TEMPERATURE DEPENDENCE OF SORET COEFFICIENT OF AQUEOUS KC1
Nov., 1957
1557
It seems desirable to leave the value of $/jliq in the equation for ei as an adjustable parameter, analogous to the constant ai in the Langmuir forcixa e i 2 * * * n= = eix (17) malism. However, the choice of ji/jliq is restricted (1 - ~ ) ( 1- x Cix) by the generally accepted hypothesis that it Thus should be of the order of magnitude of one in most -Ea = ( 1 - 3) OiNi [ ~ i Rd In ji/a(l/T)] + cases. The valueof b lnji/a(l/T) can be estimated, i as in the Langmuir case, by assuming a likely configx eiNiBliq (18) i uration for the state of theadsorbed particle and takThe analogous equation for the energy of a B.E.T. ing the temperature derivative of the partition funcfilm on a uniform surface has been given by Hill." tion for an atom in such a state. Ea is obtained Remembering that Bi N; = ZJ,, equation 18 can from equation 2, and &'Eq N AHfi, Rg. Thus, the i parameters necessary to compute the terms on the be rearranged to give right-hand side of equation 19 can be obtained from Ea - X V S l i q + vaR 3 In j i = the experimental data for various values of 2, and sieiNi (19) 1-x W/T) i the Ni can be calculated by following the general procedure outlined previously. (17) T. L. Hill, J . Chem. Phys, 1'7, 772 (1949). Oil
=
cix
1 -x+cix
=
ei(l
- 3)
(16)
+
+
~
THE TEMPERATURE DEPENDENCE OF THE SORET COEFFICIENT OF AQUEOUS POTASSIUM CHLORIDE BY L. G. LONGSWORTH Contribution from the Laboratories of the Rockefeller Institute for Medical Research, New York, N. Y . Received June 3,19.57
Using a twin-channel cell filled with solution and solvent, respectively, through which a downward flow of heat is maintained, the resulting thermal diffusion of the solute has been determined with the aid of Rayleigh interferometry. Aqueous solutions of KC1 have been studied a t concentrations from 1 to 4 m over the temperature interval from 10 to 50" in 10" steps. The increase in the migration of this salt to the cold plate with rising temperature is quite marked.
Thermal diffusion in liquids is the systematic relative motion of the components of a solution that is coupled with the convection-free flow of heat. For example, if an aqueous solution of potassium chloride is brought into contact with a warm metal plate above and a cool one below the salt migrates to the cold plate until a balance is attained between the separating effect of thermal diffusion and the mixing effect of ordinary diffusion. The movement of salt may be described by the relation mass flow = -D'm(dT/dh)
- D(dm/dh)
(1)
in which D and D' are the ordinary and thermal diffusion coefficients, respectively, m the concentration in moles per 1000 grams of solvent, dT/dh the temperature gradient and dm/dh the concentration gradient resulting from thermal diffusion. The Soret coefficient u is defined as the fractional change in concentration for unit difference of temperature, (l/m)dm/dT, when the system is in a steady state. The mass flow is then zero and equation 1 becomes u =
(l/m)dm/dT = -D'/D
(2)
a relation that defines D'. Previous work's2 has suggested that the Soret coefficients of aqueous salt solutions increase in magnitude with rising temperature but no systematic study of the effect of both this variable and concentration has been reported. It is the purpose of this paper to describe a new Soret cell, in which the (1) C. C. Tanner, Trans. Faraday Soc., 28, 75 (1927). (2) K. F. Alexander, 2. phyrik. Chem., 208, 213 (1954).
concentration changes are observed in situ with the aid of Rayleigh interferometry, and to report measurements on aqueous KC1 at concentrations from 1 to 4 m in 10' intervals over the temperature range from 10 to 50'.
Experimental In the partially exploded view of the Soret cell shown in Fig. 1 the glass frame is clamped between silver plates provided with connecting annular channels through which water is circulated in maintaining these plates a t the desired temeratures. Not shown in Fig. 1 are the two lightly greased oroseal gaskets of 0.2 mm. thickness that are interposed between the glass frame and the silver plates or the two 1 mm. gaskets between the silver and Bakelite plates that complete the annular channels. The assembled cell is provided with a spirit level8 having a sensitivity of 5 minutes of arc and is dismantled for cleaning between experiments. A novel feature of the cell of Fig. 1is the central glass partition that permits both solution and solvent to be exposed to a given temperature gradient simultaneously. The crosssection of each of the two channels thus formed is 17.5 X 50 mm. The height of the channels in Fig. 1 is 10 mm. but a second frame of 15 mm. height is available and has been used to test the dependence of the relaxation time e on the square of this dimension. The concentration changes accompanying the heat flow have been followed with the aid of the same Rayleigh interference optical system as that used in this Laboratory for the measurement of isothermal diffusion.' As shown in Fi monochromatic light from the illuminated vertical slit made conver ent by the lens L and is split, after passing through the foret cell, into two beams by the vertical slits in the mask M that straddle the cell partition. The spherical lens 0 is focussed on the cell whereas the cylinder lens C,
%
k2
( 3 ) 9. Prager, J . Chem. Phys., 83, 1742 (1955). (4) L. G . Longsworth, J . A m . Chsm. Soc., 74, 4155 (1952).
,
1558
L. G. LONGSWORTH Hot water
*
I
c
Bakelite
Ag filli
ne15
I / )
31lvep
ut i
Cold water Fig. 1.-The Soret cell. M
Fig. 2.-The Isothermal
150
0
C
P A
optical system. 1800
17000 see.
Isothermal
horizontal coordinates of the source slit image on the photographic plate at P. The fringes above and below those conjugate to the cell are due to slits in the mask M outside the cell and serve in aligning the plate in the comparator. With the cell isothermal the Rayleigh fringes in the image plane conjugate to the channels are nearly vertical, as shown in the central pattern of the f i s t exposure of Fig. 3. I n this example the liquids in the channels were HzO and 3 m KCl. Even in the isothermal state the path difference between solution and solvent, although independent of the height, is large and the fringes would be poorly defined if compensation were not made as follows. A glass plate of 3 mm. thickness is placed in the path of the light through the solution whereas two halves of a 4 diopter ophthalmic prism that has been cut normal to its base is placed in the path of the light through the solvent. These halves are in contact so that the outside faces are parallel and by sliding the two halves over each other a plate is obtained whose thickness can be adjusted to any value from 3 to 6 mm. This 3 mm. adjustment corresponds to 2900 waves and thus affords adequate compensation for a 5 cm. depth of any aqueous solution whose refractive index does not exceed that of water by more than 0.032, e.g., 4 m KC1. I n each experiment the thickness is adjusted to give sharply defined fringes when the filled cell is isothermal and then left undisturbed. Since small path differences do not lead to perceptible deterioration of the fringe definition the adjustment is not critical. Although the compensator introduces some distortion the departure of the fringes from the vertical in the fist exposure of Fig. 3 is due mainly to a prismatic tilt resulting from the 16 minute angle between the windows of the cell frame. This introduces a “base line” correction that is pro ortional to the concentration but nearly independent of t i e temperature. Subsequent exposures of Fig. 3 were recorded a t the times indicated after the flow of heat began. This is done with the aid of three thermostats at T h , Toand Tm = ( T h f T o ) / 2, four two-way T-valves and two gear pumps, each of which circulates 2 liters per minute through a silver plate a t 170 r.p.m. Tygon tubing 8/8 in. i.d. is used and it is essential that the pump for each plate be in the return line. At zero time the circulation of water a t Tmthrough both silver plates is replaced by water at Th through the top plate and at To through the bottom one, operations requiring about five seconds. With this arrangement, however, a valve is in the outgoing line to each plate and contributes, when Th - To = lo”, to the “line loss” of 0.24 to 0.30” to be described below. I n future work the valves will be eliminated by transferring, a t zero time, the pair of Tygon tubes serving each plate from the thermostat at T, to those a t Th and To, respectively. Not all of the twelve exposures that are made at increasing intervals during the thermal diffusion period are shown in Fig. 3, but the final one, made after restoration of the isothermal condition, demonstrates that a concentration gradient is, in fact, developed by the heat flow. I,n the example of Fig. 3 the temperature interval was 4050 I n this interval the temperature coefficients of refractive index of HzOand 3 m KCl are approximately equal and the fringes remain nearly vertical on establishing the heat flow. The concentration gradient resulting from thermal diffusion then becomes apparent as a tilt in the fringes. With aqueous KCl at lower temperatures the fringes become inclined on initiating the heat flow and this increases as the Soret distribution, corresponding to zero mass flow, is established. If the temperature distribution in each channel remains invariant in time the number, i h , of diagonal fringes intersecting a vertical between two points on a pattern is a linear function of the concentration difference, Smh, between the conjugate levels in the solution, L e . 6mh = k(jh - j h O ) (3) Here k = A’/l(An/Am) where the wave length, A, of the light is 5461 A., the channel depth, I , is 5.00 cm. and An/Am is the variation of the refractive index with the concentration. The An/Am factor, which depends on both temperature and concentration, is obtained as a by-product of measurements of the isothermal diffusion coefficient. The values given below in Table I1 are taken as constant over the temperature interval of the thermal diffusion experiment. Although equation 3 is valid for any pair of levels the subscript h is used to indicate that these are a t h and a - h where h = 0
.
Fig. 3.-Rayleigh fringes recorded during the thermal diffusion of 3 m KCl, 40-50’. whose axis is vertical, is. focussed on the image plane of L. Together 0 and C constitute an astigmatic camera that reproduces the vertical coordinates of the Soret cell and the
Vol. 61
Nov., 1957
TEMPERATURE DEPENDENCE OF SORET COEFFICIENT OF AQUEOUS KCl
1559
at the cold plate and h = a a t the hot one. This symmetrjcal pairing of the levels is considered in the discussion. j m is the value that j h would have a t zero time if it were possible to establish the temperature gradient instantaneousb. Correction for the thermal diffusion that occurs during the time required for the heat flow to become steady h?s proved O to be difficult and made it essential to evaluate J ~ independently as follows. With the cell filled with HzO and 3 m KC1, say, water Fig. 4.7Scanning photograph of the masked Rayleigh from a bath whose temperature is raised slowly is circulated through both silver plates. Since the cell is essentially iso- fringes with the cell isothermal a t any instant but with the thermal at any instant the refractive index difference be- temperature increasing slowly. tween solution and solvent is independent of the height throughout this process but changes with time. Thus the fringe pattern, although apparently the same when viewed at intervals, actually moves across the qiffraction envelope at a rate proportional to the difference in the temperature coefficients of the index, i . e . , (dn/dT)a KCI - ( ~ z / M ' ) H ~ o . This movement is recorded by masking the image of t h e fringes at the photographic plate with a stationaFy vertic?l slit and moving the plate horizontally past this slit a t a uniform rate. The result for the 20-30" interval is shown in Fig. 4 where the slope and curvature of the fringes result from the prismatic and compensator distortion mentioned above. Although this curvature is magnified by the scanning procedure it is not a source of error, the number of fringes between any two temperatures being independent of the height. I n a cell of 5 cm. depth one fringe corresponds to 1 X 10-b in refractive index and those of Fig. 4 can be located to within of their separation or better. The method outlined here will be recognized as a differential measurement of the effect of temperature on the refractive index of liquids with an accuracy of a few units in the seventh decimal. The temperature distribution in the cell with heat flowing also has been determined optically. By rotating the source slit and cylinder lens to the horizontal position, and masking the cell with a movable horizontal slit of 1.5 mm. width, the refractive index gradient over the entire cross-section of a channel may be measured as a functjon of the height. Some results for the 20-30" and 40-50" intervals are shown in Fig. 5. I n each interval the essentially straight line represents the value of the gradient computed with the aid of the NBS tabless for HzO and the assumption that dT[dh is constant and e ual to (!& - Tc)/a. The unfilled circles represent the %served value of the gradient with silver plates whereas the filled ones are for plates of Carpenter stainless steel. The squares represent the gradient in an initially 2 m KCl solution after the steady-state concentration distribution had been established whereas the triangles were obtained with water in the channel but with a 0.2 mm. thickness of Koroseal at each Ag-HZ0 interface. 0 - 1 2 3 4 5 6 7 8 9 10 Integration of the experimental curves indicates that the temperature drop in the water is 2.4 to 3% less than Th - T, Height in mm. above cold plate. with silver plates and 7% less for stainless steel. This "line loss" has been taken into account in the evaluation of the Fig. 5.-Variation of the refractive index gradient with Soret coefficients. height in a single channel of the Soret cell. Interpretation of the Patterns.-In the interpretation of the fringe patterns Bierlein's relations has been used. It is plotted in Fig. 6 for several reduced times where the sigmoid the points from patterns obtained during the first 10 to 15 shape of the early concentration profiles will be noted. This minutes, L e . , t / e 5 0.1, cannot be aligned with later ones relation is symmetrical about the center of the column at h and have been ignored in the evaluation of the parameters. However, once 0 has been evaluated the features of the = 4 2 and gives, for the concentration difference 6mh experiment are most clearly illustrated with a plot of jn between the levels h and ( a - h ) versus exp( - t / 0 ) since equal weight is thereby accorded the 6mh = A(1 - 2h/a) j h values. Such plots for a typical case are shown in Fig. 7 where the uppermost line represents the entire height of the A(8/re) cos ( ~ h / aexp( ) --t/B) = k ( j b - j h o ) (4) pattern, which is 94% of the plate separation, whereas the Here A is the steady-state concentration difference between lowest one corresponds to the central 40% of the liquid the cold plate a t h = 0 and the hot one a t h = a while the columns. relaxation time is B = a 2 / r a D . n Table I the slopes s of the lines of Fig. 7 are tabulated With the aid of a two-coordinate comparator the number in Ithe second column and the values of A / k computed therej h of fringes between the levels h and ( a - h ) is determined with the aid of equation 4 in the next column. These to the nearest 0.01 fringe for each pattern and plots of log from values of A/k, which would be constant if equation 4 were ( j h - - j h ) versus t prepared, the number of fringes at instrictly applicable, actually decrease 6% as h / a increases. finite time, j h m , being adjusted to give a straight line. If This be compared, however, with. the 25q/o variation in thermal diffusion has proceeded unti1.95010, or more, of the A/k, may column 4 of Table I , that occurs if the sigmoid characconcentration change has occurred, $.e., t/e 2 3, this pro- ter of the concentration profiles is neglected and A / k is taken vides a sensitive evaluation of j m and the slope of the res/( 1 - 2h/a). The de Groot approximation7 replaces sulting line affords a value for e and hence D . I n general as ( 8 / ~ * cos( ) & / a ) by ( 1 - 2h/a) as the coefficient of the exponential term of equation 4 and has beon used in some re( 5 ) L. W. Tilton and J. K. Taylor, J . Research Natl. Bur. Standards, 20, 419 (1938).
(6) J. A. Bierlein, J . Chem. P h m , 2 3 , 10 (1955).
(7)-S.
R. de Groot, Phgsioa, 9,
699 (1942).
1560
L.
G.LONGSWORTH
Vol. 61
cent work.*lg The two approximations become identical at h/a = 0.12. I n order to determine which value of A / k in column 3 of Table I should be used to evaluate u, these have been comjho)/(l - 2h/a) pared with the values of A / k = ( j h m given in column 7. Here j h m is the value extrapolated as in Fig. 7 and j b o is determined independently as in Fig. 4. It is only a t h/a 0.2 that the two values of A / k agree and this is used in the computation of u with the aid of the first equality of e uation 2 in incremental form. The failure of A / k in column 7 to be independent of h/a the values probably arises from the non-linear variation of temperature in the columns and will be considered in the discussion.
-
01
Results
m-mo A ' of the Bierlein relation.
Fig. 6.-Plots 4a
I
I
I
3MKC1 2Oo-3O0C.
The results are assembled in Table 11. The four entries for each temperature and concentration in this table are (a) the refractive index increment, An/Am, where Am = 0.2, (b) the independently measured isothermal diffusion coefficient, D,(c) the difference, in per cent., between this value of D and that, De,computed from the relaxation time and (d) the Soret coefficient. The diffusion coefficients of Table I1 were obtained from measurements, with the aid of Rayleigh interferometry, a t 1, 13 and 37' to supplement existing data at 25O.lo In making the interpolations, or extrapolation to 45O, advantage was taken of the fact that the small temperature dependence of the Stokes radius, r = kT/6aqD, is essentially linear,'lq being the viscosity of water a t T . The Soret coefficients of Table I1 are plotted as functions of the temperature and concentration on the left and right, respectively, of Fig. 8.
Deg~eesCentigmde
.
Molality.
Fig. 8.-The Soret coefficients, s, as functions of (a) the temperature and (b) the concentration.
I
I
0.0
0.2
I
Fig. 7.-Plots of j h
I
I
0.6 0.8 1.o - t/e e . versus exp ( - t / t I ) for different fractions of the cell height.
0.4
TABLE I RAYLEIGH FRINGE PATTERNS 3 m KCl, Th = 30.0°, To = 20.0"
INTERPRETATION O F THE
2
3
h/a
8
& :lein
0.0304 .1158 .2118 .3079
16.90 15.75 12.84 8.93
1
20.94 20.80 20.05 19.60 6.7%
4
6
8
7
3hQ
t\/h direct
19.48 19.87 20.66 20.84 6.8%
Groot
&7
Fig. 4
17.99 20.50 22.09 23.23 26.1%
45.52 37.48 28.54 19.28
27.22 22.21 16.63 11.27
I n Table I11 values of u for 3 m KC1 at a mean temperature of 25' are reported in which specified experimental conditions have been altered systematically. Within the average deviation of 0.7% the Soret coefficient is independent of the alterations listed in the table. It should be noted, however, that with a slit separation of 6 mm. the light forming the fringes passes within 1 to 2 mm. of the glass partition and the fringe envelopes are distorted by a wall effect due,. presumably, t o the unequal thermal conductivities of glass and water. The average deviation of 0.7y0 in this series of experiments corresponds to an uncertainty of 0.1 fringe in j . At T , = 15' and 2 m, where j h m jho 'v 0.4 the possible error in u is thus quite large. (8) C. C. Tanner, T ~ a n sFaraday . Soc., 49, 011 (1953). (9) J. Cham and J. Lenoble, J . chim. phus., 63, 309 (1956). (IO) L. J. Gosting, J . A m . Clem. rSoc., l a , 4418 (1950). (11) L. G. Longsworth, THISJOURNAL, 68, 770 (1954).
Nov., 1957
1561
TEMPERATURE DEPENDENCE OF SORETCOEFFICIENT OF AQUEOUS KC1 TABLE I1 SUMMARY OF RESULTS ON
T,,."
(a) (An/Am)lOa ( b ) D(direct)lO5 De)/D (c) l O O ( 0 (d) --c X 10'
-
m - 2
m = 3
m = 4
25'
15'
OC.
m = 1
AQUEOUS KC1 8.78 1 .goo
8.93 1.483
... ...
...
0.35 7.83 1.985 5.7% 0.76 7.03 2.083 5.3% 1.05 6.35 2.165 1.5% 1.33
7.93 1.572 0.08 7.11 1.663 6.5% 0.45 6.40 1.743 4.2% 0.86
TABLE I11 SORET COEFFICIENT OF 3 m KCl AT 25" Effect of alteration of following standard conditions: Tr = 30.0", To = 20.0'. a = 10 mm., slit separation = 12
mm., Ag plates Alteration - u x 10' None 1.051 None 1.064 Stainless steel plates 1.062 a = 15mm. 1,040 a = 15mm. 1.028 Th = 27.5", = 22.5" 1 * 048 Slit separation = 18.5 mm. 1.055 Slit separation = 6 mm. 1.045 Mean 1.049 Av. dev., yo 0 . 7
Molalities have been used for convenience since on this scale the concentration of a given solution is independent of the temperature. If molarities were substituted in the defining equation 2 the Soret coefficients would have values different from those reported here. Insofar, however, as the proportionality between refractive index and concentration can be taken as constant over the increment developed in the Soret cell or used in the isothermal diffusion experiments the value of D,and De, for a given solution is independent of the concentration scale used to express its composition. The proportionality factor does not appear in Fick's second law, the integrated form of which is used in the evaluation of D , and the refractive index changes refer to heights in a channel of uniform cross section thus utilizing, in effect, a volume scale. On the other hand, the frame of reference to which the mass flow of equation 1 refers, together with the most appropriate concentration scale, would require careful consideration if an attempt were made, for example, to relate Q to an Onsager COUpling coefficient. Discussion In measurements of the simple Soret effect it is generally assumed that the temperature gradient in the liquid is uniform. The plots of Fig. 5 indicate, however, that this assumption is not justified in the
350
8.68 2.340 14% 1.09 7.75 2.443 6.5% 1.40 6.95 2,547 2.8% 1.58 6.29 2,630 1 .O% 1.73
450
8.61 2.825 16% 1.78 7.68 2.929 3.4% 1.92 6.89 3.036 3.8% 2.03 6.23 3.116 1.5% 2.10
work reported here. The curvature of the experimental d o t s of this figure cannot be ascribed to the known temperaturedependence of the thermal conductivity of water. This dependence would change the slope of the computed line slightly but would not make it markedly curved. The observed gradient becomes too steep as either the hot or the cold plate is approached. In work now in progress much of the curvature of the refractive index gradient plots of Fig. 5 has been eliminated by replacing the 0.2 mm. Koroseal gaskets with 0.04 mm. polyethylene. It may be noted, however, that Bates12 observed a somewhat similar phenomenon while using a thermal guard ring to eliminate wall effects. In his study of the thermal conductivity, K , of water he found that the temperature distribution, as measured with thermocouples at different levels in a 50 mm. column, corresponded to an increase in K of about 0.3% per degree but could not be extrapolated smoothly through the 5 mm. separation of the couple nearest a plate to the plate temperature. With the plates at 20 and 60°, respectively, the excess gradient in the neighborhood of each plate was 1 to 2'. Bates termed the phenomenon an interface effect, The phenomena illustrated in Fig. 5 should probably be described, however, as a wall effect. The feature of Fig. 5 of immediate interest, however, is the improved linearity when a concentration gradient is superimposed on the temperature gradient. This would account for the variation in A/k, column 7 of Table I. The Rayleigh fringes represent a comparison of optical path length a t equal heights in solution and solvent and the excess temperature gradient near a plate in the water channel has been interpreted as a deficit in concentration gradient in the solution channel. In the evaluation of v, however, only the central 60% of the pattern, where the temperature gradient is most nearly uniform, has been used. As consequences of the temperature dependence of u, Fig. 8, the early concentration profiles are skew and the concentration gradient in the steady state increases with height. The skewness is (12)
0.K. Bates, Ind. En#. Chem., 36, 431
(1933).
1582
L. G. LONGSWORTH
essentially symmetrical, however, and does not become evident if, as in the present research, the fringes are counted between levels paired symmetrically about the center of the column.'8 Although the temperature dependence of r is qualitatively apparent in plots of individual profiles, evaluation of the dependence from the skewness will be deferred until the wall effect has been minimized. Similarly, no evaluation of r at Th, or To,has been attempted utilizing the equivalent of Archibald's suggestion for the ultracentrifuge. l 4 If T and D' of equation 1 are replaced by the gravitational potential and sedimentation constant, respectively, the centrifuge equation for a cell of uniform cross-section in a homogeneous field is obtained. Since there is no mass flow across the phase boundaries in either the Soret or centrifuge cell the solution of equation 1 that is valid for all values of h a t infinite time, i.e., equation 2, is also valid for all times at the interfaces. Moreover, in the Soret cell the change in m is usually small in comparison with the steady state gradient. Consequently, on initiation of the heat flow the gradient in the immediate vicinity of a plate very quickly acquires its final steady value. This is qualitatively apparent in the patterns of Fig. 3. With the establishment of the heat flow the solute starts to move as a column to the cold plate. This produces no concentration change in the body of the solution but since salt can neither leave through the cold plate nor enter through the hot one gradients are quickly established here that slowly extend out into the body of the solution as the Soret distribution is approached. As yet unsolved is the problem of extrapolating for j h o with the aid of the early fringe patterns. Part of the difficulty is in the failure to use higher terms in the expansion leading to equation 4. Part is due, however, to the manner in which the temperature gradient is established. The thermal diffusivity of silver is several hundred times that of water and for several seconds after turning on the heat very steep temperature gradients are present in the liquid in contact with a plate. Thus the initial mass flow does not correspond to the boundary condition that the temperature gradient is uniform at zero time. An alternative procedure would be to use thermostats serving the top and bottom plates, respectively, with both initially at T,. The temperatures of these two baths could then be changed slowly to terminal values of Th and To,respectively, so that the gradient in the liquid would be essentially independent of height (13) J. M. Creeth, J . Am. Chsm. Soc., 77, 6428 (1955). (14) W. J. Archibald, THISJOURNAL, 51, 1204 (1947).
Vol. Gl
at any instant. The mass flow during this interval would be comparable to that occurring in the ultracentrifuge during acceleration and a conventional zero-time correction, common to a11 levels in the cell, might then be applicable. At present the principal interest in the Soret coefficients of aqueous salt solutions is in their relation to the ionic heats, and entropies, of transport and hence to the e.m.f. of electrolytic thermal cells. This relationship is shown clearly by the work of Agar and BrecklB-l7who also have devised a conductometric method for the study of the simple Soret effect in dilute salt solutions. Unfortunately the optical methods cannot be adapted readily to dilute solutions and in the case of potassium chloride there is no overlapping concentration range in which comparison is possible. I n more favorable cases, e.g., CdS04 and AgN03, accurate optical measurements at concentrations as low as 0.1 m can be made and present work is aimed at a direct comparison of results by the two methods. I n Fig. 8 the triangles represent the values obtained by Chanu and L e n ~ b l e ,with ~ an optical method, at a mean temperature of 26". When allowance is made for the l O difference in temperature the values at 25" reported here appear to be slightly more negative than theirs although the difference could arise from the manner in which they interpreted their data. This is also true of Tanner's results although his 1927 values' are appreciably higher than those reported in 1953.* The 28% variation in A/k noted in column 4 of Table I when account was not taken of the sigmoid shape of the early concentration profiles suggests that differences in u of this order can arise in the interpretation. It is the author's impression that the interpretation Tanner gave his early data is more nearly in accord with the procedure adopted here than in his 1953 work and that his 1927 results will continue to afford a reliable guide to the concentration and temperature dependence of the Soret coefficient for a wide variety of electrolytes in concentrated aqueous solution. Acknowledgment.-It is a pleasure to acknowledge the care with which D. A. MacInnes reviewed this manuscript and with which Emil Maier of the Pyrocell Mfg. Co. constructed the many glass frames that were tested in the course of the work. The author is also indebted to J. N. Agar, 0. K. Bates, G. S. Hartley and C. C. Tanner for clarifying correspondence on various aspects of the problem and to Sonia Austrian for the isothermal diffusion measurements at 13 and 37". (15) R. Trautrnsn, ibid., 60, 1211 (1956). (18) J. N. Agar and W. G. Breck, Trans. Faraday SOC.,63, 167 (1957). (17) W. G. Breck and J. N. Agar, ibid., 63, 179 (1957).
i
