NOTES
July, 1961
1277
experimental difficulties encountered in attempting to extend the triple-point method to lower pressures and more dilute solutions ( i e . , the slow establishment of the equilibrium) led to their observation of higher pressure values a t the lower temperatures. Extrapolations of the Goldfinger-Drowart data and t,his work show reasonably good agreement when considering the range of pressures measured. The authors express their thanks to Dr. K. Weiser and Dr. G . A. Silvey for valuable discussions. 4690
THE SORET EFFECT AS A SOURCE OF ERROR IN CONDUCTANCE MEASUREMENTS BYR. H. STOKES Department of Physical and Inorganic Chemiatry. UniuerailU of Xew England, Armidale, N.S. W., Australia Receiiied Januarzi 20, 1061
Agar,' iii a paper on the rate of attainment of Soret equilibriunn, recently predict'ed that "there will be small transient changes of composition in a conductivity cell when it' is transferred from the ambient temperature into a thermostat." The reality and. considerable importance of this effect are demonstrated by the findings now reported. Two conductance-cells were used. Cell A consisted of two electrode-bulbs ahoiit 2.5 cm. in diameter, joined by 6 cm. of tubing of 6 mm. inkrnal diameter; its cell constant was 20.71 cm.-l. Cell 13, of constant 4.595 cm.+ was of similar constriictioii rxccpt that the central section was only about 1 cm. long. Filling tubes were attached to both electrode-bulbis, and the leads to the electrodes were carried through glass side-arms well separated from the filling-tubes and each other. After the detection of the effect reported below, the filling-tubes were fitted with mixing-bulbs to facilitate the mixing of the cell contents without removal of the cl.4 from the thermostat. The electrodes were lightly coated with platinum-black; frequency-dependerice in the range 1-4 kc./sec. was less than 0.002% with cell A and 0.008% with cell B. This small residual dependence was extrapolated out by an R us. f plot. The lead resistances mere measured by filling the cells with rnercury, and calibrations were made with the Jones and Rradshnw 0.1 dema.1 potassium chloride standards a t 25'. The cells were filled with 0.001 M hydrochloric acid and heated in a thermostat to 50 ; a t this temperature their contents were thoroughly mixed. They were then transferred quickly to a (hermostat held a t 25 & 0.001'. Here the resistances were measured over a period of several hours by a calibrated Jones bridge. I t was established by a prev; ions study that the contents of the cell must bp within 0.001 of the thermostat temperature after 20 minutes; hence any changes occurring after this time cannot be ascribed to tempuature changes. Results such as those shown in Table I n-erc consistently observed.
TABLE I .4PI'AREST
25"
SPECIFIC C O N D U C T A N C E S I N
AT YARIOUS
Time, hr.
rrIP,fssFOLLOWISG CELLSTO 50' Cell A
OHM-' cM.-'
PREVIOUS
% low
AT
HEATING OF
Cell B
pZ low
0.58 0.0043969 0.304 0.0044067 0.077 1,58 ,0043974 .295 ,0044075 .059 5.42 .0013091 ,254 ,0044082 .043 Aftcrmixing:tt 25" ,0044103 ,000 .0044101 ,000
The results from the two cells a t all times differed far more than could be ascribed t'o measuring or cdibration errors. But when the cell contents (1) J. N. Agar, Trans. Faradau Sac., 66, 776 (1060)
I
I
,
I
10 20 30 Time, hours. Fig. 1.-Change of resistance with time in cell A containing approximately 0.01 N hydrochloric acid. Cell thermostated a t 50', then transferred to 25' thermostat a t zero time. Temperature equilibrium is known to be attained before the time of the first point plotted. 0
were thoroughly mixed at 25', agreement was immediately established, and no further drift in readzngs then occurred f o r several days. Furthermore, the results after the mixing were in agreement with Shedlovsky's values2 within O.Olyo. Exactly the opposite effect was observed 011 moving the cells from a 25 to 50" thermostat: the results again differed considerably, but this time both cells showed higher conductances than the filial true values attained after mixing of the cell contents. I n aiiother experiment, cell A was heated to 50" in a water-bath, and its contents were mixed a t this temperature. The bath and cell were then allowed to cool slowly to 2 5 O , oyer a period of about 1.5 hours. The cell was then transferred to the 25' oil-thermostat for measurement. On reaching temperature equilibrium, the resistance was 4696.4 ohm, and on mixing the cell (iontents this value changed only to 4696.1 ohm, i.e., 0.0077,. The effect, then, evidently arises froin szrdden changes in cell temperature, and is therefore not to be ascribed t o differences in adsorption of hydrochloric acid at the electrodes a t different temperatures. An explanation in terms of adsorption also seems to be ruled out hy the fact that the effect is of much the same relatire magnitude for a wide range of hydrochloric acid concentrations. It seems clear that the effect ariws from thermal diffusion of hydrochloric acid into or out of the central portion of the cell during the period of rapid temperature change-w., the first few minutes at the new temperature, while there are large temperature gradients between adjacent parts of the cell. The persistent nature of the resulting concentration-disturbance is at fkst sight surprising, though once again it is in accordance with Agar's predictions.' In Fig. 1 is plotted another series of measurements on cell A, which were followed this time for 24 hours before the cell contents were mixed; after this time, isothermal diffusion had only reduced the original disturbance to half its initial value, and it seems likely that at least a week would be needed to get a result correct within O . O l ~ o ,unless provision is made for thorough mixing of the cell contents as soon as temperatureequilibrium is reached, The initial disturbance is
1278
NOTES
apparently ai; the ends of the central tube, and diffuses away both outwards into the bulbs and inwards to the center of the cell; thus in cell A with its long central tube the effect lasts much longer than in cell 13, where density-gradients would help to produce uniformity. That the effect is so large with hydrochloric acid is due t o its large Soret coefficient; with potassium chloride, the effect is still found but is smaller. Thus with 0.1 D KC1 in cell A, the initial error found on rapidly transferring the cell from 25 to 50’ was 0.097,. It is also still significant with hydrochloric acid even with the small temperaturerise from a room temperature of 22 to a 25’ thermostat; here the initial error with 0.01 N HC1 was O.OlS%:, for cell A. Dr. J. N. Agar has pointed out to me that Ihe sign of the observed effect is unexpected. One would expect the central tube to cool down more rapidly than the bulbs, so that in the early stages of the temperature-change hydrochloric acid should diffuse into the ends of the tube, with a consequent increase in the apparent conductance. The effect is perhaps due to differences in wall thickness, for in the region where the central tube joins the bulb the glass is certainly thinner. It seems likely that many published conductance measurements a t temperatures far removed from room temperature may have suffered from this error, for the usual criterion of temperature equilibrium is coiistancy of the resistance within about 0.017, over a period of an hour or two: Table I and Fig. 1 make it clear that constancy within this limit may be observed while the Soret disturbance is still present to an extent which causes several tenths of 1%;?error. The error would not be significant, (a) where “flask cells” with attached conductivity cells are used, and the solution is passed into aird out of the cell section several times between rneasui*ements; (b)where the cell temperature is changed only slowly, as will be the case if the cell is put into a thermostat at room temperature and this iq then heated up to the measuring temperature, or (c) where the solution is first thermostated and then driven over into the empty cell. The ordinary form of ( d l used here is, however, c.stremely convenient to use; it is also convenient i i ~work involving se\ era1 temperatures to have a beparat e theimostat for each temperature and move the cell to each in succession. This can be done without Soret error provided the cell is fitted with mixing b d b s so that its contents can be mixed while it is completely immersed in the thermostat. I have reccantly used such cells t o measure the conductance of hydrochloric acid with, I believe, an accurary of 0.00t55%; the results will shortly be published. ‘The possibility of using a conductancevel1 deliberately designed to enhance the effect, for the measurement of Soret coefficients, is also being examined. (2) T. SheiilovAv, J . Am. Chem SOC, 54, 1411 (1932).
Vol. 65
When solutions of sodium hydroxide, a lead salt and thiourea are mixed, lead sulfide gradually forms, first as a colloid and later as a precipitate. Studies of the reaction have been made by Bruckmann,’ Pick2 and W h i t ~ h e r , using ~ lead acetate. In addition, it has been discussed by Sahasrabudhey and Kral14 and Kicinski.5 The mechanism and even the stoichiometry of the reaction have been debated. It is the purpose here to offer evidence shedding some light on the former and establishing the latter, using lead nitrate. Experimental Reagents .-Powdered lead sulfide was prepared by the lead nitrate-thiourea reaction. The sodium bromate was recrystallized reagent grade material, dried a t 175’. Concentrated solutions of thiourea contained a small amount of insoluble impurity that was removed by filtration through a fine porosity, sintered-glass buchner funnel. &illchemicals were reagent grade. Procedures for Making Runs. Series 1,2,3.-Solutions containing sodium hydroxide (0.4-1 .O M ), lead nitrate (0.01-0.06 X )and thiourea (0.1-0.4 M) were prepared by mixing the appropriate stock solutions in that order. In Series 1, the initial lead concentration was varied, keeping the thiourea and hydroxide ion concentrations constant; in Series 2, the initial thiourea concentration was varied; and in Series 3, the initial hydroxide ion concentration was varied. The runs were made a t 23.00 =k 0.02’. The reaction was followed by periodically withdrawing samples, quenching them in excess perchloric acid to stop the reaction (final p H ca. 1.5), and analyzing them to determine the amount of hydroxide ion and lead consumed during the reaction. The lead sulfide present was removed by filtration prior to the lead determination. Series 4.-Two solutions having the initial concentrations, 0.7 M NaOH, 0.035 or 0.060 M Pb(NOa)2and 0.2 (“2)~CS were prepared. Periodically, samples were withdrawn, quenched in excess acetic acid, and filtered to remove the lead sulfide present. A portion of the filtrate was analyzed for lead. A second portion was analyzed for thiourea after lead had been removed as the sulfate (lead interfered with the thiourea determination). Series 5 .-Three identical solutions having the initial concentrations 0.7 M XaOH, 0.035 X Pb(N03)2 1.0 g. of powdered PbS/250 ml. of the solution, and 0.2 1M (NH2)zCS were prepared. Periodically, samples were withdrawn and quenched in excess perchloric acid. The amount of hydroxide ion used up during the reaction was determined, and from this the amount of the lead remaining was calculated. Series 6.-Four solutions having the initial concentrations, 0.6 M NaOH, 0.054 M Pb(S03)2,0, 0.50, 1.00 or 2.00 g. of powdered PbS/50 ml. of the eolution and 0.3 ‘I4 (T\”2)2CS were prepared. Samples were withdrawn from the solutions and 5.2 mni. after the beginning of the reaction they were qurnchrd in perchloric acid. Theamount of hydroxide ion used up was determined and, from this, the amount of lead remaining was calculated. Series 7.-Two groups of solutions wtw prepared. In v the first group (0.7 J I NaOH, 0.035 31 Pb(NO&, 0.2 1 (SH2)ZCS) half of the solutlons were prepared from sodium hydroxide that had brcn stored for varying lengths of time i n a Pyrex bottle and half from that stored similarly in a polyethylene hottlr. In the second group (0.8 -l4XaOH, 0.048 JI Pb(Ii08)2,0 3 JI (TH,),CS) half ot the solutions were stirred for 12 nun. and the other half for only 0.3 min. At a fixed time (for each group) after the beginning of the reaction, one sample was wlthdrawn from each run and quenched in perchlorlc acid. The amount of hydroxide ion used up was determined and, from this, the amount of lead remaining was calculated. Alkaline Decomposition of Thiourea.-*i 0.3 Jf thiourea0.7 1f sodium hydroxide solution was prepared and allowed (1) G. Briickmann. Kolloid-Z., 65, 1 (1933). (2) €1. Pick, Z. Physilc, 126, 12 (1949).
(3) S. Whitcher, CNL-TS-P9, Chicago Midway Laboratories. Cnirwsity of Chicago, Chicago, Ill.. 1954. (.$) R. Pahasrabridhe), iin
