (21) Ping-Yao Cheng, J. P h y s . Chern., 61, 695 (1957).

-

tion factor, it is apparent that addition of the quantity A yj(ro)*ro will compensate, in the estimation of the integral, for the use of the plane ( Rrn)llas the lower limit. I n practice, was determined separately in each experiment: values ranged from 0.005-0.009 om. (iij Base-line Errors.-The procedure described eliminates errors arising from the time-independent pressure effect. It also follom that any consistent error in the baseline subtraction is eliminated in determining the timedependence of the integral, provided that the mme set of r values is used for all measurements. Thus base-line corrections of both types may be ignored, if desired. However, it has been found advantageous here to include both effects in a single correction, so that a true measure of the concentration is obtained. The effect of random errors in locating the base-line must now be considered. An error, Sj, made in locating the zeroth fringe will introduce an error 6j(rx2 - rmz)/2 in the integral; in order to reduce this to 1%of the mean value of the integral in an experiment with, e.g., TlzB04a t 2 g..dl.-I, 6 ’ must not exceed 0.01. This corresponds to 3 ,u in the dsplacement y, and it is at once clear that, as Van Holde22 found, this source of error is likely to be serious, for experience has shown that even with the greatest care in measurement, errors of at least 5 I.L are unavoidable. Fortunately, once again this error may be controlled fairly accurately, the basis of the procedure being the recognition that the lateral shift, E, with time of the zeroth fringe is given in terms of j by (cf. ref. 14, 15) € ( t ) = 2wastcon’djX

+ ..

(14)

I

and may thus be predicted if an approximate s value is first obtained. By adding to the integral at the nth exposure the quantity [€,(observed)

- En(predicted)](rxz- r m 2 ) / 2

where the predicted value is obtained from (14), the error may be almost entirely eliminated. Application of this correction was found to reduce considerably the scatter in the plots of the integral us. time (cf. Fik. 2B); it is an illustration of the versatility and convenience of the Rayleigh optical method that this correction can so easily be made. An analogous correction is equally important in methods based on the refractive index gradient curve, but in that case there is no shift in the base line which can be used to assess, and then eliminate, the error. The time-dependent error, arising from the changing pressure in the plateau region, wm eliminated by making a correction only to the first and last exposures of an experiment. Having obtained the apparent time-dependence of the integral J j ( r ) r dr, the integral JAj(rk)(rx2 - rk2)r dr mras obtained similarly: A j is the difference, a t Tk, between the j values found in the last and the first exposure. Division by the time interval, and conversion by the appropriate constants, gave the subtraction correction to the slope term.

Results (1) Partial Specific Volume Factor.-The

densities, at 2 5 O , of aqueous thallous sulfate solutions found in this work may be represented by the equation p = pa

+ 9.08 X IO-’ C; 0 < c < 5.0

where c is in g. dl.-l. These values are in good agreemeiit with the earlier, more limited data.23 The quantity (1 - 8,p) was obtained directly, by the method of Kraeme1-.~4 The results are shown in Fig. 1; the line is for interpolation purposes only. (2) Refraction Increment.--From the results reported previously, l 2 the differential refraction increment (in dl. g.-l) of TlaSOl in aqueous solution at 25.00’ may be obtained as n’ X lo4 = 9.823 - 0.347c1/2 f 0.0233~;0

< c < 6.0

(22) K. E. Van Holde, ibid., 83, 1674 (1959). (23) “International Critical Tables,” Val. 3, McGraw-Hill Book Go., New Yorlr, N. Y., 1928, p. 64. (24) E. 0. Kraemer, ref. 3, p. 57.

July, 1962

TRAKSFER PROPERTIES OF

THE 8YSTEhI THALLOUS SULFSTE-JVATER

The value of (bn/bP),was taken26 as 1.4 X kg. -’, (3) Sedimentation Coefficients.--Figure 2A illuatrates both the general smoothness of. the j ( r ) vs. r relation always found, and the application of the time-independent pressure correction to the first and1 last exposures of a typical experiment. ThLe elimination of the ((tail”in the first exposure is clear. Figure 2B shon s a plot of .fj(r)r dr (cf. eq. 13) us. time, and the scatter is a direct indication of the procision of the resulting s value. Also shown on this group are the values of the integral before application of the ‘(e-correction” (see Experimental section); the smoothing effect of this correction is apparent, while the value of the slope is also significantly affected in this case. ‘The experimental results of the whole series of sedimentation measurements are shown as crosses in Fig. 3. A significant positive dependence of s upon c is revealed. Discussion Before a useful comparison may be made between the results of this study and those expected on the basis of irreversible process theory, three questions concerning the validity of the results must be examined. (i) R.eference Frames.-This question becomes important a t moderately high concentrations, It is clear from the flow equation for the centrifuge which defines s (e.g., eq. 41, p. 756 of ref. 6) that the latter is a function of the reference frame. I t follows from the Gutfreund-Ogston theory and eq. 13 of this paper that the calculation procedure gives a “volume-fixed” sedimentation coefficient, as the meniscus is taken as the significant limit in the integration. Since the partial specific volume of T1,SCh is small, varies only slightly with concentration, and the concentration itself changes only to a minor extent in the experiments, the volume-jtixed frame becomes identical with the “cell-fixed” frame,26as mas the case with the diffusion coefficient values. Thus both the sedimentation and diffusion coefficients are cell-fixed values, and may be used in (1) without error, and th14 question of ‘(back-flow” of solvent2’ during the Sedimentation experiment does not arise. The “back-flow” is, of course, non-zero on any reference frame other than the solvent-fixed, but is identical in the sedimentation and diffusion processes provided the same reference frame is used for each. (ii) Effect of Pressure.-In general, both d and y in (1) are functions of pressure; however, it follows from elementary thermodynamic relations th,st the pressure dependence of the thermodynamic term is directly related to the concmtrationdependence of 8. Since the compressibility of electrolyte solutions is generally very 1 0 ~ 9and in this case does not vary significantly with c, it seems very unlikely that significant errors will ( 2 5 ) V. Ilaman and K.

S.Venkataraman, Proc. Roy

Soc. (London),

Al’ri, 137 (1939). (26) L. J. Gosting and R, P. Wendt, J . Phus. Chem., 63, 1287 (1959). (27) C/. H. K. Sohaohman, “Ultracentrifugation In Biochemistry,” Actidemio I’resa, Ino., New York, N. Y., 1959, p. 92. Earlier references are also cited in this summary.

1231

2 3 4 5 c (g. d1.-1). Fig. 1.-Results of pycnometric measurements on Tl2SO4. the quantity (1 -- & p ) obtained from Kraemer’b equation, as a function of concentration.

1

c

R

6 h

h

K 4 2 ==&-&-I

0

0

0.1 1 5 R - ( R , h (cm.). Fig. 28.-Typical results of j ( ~ )plotted , as a function of distance from the apparent meniscus position on the photographic plate. The points shown are for the first exposure ( 0 ) and last exposure (a) in an experiment at c = 4.101 g. dl.-1. After applying the correction for the tirne-zndependent pressure effect (see Experimental section) the j values are decreased and then fall on the curves shown. The individud corrected points have been omitted, t o aid clarity but their de arture from the smooth curves may be judged from the beimior of the uncorrected points. 0.5

arise from this cause, particularly as the pressure at the rx plane was fairly low (-40 atm.). Pressure effects on the solvent, such as t,hose producing changes in viscosity, will in principle also affect the mobility (the phenomenological coefficient in the flow equation, cf. ref. 6, p. 749). Since it was found (after allowance had been made for the primary effect of pressure) that a plateau region existed in these experiments, it may be concluded28 that pressure effects of this kind were negligible. It is therefore not inconsistent to consider only the effect of pressure on the refractive index of water. (iii) Concentration-Dependence of Sedimentation Coefficient.-It is assumed in the derivation of (2) that s does not vary with c . * ~ + The result, however, is still valid for arbitrary dependence of s on c provided that, in the plateau region, the concentration changes so slowly with time that the s (28) H. Fujita, J. Am. Chem. Soc., 78, 3598 (1956). (288,) It i s not possible t o write a simple form of the GutfreundOgston equation applicable to the case where a varies with c (c/. ref. 7). The restriotion is not important in practice.

J. AI. CREETH

1232

I

/ I

I

1

I

I

I

1

2 3 4 5 6 Exposure no. Fig. 2B.--A typical result for the time-variation of the first integral in eq. 13: the experiment was a t c = 3.484 g. d1.-1. Filled circles nre values off; j(r)r dr (obtained ky the summation proccdure indicated) before applying the e-correction"; the crosses are the values after this correction has been applied. The solid line represents the best straight line through the crosses. Exposure interval was 8 min. 1.3

0.9

1 I

I

I

I

I

I

2 3 4 5 c (g. d1.-1). Fig. 3.-Observrd and calcrilatcd values of the sedimentation coefficient of TlzSOl.rtt 25". Experimental points are shown as X, while the solid line has been calculated from the known diffusion and thermodynamic characteristics, using eq. 15. 0

1

a t that point can be considcrcd constant. This condition is certainly met in these experiments, so that no error arises from this cause. It follom that the s obtained in an experiment refers closely to the original concentrat,ion of the solution. Rewriting (1) explicitly in tcrms of the scdimentation cocfficicnt of a 1:2 electrolyte we have where MI is the formula weight and y* is the stoichiometric mean ionic activity coefficient. Values of the mobility, Dl(1 d In y,/d In c ) , for TlzS04, have becn calculated12 from differential values of D and the appropriate thermodynamic factors and thus refer to specific values of c. By combination with the part:al specific volume factors, the prcdiction of s as a function of c is made possible. This relation is shown as the solid line in Fig. 3. It is clear from this figure that the general trend of the observed concentration-dependence of the sedimentation coefficients is in good agreement with the predicted behavior. The scatter of the experimental data is quite pronounced, but is little more than must be expected from the known errors in the determination of the integrals. Applying the reasoning developed in the Experimental section

+

VOl. GG

one might anticipate minimum errors as follows: 0.6 < c < 1.0, *5%; 1.0 < c < 2.0, f 4%; 2.0 < c < 5.0, f 2%. Most of thc experimental points lie within these limits, and whilc the mean curve drawn through the experimental points would lie some 1-2% below thc predicted curve, this cannot bc corisidcrcd to be significant. Thus, within the limits of crror, the validity of the extended Svedberg equation must be considered to be established. It may further be concluded that a single property of a solute-solvent system exists which defines its response to thc application of a force, whether that force arises from a gradient of gravitational or chemical potential. The concept of a mobility (or its reciprocal, a frictional cocfficicnt) is thcrcforc mcaningful a t any conccntration, and no reference need be made to the particular transport situation, provided that the force can bc dcfiricd in macroscopic terms. It might be emphasized that these conclusions are valid whatever thc microscopic situation in solution may be: thus T1,S04 is certainly incomplctcly dissociated, and probably hydrated. Because thc stoichiometric values of 9 and y* are used, the stoichiometric molecular weight will be obtained in an application of (1) to the s and D valucs, provided thesc are on the correct frame of reference. The large positive slope of the s-c curve is duc to an unusual variation of thc mobility (consequent upon incomplete dissociation) and is not a general property of electrolyte solutions. In general, the mobility can be expected to remain roughly constant over the range 0-0.1 molar, so that little concentration-dependence of s should occur, at least in systems whcrc fl is small. In an investigation of the systcm Os04-Hz0, Van Holde22 found a positive slope for thc depcndcnce of s on c; this cannot be due to a similar cause, as the dissociation constant is very small, implying that little variation of the proportions of the constituents can occur. Tests of thc Svedberg equation in its limiting form for infinite dilution have been made by Baker, Lyons, and Singer29 using silicotungstic and phosphotungstic acids in buffered solution; notably good agreement betwcen known and calculated molecular weights was observed. It is now recognizedsJeaOthat in systems of more than two components, the appropriate form of the molecular weight cquation contains cross-diff usion and crossactivity terms which do not necessarily vanish a t infinite dilution of the component studied, and the reasons why this was not a source of error here have been discussed by Sch0nert.3~ The results of Brown, Kritchcvsky, and D a v i e ~on~ digitonin ~ in the mixed solvent system ethanol-I&O may well have been complicated by these cffccts, however, as a 6% discrepancy was reported h c t m r n predicted and obscrved molecular weight. The present results appear to be the first on a strictly twocomponent system, but bccausc of the relatively (29) A I . C. Baker, P.A. Lyons, and S. J. Singcr, J . Am. Chem. Soc , 77, 2011 (1955): J . Phy8. Chem.. 69, 1074 (1955). (30) R. L. Baldain. J . d m . Chem S a c . 80. 496 (1958). (31) €1. Sohonert. J . Phvs. Chem.. 84, 733 (1960). (32) R. .I.Brown. D. Krltchevskv and M. C. Daviea, J . Am. Chem. Sac., 1 6 . 3312 llR54).

July, 1962

OXIDATIONOF WOCTYLMERCAPTAN BY FERRICYANDE

low values of s found, it would still be very desirable to perform a similar test with a solute of larger molecular weight, so that the full potential accuracy of modern ultracentrifuges could be realized. Two points which may confer advantage on the Rayleigh method of determining s by the Gutfreund-Ogston procedure must be mentioned in addition to those discussed earlier. These are: (i) the cylindrica,l lens magnification factor is not directly required, and errors in its equivalent, the

1233

fringe separation, are relatively unimportant ; and (ii) as measurements are based on determining the positions of intensity minima, the results are independent of exposure time. Acknowledgments.-The author is greatly indebted to Professor J. W. Williams for his interest in, and critical comments on, this work, and to Professor L. J. Gosting for many discussions. The work was supported by a grant from the National Institutes of Health, Eo. A3030 (C6).

OXIDATIOX OF n-OCTUL MERCAPTAN BY FERRTCYAKIDE IN ACETONEWATER SOLUTION1 BY I. M. KOLTHOFF, E. J. MEEHAN, M. 8. TSAO, AND &. w.CHOI School of Chemistry, University of Minnesota, Minneapolis, Minn. Received October 16, 1961

The Oxidation of n-octyl mercaptan (RSH) by potassium ferricyanide (Feic) in acetone-water (60-70% acetone) has been studied. T’heover-all reaction is first-order to Feic, RSII, and OH-. In alkaline medium the kinetics correspond to a ratedetermining bimolecular reaction between RS- and Feic. There is a pronounced specific ion effect; potassium ion accelerates much more than Naf, whereas the effect of tetramethylammonium ion is considerably less than that of sodium. The salt effects are accounted for on the basis of incomplete dissociation. The addition of cyanide reduces the rate markedly M . It is concluded that in the absence of but the rate becomes independent of cyanide concentration above ca. 4 X cyanide the rate-determining step is a reversible substitution of CN- in Feic by RS-,followed by rapid decomposition of the substituted product to Feoc and RS.. The substitution reaction is practically suppressed in the presence of sufficient CY-. The rate-determining step then is postulated to be Feic RS- -+ Feoc RS., followed by rapid oxidation by Feic of RS. to RSC.

+

Introduction

At3 part of a study of the reactions of mercaptans with oxidizing agents, the oxidation of 2-mercaptoethanol by ferricyanide in acidic aqueous medium has been investigated in this Laboratory.2 I n the ferricyanide oxidation, both of this compound and of 3-mercaptopropionic acid,3 complex kinetics were observed which could not be interpreted completely. The present paper describes the somewhat simpler kinetics observed in the oxidation of n-oclyl mercaptan (RSH) by potassium ferricyanide (Feic). In order to carry out the reactions in homogeneous medium, acetone-water mixtures were used as solvent. Most of the work was carried out in 60% (by volume) acetone, which has a dielectric constant of 45. Because of the limited solubility of many inorganic compounds in this mcdium, the maximum ionic strengkh used was about 0.06, In. acid medium the reaction was found to be very complex and not to correspond to any single or a combination of two single simple mechanisms. Most of the work reported in this paper has been carried out in alkaline medium. The over-all kinetics of oxidation of RSH in alkaline rnedium appear to correspond to a bimolecular reaction between RS- and Feic. There is a large salt effect which must be attributed to a specific cation effect. This effect may be related to the incomplete dissociation of potassium ferricyanide in the reaction medium. (Many of the experiments de(1) This investigation was carried out under a grant from the National Science Foundation. (2) E. J. Meehan, I. M. Kolthoff, and H. Kakiuchi, J . Phgs. Chem., 66, 1238 (1962). (3) J. J. Bohning and K. Weiss, J . Am. Chem Soc., 8 2 , 4721 (1960).

+

scribed in this paper were carried out before the magnitude of the effect was realized. Potassium ferricyanide was used in all the experiments, although it would have been preferable to use the sodium salt in the presence of sodium buffers.) There is no evidence that oxygen is directly involved in the reaction, but all the work has been carried out in the absence of oxygen to prevent oxygen-oxidation of RSH. Experimental Chemicals.-n-Octyl mercaptan was purified by vacuum distillation of commercial products a t 3-4 mm. Various samples after distillation had mercaptan contents of 98.5 to 99.5% of the theoretical value, as measured by amperometric titration with silver nitrate.4 The disulfide was prepared by oxidation with iodine. C.P. acetone was treated with sodium carbonate and calcium sulfate and distilled; the middle fraction was collected and stored over calcium sulfate. Feic and potassium ferrocyanide (Feoc) were recrystallized from analytical reagents and stored in the dark. Other chemicals were reagent grade and were used without purification. Conductivity water was used to prepare aqueous solutions and Linde “high purity” nitrogen to deaerate solutions. To prevent changes of composition during deaeration, the gas was first passed through two solvent mixtures of appropriate composition a t 25”. Experimental Procedure.-Unless otherwise specified, the reactions were run at 25’ and in 60 vol. % ’ acetone. I n most experiments with an excess of RSH the following simple procedure was used. Twenty ml. of deaerated aqueous buffer solution was added to 30 ml. of deaerated acetone in a 50-ml. volumetric flask. After mixing, sufficient deaerated acetone-water mixture mas added to fill up to the mark, to compensate for the volume contraction. RSH solution and Feic solution were prepared separately in 10-ml. volumetric flasks in the deaerated acetone-water buffer solution. For each experiment the solutions were (4) I. M. Kolthoff and W. E. Harris, Ind. Eng. Chem., Anal. Ed., 18, 161 (1916).