J . h'. AGARAKD J. C. R. TURNER
1000
Vol. 64
rare gases eliminates the possibility of chemisorption, which recently has been found t o occur with N2 a t low temperatures on certain metals, e.g., NiZ2 and W.23 Of course, krypton and argon adsorption can be affected by the presence of chemisorbed or strongly physically adsorbed surface c ~ n t a m i n a t i o n ,but ~ ~ ~one ~ ~ usually attempts to measure surface areas in the absence of conttlmination. The presence of phase changes in adsorbed films, appearing as discontinuities in the isotherms, might have been thought to cause poor surface area results,12but this has been shown not t o be the case for k r y p t ~ n . ' ~ .It~ ~is of course also well known that with certain types of adsorbents, different gases will measure different areas; for example, a zeolite such as Molecular Sieve 4A (Linde Co.) adsorbs krypton only on the external surfa~es,~' while admitting oxygen into the latticezY with a spectacular difference in apparent area. For these reasons, therefore, it is certainly necessary t o consider the nature of the adsorbent 0 20 3 05 G 10 GiS VID, and possible interactions between it and the adsorbFig. 1.-BET plots for krypton adsorption at 77.4"K. ate before selecting a gas for surface area measureon vsrioi s solids (crosses indicate monolayer coverage eval- ment. If there is uncertainty about the likelihood uated from c) (see Tatde 111). of such specific effects, it is probably wisest to make measurements with more than one adsorbate. TABLE I11 We are indebted to Miss C. P. Rutkowski, who DATASHOWN I N FIGURE 1 performed all of the adsorption measurements W t . of Surface area, described, and t o Dr. R. I-I. Zimm for a critical Ciirve Sample sample, g. m.*/g.a C review of the manuscript. 1 Sintered Ag 34.30 0.0085 52 I
!
~
2 3
MoSz I T powder With U K ~= 19.5 A,*.
4 5 a
Glass powder Mica paper
6.24 1.00 0.170 1
TO
0.11 1.92 8.31 0.90
80 15 64 215
Malden and Marsh4 have criticized the use of krypton on the basis of lack of general utility. We feel from our own results and those cited in this paper that the general applicability has been amply demonstrated. Furthermore, the use of the
(22) R. J. Kokes and P. H. Emmett, J . A m . Chem. S o e . , 80, 2082 (1958). (23) G. Ehrlich. T.W. Hickmott and F. G . Hiidda, J. Chsm. Phys.. as, 506 (1958). (24) F. S. Stone and P. F. Tiley. h'alure, 167, 6.54 (1951); P. F. Tiley. {bid.. 168, 434 (1951). (25) P. Cannon, Tms JOURNAL, 63, 1292 (1959). (26) B. B. Bisher and W. G. McMillan, J . Chem. Phye., 28, 549 (1958). (27) P. Cannon and C. P Riitkowski. unlxiblistied data: surface area measured 8.20 m.l/g. (28) D. W. Breck, et nl.. J . A m . Chem. S a c . , 78, 5963 (1956): surface area measured, 7% n:.'/s.
S E W APP,1RA4TUSFOR MEASURING THE SORET EFFECT BY J. K.AGARAXD J. C. R. TURXER' Department of Physical Chemistry, University of Cambridge, Cambridge, Enqland Reccmued \ I member 96. 1969
'4 simple conductimetric method of measuring the Soret effect in dilute aqiieous solutions of electrolytes is reported. The construction and operation of the thermal diffusion cell are descrihed, and results for dilute solutions of CdSO,, AgYO,, S a B r and T1,SOd are given. These are in satisfactory agreement with results obtained by other methods.
Introduction Inforrnation about the Soret effect in dilute aqueous solutions of electrolytes is sparse. I:or solutions of higher concentration, methods based on optical interferometry have been developed, most recently by Longsworth.2 I n dilute solutions such methods are insufficiently sensitive, and other techniques must be devised for measuring the concentration changes. Agar and Breck3 followed (1) Depf. of Chemical Engineering, University of Cambridge, Pembroke St.. Cambridge, England. (2) L. G. Longsuorth, THISJOURVAL.61, 15.57 (1957).
the concentration changes by measuring the e.m.f. of a non-isothermal cell, but this method is applicable to only a few systems. Measurements of conduction offer good prospects and we shall describe here a simple conductimetric cell (cell A) which gives a clear demonstration of the Soret effect in dilute solutions. Details of a different design of cell (Cell B) are given elsewhere4 and (3) J . N. Agar and W. G. Rrech. Trans. F a r a d a y Soc., 63, 167 f 19.57). (4) (a) J. S . Agar and J. C.
255
R. Turner, Proc. R o y . SOC. ( L o n d o n ) ,
A, 307 (19(0): ( h ) J C. N Tnrnrr. Ph.L>. ' ~ h e r l s ,University of
Cambridge.
A
August, 1960
1001
XEW APPARATUS FOR l I E . 4 S C R I X G THE S O R E T E F F E C T
further results ohtained with a later cell will be forthcoming. Apparatus - - T ~ Pw l l (Fig. 1) consists of two rectangular silver end-platw (.ig) svrrwed to a Pcrspex block ( P ) . The solution (8) is contained between the plates in a cylindiical hole in the Perspeu, thin rubber gaskets being used to make a liquid-tight joint between the platrs and the Perspex. A narrow-bore filling hole ( F ) is used for filling and emptying the rc.11. The four platinum wires (E) of diameter mm. and protruding about ' I mm. into the solution compartment, are used as conductance electlodes. .\ satisfactory seal between these wires and the Persprx (superior t o that obtained with adhesives) was made heating them and forcing them through the Perspex while hot. The protruding ends of the wires were platinized before the end-plates were attached. To commence a run, the cell, containing the desired sclution, was placed between two copper cylinders maintained at 20 znd 30" by circulating water from two thermostats. T o minimize convection, the top of the cell was kept a t the higher temperature (30"), the sides were lagged, and the rell was acrurately levelled. The resistances of t h r solution between the top pair and between the bottom pair of electrodes m-ere measured a t intervals using an audiofrequency bridge sensitive t o 1 part in 10'. The steady temperature distribution is established in about 12 minutes, and during this period there are large changes in the measured resistances. To ensure that subsequent resistanrc changes are Glue t o changes of concentration and not to further rhanges of temperature, it is necessary to keep the temperatures constant to within 0.01'.
Theory of the Method During the approach to the steady state the molality (vi) at time ( t ) and distance (x) from the lower plate should be given to a siifficiently good approximation5 by 4 7rx ,z cos a x
e-t/o
(I)
provided t > 6 / 3 . In this equation mo = initial uniform molality a = total height of cell u = Soret coefficient d T = temp. difference between the ends e = U * / T ~ Dthe , characteristic time D = diffusion coefficient
For times less than 6 / 3 , additional terms are req~ired.51~The derivation of (I) assumes a uniform tempclrature gradient and ignores the temperature dependence of D and u. "Warming-up" corrections6 are sinall and also have been ignored in this work. The measured resistance (R) of either pair of electrodes is proportional to the specific resistance ( p ) a t the rcblevant height in the cell, and changes in K , p and m can \)e related by ti
I n I? = d In
p =
- B d In m
(2)
where and A is ihe equivalent conductance. The coefficient B can be calculated from published data and can be treated as constant over the ranges of temperature and molality occurring in any one experiment. Since d In m is small we may write (3) (a)
J. A . Bie..!ein, .I. C i i r m . Ph!:s.. 23, 10 (195.5). (G) J. X. Agar. Trarir. F u r o d a ~SOC.,56, 776 (1960).
/ / / / / I Fig. 1.-Cell A3 (height = 1.34, cm.), approximately to scale. 1)imensions of cells .11 arid A:! are aimilar except for their heights (see Table I).
\There Ro is the resistance a t t = 0 (uniform solution). Equation 1 thus become4 BuATRo 5Z-R.
(;
-
i) +
f2
cosz:
x
e-t/s
(4)
where x now refers to the effective position of one or the other electrode pair. l'or the steady state ( t + m), we obtain -~
-
BuATRO
-
and (4)can thus be rewritten in the form In
In - I I , /
= I11
1x0
-
n-1
+
The effective positions of the electrodes may be deduced from resistance measurements with a uniform solution in the cell under the following conditioiis: (a) isothermal a t 20" ( T I ) , (b) isothermal a t 30" ( T 2 ) ,(c) with the upper end plate at T 1and the lower at T I . By interpolation, the effective temperatures a t the electrodes under the usual operating conditions (c) can be determined. A small correction is necessary for non-linearity in the temperature-conductanre relationship. Assuming a uniform temperature gradient, the effective positions x: then follow. The resistance measurement (e) variei with time due to thermal diffusion in the solution. It is thus nececsary to extrapolate back to zero time to obtain the resistance appropriate to a uniform solution, bearing in mind that the unsteady temperature distribution in the first few minutes renders useless any readings in that period. We have used free-hand extrapolation and thi. introduces an uncertainty into the value of xla deduced from the reqi*tance readings. The possibility of error in the extrapolation is clearly reduced if the Soret Coefficient is small ; with this in view we have used 0.02 m solutions of SaC1. KC1 and LiCl and, in these cases a t least, graphical extrapolation is quite adequate. For cell A3 the preferred values of z / a by this method are 0.852 and 0.186. All measurements (using the three solutions mentioned above and some otherg) lie within + 0.005 of these values, and the error due to the extrapolation seems to be within *0.001. L o n g s ~ o r t hfound ~ ~ ~ that the temperature gradient in his cells was not uniform, which implies some lateral flow of heat through the malls. This
J. S . AGARAXD J . C. R. TURNER
1002
1-01. G4
that should replace the single tinie-dependent term in (1) is
which r-aiiishes when ? / a = 116 or 5 (i aiid very nearly vniiislieh nheii x a = 0.186 or 0.832, as in cell A3 ( c f . Hariied aiid Frenchs). 111 ai1 experiment of sufficiently long duration the observed R approaches R , closely. 4 I BOTTOM 111 order to save time, it iq more coiiELECTRODES I ,.',/" venient to extrapolate the obfierved R to t = 03 with the aid of (4). Csiiig arough estimate of 8, a plot of R against p - t / @ is constructed aiid extrapolated to = 0. The interrept ( X , ) i. inieiisitive to errors in 0. 8 16 24 32 40 48 IJTheiiIZ, has heen deterniined, 0 mag' he Time, hr. found froin a plot of In R - R,l againqt Fig. 2-0.045 m cadmium sulfate: 0-24 hours, tlirrnial cliffusion t (see (6))) although accurate values of 0 run (30-20O") r = (obsd. resiPt,aiicc,)j(rrsi,t~inc(~wtraptl. to zero h r , ) ; 2.4-48 hours, isothermal return rim (20") r = (ol)sd. resiscaiiiiot be obtained in caies ?There the tance)/( resistance with iniiform s o h . at 20' 1. Soret coefficient is small-for example, 0.02 m XaBr (Table I). Equation 6 also is less likely to orcur in our cells, since the thermal s11o\\-s that 'R,, - R , (and heiire R,,, mav be conductivity of their I'erspex n-alls i q much lehi eitimnted by extrapolatioii of the linear p a h of than that of the glass I\-alls used in Loiigsv-orth's the In I? - K , 11s.t graph to t = 0. cells. We therefore think that the assumption of -klternativeiy, Ro may be ol,taiiied by a freeuniforiii temperature gradient is unlikely to intro- hand extrapolation oi the R zs. f curve to t = 0; duce cerious errors into our estimates of .r a. the mlues of iRo - R , obtained iii this wag' are As far as steady-state observatioiis are concerned, always slightly greater thaii those obtained by the the poiiit is in aiiy rase uiiimportant, because the log plot, although the rewlting difference.: in difference iii I n m betneeii the two electrode pairh u do not exceed 0.2 x deg.-'. The estrapis governed 1)y the difference in T rather thaii that olatioii of the log plot is not entirely satisfactory iii .c. on-ing to the aiiomalie.; in the early stage
