1158
WESTONB. KENDALL AND RALPHHULTGREN
sidered where Dz >> [HDI2/4[Hz] as in the present case, the simpler expression is adequate. I n Fig, 5 , [HD] does not continue to increase; it attains a maximum at 2 = 0.25 cm., T = 1000”K., and then decreases again. At the maximum, the formation of [HD] due to reaction 6 is equal to its destruction which can be supposed to occur at a rate ([HD]/[Hz]) d[H,O]/dt. Then measured quantities can be combined to give the left-hand side of the equality
and taking Ice at 1000°K. from the recent literature,1° one gets [HI = 2.3 X 10-5 mole/l. at %, = 0.25 cm. This value of [HI can be compared with [HI as measured farther downstream by the heavy water method. At 2 = 0.5 cm. [HI via heavy water was 91% of [HI a t 0.25 cm. as determined via reaction 6 . Assuming that [HI is fairly constant across the flame, one can conclude that the heavy water method gives [HI values which are also consistent with values determined via reaction 6. (10) G. Boato, G. Careri, A . Cimino, E. Molinari and G. G. Volpi, J . Chem. Phye., 24, 783 (1956).
Vol. 63
Another indication of the degree of reliability of the radical determinations was obtained by Dr. W. E. Kaskan of our group who measured [OH] by absorption spectroscopyll through the flame and the post-flame gas described by Fig. 5. In the postflame gas, Kaskan infers [HI from [OH] under the assumption that reaction 3 is equilibrated; and here [HI via optical measurements proved to be 2.0 f 0.1 times larger than [HI obtained via the heavy water method. In the early part of the flame, [OH] can be estimated from the rate of formation of carbon dioxide under the assumption that it is formed only via the reverse of reaction 5 ; and over the range 2 = 0.25 to 0.4 cm. [OH] via optical measurements was 0.8 f 0.1 of [OH] via the rate of carbon dioxide formation. This comparison of [OH] is also a comparison of the heavy water method of [HI determination with optical [OH], because the rate constant k--6 was obtained from measurements of ks which involved [HI determinations via heavy water. The two comparisons suggest that some error may afflict one or both of [HI via heavy water, or [OH] optically. But it would seem unlikely that errors in [HI could cause an error of more than a factor of two in kz,kd, ks as obtained in this or in a previous papers8 (11) W. E. Kaskan, C*ombustion& Flame, a, 229 (1958).
THERMODYNAMICS OF THE LEAD-TIN SYSTEM BY WESTONB. KENDALL AND RALPHHULTGREN Institute of Engineering Research, University of California, Berkeley, Calif. Received December 16, 1968
The heats of formation of solid solutions of tin in lead have been measured at 450°K.by liquid tin solution calorimetry. These data have been correlated with published thermodynamic data and with the phase diagram in order to establish a complete and reliable set of thermodynamic properties for both the liquid and the solid alloys.
Introduction Alloy systems for which complete thermodynamic data are available are few in number. In fact, of those simple eutectic systems of limited solid solubility listed in Kubaschewski and Catteralll the only one for which the entropies of the solid can be computed with reasonable accuracy is B i S n . Data of this type are certainly desirable because of the important role they play in the development of theories concerning the physical properties of alloys. Up to the present time the only significant measurements which were lacking for an accurate determination of the entropies of solid lead-tin alloys were the heats of formation of these alloys. By measuring these in a liquid tin solution calorimeter it was found possible to establish for the entire system a complete and self-consistent set of thermodynamic properties. For the phase diagram2 see Fig. 1. (1) 0. Kubaschewski and J. A. Catterall, “Thermochemical Data of Alloys,” Pergamon Press, New York, N. Y., 1956. (2) A i . Hansen, “Constitution of Binary Alloys.” 2nd Edition, MoGraw-Hill Book Co., Ino., New York, N. Y., 1958.
Experimental Materials.-The lead used in this investigation was obtained from the Consolidated Mining and Smelting Go., Ltd., Canada. The manufacturer y v e the purity as 99.999%. The tin was procured rom the National Bureau of Standards, Washington, and had a reported urity of 99.997%. Spectrographic analyses made in this h b o r a t o r y tended to support the reported purities. Preparation of Alloys.-A 10-g. ingot of each alloy was prepared by melting together at 360’ weighed amounts of the pure components in sealed, evacuated Vycor tubes. The tubes containing the completely molten samples were agitated for ten minutes to ensure thorough mixing of the components, then they were quenched in ice water to prevent macrosegregation. The weight losses encountered during the alloying process were in d l cases less than O.Ol%, so the compositions of the resulting ingots were taken to be the same as those of the mixtures from which they were prepared. The ingots were cold-worked, resealed into Pyrex tubes, homogenized for two weeks a t temperatures ranging from 20 to 35” below the solidus, and quenched in a mixture of Dry Ice and acetone. Microscopic examination disclosed no traces of a second phase, and X-ray diffraction studies confirmed the homogeneity of the alloys. Calorimetry.-The heats of formation of the alloys were determined by liquid tin solution calorimetry. A detailed description of the experimental method and apparatus may be found in a recent publication8 and will not be repeated
1159
THERMODYNAMICS OF THE LEAD-TIN SYSTEM
July, 1959
TABLE I EXPERIMENTAL RESULTS Sample comp. (at. -% tin)
no.
Ti (OK.)
58-3 59-3 59-15 60- 15 59-5 59-7 58-5 59-13 58-7 59-11 60-5 60-13 60-7 60-11
449.9 450.8 450.5 451.3 448.6 448.9 450.3 451.6 450.9 447.2 454.6 451.5 454.6 452.4
Run
Pure lead
5.00 10.00 14.10 20.00 25.00
Bath concn.
kkl?
Ti (OK.)
0.144 .146 .960 1.021 0.346 ,552 .317 .867 .477 .727 .338 .800 .506 ,659
612.0 613.0 613.0 611.0 613.0 613.0 612.0 613.0 611.9 613.0 611.0 611.1 611.0 611.0
AHsoln
(cal./
atom$.-
3748 3742 3693 3691 3529 3542 3385 3245 3197 3180 3021 3007 2883 2893
AHf, m ° K . (tal/
-
atdm7
+179 154 +263 +375 +404 +442 +505 +520 +592 +591
+
here. The samples were all dropped from a temperature of During the alloy -450OK. into a tin-bath at -612’K. runs the concentration of lead in the tin-bath was never allowed to exceed 1 at. %. In these dilute solutions the heat of solution of the samples was found t o be nearly independent of the lead concentration so that only a small correction was necessary. The concentration effect was determined by dropping pure lead samples into the bath and plotting the results as a function of concentration. Experimental Data.-The results of the heat of solution measurements are given in Table I together with the calculated integral heats of formation of the alloys at 450°K. In these calculations (Hela Ho) for tin has been taken as 2885 cal./g.-atom. This value is about 25 cal./g.-atom smaller than that derived from Kelley,4 as suggested by the recent work of Heffans on the heat capacity of liquid tin. From these data the partial molar heat of solution of liquid lead in liquid tin at infinite dilution is calculated to be (A~PLJB~IOK., rsn 1 = 1490 cal./g.-atom.
-
-
Evaluation of Thermodynamic Data. Liquid Alloys.-Kleppas recently has measured the integral heats of formation of liquid lead-tin alloys at both 623 and 723°K. His results indicate that the heats of formation are independent of temperature over the range studied. By extrapolating his curve from 4 to 0% lead he obtained ( @ P ~ , ) ~ ~ ~ - I= 1350 cal./g.-atom, in good agreement with our more directly measured value. An earlier set of measurements by Kawakami’ shows more scatter and mgch poorer agreement with our above value of (AHpb)zsn-l; hence the data of Kleppa have been selected without modification. Vapor pressure measurements on this system are not yet available, and e.m.f. measurements8 are unreliable due to the very small difference between the electropositivities of lead and tin. However, Elliott and Chipmans made cell measurements of Aped in the ternary system PbSn-Cd, and performed a Gibbs-Duhem integration of the activity of cadmium a t 773°K. for the ratios, Pb: Sn = 1 :2 and 2 :l. In this manner they were able to obtain the integral free energies of formation (3) R. L. Orr. A. Coldberg and R. Hultgren, Rev. Sei. Inatr., 28, 767 (1957). (4) K. K. Kelley, U. S. Bur. Mines Bull. 476, 1949. (5) H. Heffsn, Master’s Thesis, University of California, 1958. (6) 0. J. Klepps, THIE JOURNAL, 69, 175 (1955). (7) M. Kawakami, Sci. Rep. TohokuZmp. Uniu., [I]. 16, 915 (1927). ( 8 ) R. Schaefer and F. Hovorks, Electrochem. Sac., Reprint No. 87 25, 267 (1945). (9) J. Elliott and J. Chipman, J . A m . Chem. Soc., 18, 2682 (1961).
Pb
X S ~ I ATOMIC FRACTION TIN,
Fig. 1.-Phase
Si
diagram of the lead-tin system.
at two points on the Pb-Sn binary side of the diagram. If Elliott and Chipman’s values of AF are combined with Kleppa’s values of A H , the entropies of formation of PbSnz and PbzSnare found to be ideal within 0.03 e.u. Until further data become available it seems reasonable to assume that the entropies of formation of the liquid alloys are ideal at all compositions (regular solution), and to compute the thermodynamic functions of the liquid alloys at all temperatures and compositions from Kleppa’s heats of formation. Solid a-Phase Alloys.-The experimental results given in Table I are shown in Fig. 2 along with some more recently completed measurements of Murphy and Oriani’O which agree excellently. One method of establishing the thermodynamic functions of the solid alloys would be to make use of the phase diagram and the free energies of fusion of lead and tin to transfer the liquid free energies across the two-phase region to the solidus. If it is assumed that the heats of formation do not vary with temperature (an assumption supported by the (10) W. Murphy and R. Oriani, Acto Met., 6, 556 (1958).
WESTONB. KENDALL AND RALPHHULTGREN
1160
Vol. 63
tained are less than ideal by only 0.05 e.u. a t zsn = 0.25 and by only 0.07 e.u. a t xsn = 0.50. Tabulated Values of Thermodynamic Properties. -Selected values of the thermodynamic properties of solid and liquid lead-tin alloys are summarized in Tables I1 and 111. The units of 4F and AH are cnl./g.-atom, and those of 4S are cal./(g.-atom X deg.).
(1
a u
z 0 t a
z
e LL
0
c '
a W r
O
'ool/I 0
0
PRESENT O INVESTIGATION m
-
TABLE IT LIQUIDALLOYSAT 623'K. z)Pb(l) zSn(1) = [Pl)(l- .,Sn 111(1)
+
TS"
AF
0.00 .10 .20 .30 .40 .50
0 -270 -400 -470 -510 -530 (f40) -520 -480 -410 -280
.60 .70 .80 . 90 1.00
0
MURPHY and ORlANl
0
.
aPb 1.000 0.915 ,847 ,785 ,721 ,657 (k .021) ,584 ,499 ,390 ,236 ,000
asn 0.000 ,246 .390 .495 .575 ,646 (f ,021) ,709 ,772 .840 ,911 1,000
. ,
ff-PHASEALLOYSAT 456°K. z)Pb(s) zSn(s) = [Pb(l- .,Sn,](s)
SOLID
io 15 20 25 ATOMIC PERCENT TIN,
(f40) 310 270 210 120
AS 0.00 .65 .99 1.21 1.34 1.38 ( * .13) 1.34 1.21 0.99 .65 00
TABLE I11
523'K. 5
AH 0 130 220 280 320 330
30
Fig. 2.4ntegral heats of formation of a-phase lead-tin alloys.
close agreement of the two sets of measurements shown in Fig. 2) these values can be combined with the free energies along the solidus to obtain integral entropies of formation of the solid a-phase alloys. There is an additional and independent means of utilizing the present heat of formation_data to obtain the entropies of these alloys. AFsn along the solvus is for all practical purposes zero because the alloys are in equilibrium with essentially pure tin. Values of O J l S n derived from the present results may be combined with AE's, to obtain 4Ssn along the solvus. ASpb and subsequently A S may be obtained from a Gibbs-Duhem integration of A&,,. An analysis of the uncertainties involved in these calculations would seem to indicate that it is somewhat better to accept the solvus line given in Hansen as correct and assume that any resulting small inconsistency between the thermodynamic functions of the liquid and the solid can be attributed mainly to the assumption of ideal entropies in the liquid. That such an inconsistency is indeed negligibly small can be demonstrated as follows: if the free energies of the solid as calculated from the solvus line using the measured heats of formation are transferred into the liquid and combined with Kleppa's heats, the entropies ob-
(1 XS"
o.oa .05 .10 .15 .20 .25 .29
-
AF
-
0
80 -105 -115 -120 -120 -105 (f50)
+AH
AS 0.00 170 .55 315 .92 430 1.20 520 1.40 1.56 590 630 1.61 (f40) ( f 0 . 2 3 ) 0
aPb 1.000 0.957 ,921 ,895 ,871 ,857 ,847 (h0.045)
asn 0.000 .375 ,647 .793 ,906 ,962 ,986 (*0.065)
Summary and Conclusion Heats of formation of solid solutions of tin in lead have been determined in a liquid tin solution calorimeter. From these data together with the phase diagram, and previous thermodynamic measurements of liquid alloys, a consistent set of thermodynamic functions has been derived for both solid and liquid alloys. The self-consistency serves to confirm not only the thermodynamic measurements, but also the positions of solidus, liquidus, and solvus lines of the Pb-rich alloys. Acknowledgment.-The authors are indebted to the Office of Ordnance Research, U. S. Army, for support of the experimental work described in this paper. In addition, they wish to express their appreciation to the Atomic Energy Commission for support of the literature search and evaluation of the lead-tin system, since i t was from this evaluation, done by Linda Warner, that the need for the present study was suggested. The authors also wish to acknowledge the assistance of Raymond L. Orr in the experimental work, and the many helpful suggestions of Raymond L. Orr and Philip D. Anderson in the evaluation.
.
r
July, 1959
ADSORPTION OF INERT GASESBY MODIFIED CARBONS
1161
ADSORPTION OF INERT GASES BY MODIFIED CARBONS BY W. F. WOLFFAND PHILIP HILL Research Department, Standard Oil Company (Indiana), Whiting, Indiana Received December IS, 1968
The adsorption of nitrogen and argon by modified active carbons has been studied by a simple desorption technique. Active carbons modified by the deposition of lithium and various inorganic compounds behave normally; the amount of gas adsorbed at ordinary temperatures and pressures decreases linearly as a function of the amount of modifier. Sodium and potassium cause the development of an unexpected maximum in the adsorption capacity. This anomalous behavior appears to be associated with the formation of new pores. heated under a stream of nitrogen until water removal was Introduction complete. A temperature above the melting point of the Active carbons have been used as supports for a modifier was maintained for one-half hour. variety of catalytically and chemically active subThe modified carbons were cooled to room temperature stances. Interest in these modified carbons has under a static gas blanket. The amount of adsorbed nitrogen or argon at room temperature and atmospheric pressure centered on use of them as catalysts and treating was measured by desorption with either n-heptane or nagents; unlike the unmodified active carbons, dodecane; this procedure has been used in studying the little attention has been given to their physical molecular-sieve properties of active carbon^.^ Values given adsorption characteristics.1 Such information could for the volumes of gas desorbed are uncorrected for temperaor pressure; such gas law corrections did not signifibe of value both in extending our understanding of ture cantly affect the relative size or shape of the desorption the nature of adsorption, and in developing im- curves. proved adsorbents. Surface areas and micropore volumes of the active carTo study this type of adsorption, modified bons were determined by conventional Brunauer-Emmett(B.E.T.) nitrogen-adsorption techniques . 4 Gas carbons have been prepared by depositing alkali Teller mixtures were analyzed by mass spectrometry. metals and various inorganic compounds on comResults mercial active carbons. The adsorption of nitrogen and argon by these modified carbons a t ordinary Differing amounts of aluminum chloride, sodium temperatures and pressures was measured to acetate, sodium hydroxide and sodium trisulfide determine changes in physical adsorption caused by were deposited on Carbon A. Nitrogen adsorpthe modifying agent. tions were determined for two or more compositions of each modifier. Figure 1 shows the change in Experimental nitrogen adsorption with composition. With the Commercial active carbons, designated as A, B, C and D, were used without purification. Carbons A and B were possible exception of sodium hydroxide, the amount separate batches of an S-to-14-mesh coconut charcoal sup- of nitrogen adsorbed decreased linearly with inplied by E. H. Sargent and Company. Carbon C was a creasing concentration of the modifier. 12-to-20-mesh active carbon from the Burrell Corporabion. Similar runs were carried out with lithium and Carbon D was a 20-to-50-mesh coal-based carbon from with potassium deposited on Carbon A. I n runs Pittsburgh Coke and Chemical Company. Substances deposited on the active carbons included with lithium, only argon was used, to avoid comlithium, sodium and potassium metals, sodium acetate, an- plications due to chemisorption. The results are hydrous aluminum chloride, sodium hydroxide and a sodium plotted in Fig. 2. Lithium showed the expected trisulfide solution prepared by boiling an aqueous sodium sulfide solution with an equivalent of sulfur. Gases em- linear decrease in adsorption, but, with potassium, ployed were high- urity nitrogen and standard-grade argon the amount of argon adsorbed increased linearly to a from Linde Air goducts Company. Desorbents used in maximum and then sharply decreased. On replacemeasuring gas adsorption were n-heptane of 99+% purity ment of argon by nitrogen, an even more profrom Phillips Petroleum Company and n-dodecane from nounced maximum was obtained. Humphrey-Wilkinson. The results obtained when different carbons were The modified carbons were prepared by contacting the active carbon with the modifier in either a molten or gaseous used as supports for the potassium are plotted in Fig. state. This procedure is conventionally used to disperse 3. In all cases maxima were obtained, indicating sodium on inert supports.2 Glass equipment was used except for surfaces in contact with aqueous caustic or molten that this phenomenon is general for potassium on lithium; here, stainless-steel equipment was used. All active carbon. The differences in size and shape are operations were carried out under an atmosphere of the gas probably associated with factors such as the to be adsorbed by the finished composition. differing surface areas and ash contents of the Before depositing alkali metals, anhydrous aluminum carbons. chloride, or anhydrous sodium acetate, the carbons were Sodium as the modifying agent also gave curves dried by heating to 300’ under a stream of the inert gas. The carbon was cooled, and a weighed amount of the modi- with maxima. The data for sodium on Carbons A fier was added. The mixture was reheated, with stirring, and C are plotted in Fig. 4. The plots are sigunder a static gas blanket to a temperature above the melting or sublimation point of the modifier. Heating and nificantly different from those for the sodium comstirring were continued for about one-half hour beyond the pounds as given in Fig. 1; only with sodium hytime required to obtain a visually homogeneous product. droxide was there any evidence for even the slightest Deposition of sodium hydroxide, sodium trisulfide and of maxi ma. sodium acetate from aqueous solutions was carried out in a slightly different manner. In each case, enough solution to wet all of the carbon was added, and the mixture was (1) P. H.Emmett, Chern. Revs., 49, 69 (1948). (2) “High Surface Sodium on Inert Solids,” National Distillers Chemical Co., New York, N. Y.,1953.
(3) W. F. Wolfi, ”The Structure and Activation of Gas-Adsorbent Carbons.” presented at the 133rd meeting of the American Chemical Society, San Francisco, Calif., April, 1958. (4) 8. Brunauer, “The Adsorption of Gases and Vapors. Vol. I. Physical Adsorption,” Princeton Univ. Press, Princeton, N . J., 1943, PP. 285-299.
