Juhe, 1938
HEATSOF DILUTION AND HEATCONTENTS OF CADMIUM SULFATE
[CONTRIBUTION NO.
368 FROM THE DEPARTMENT OF CHEMISTRY, UNIVERSITY
1301
OF PITTSBURGH]
Heats of Dilution and Heat Contents of Aqueous Cadmium Sulfate Solutions BY T. H. D U N K E L B E R G E AND R ~A. ~ ~L. ROBINSON This investigation was carried out to extend pipets were filled by evacuating to the limit obtained with the temperature range of heat of dilution meas- a good water pump and introducing the solution to be diluted under this reduced pressure. urements of aqueous cadmium sulfate solution^^'^ For measuring the time current was flowing through and t o compute from such data the partial molal the heating elements the automatic switches described by ~ ~ replaced by a hand operated heat contents and heat capacities of the com- Lange and M ~ n h e i mwere ponents of the solutions. A similar study of so- switch, which opened and closed the heating circuit and dium chloride solution^^^^ led to a verification of a t the same time started and stopped an electric stop clock. The time of heating could thus be read with an the limiting law of Debye and Hii~kel,’,’~ while accuracy of 0.01 second. earlier studies of 2-2 type electrolyte solutions The cadmium sulfate was purified according to the indicated large deviations from limiting law method of La Mer and Parks.* Analysis of the dried salt behavior a t the lowest concentrations m e a s ~ r e d . ~for sulfate indicated 99.82 * 0.03% sulfate. SpectroThe results of this investigation also may be scopic analysis indicated the absence of metallic impurities in amounts more than a few thousandths of one per cent. ;I4 compared with data of La Mer and Parks8 on the it is probable that the principal impurity was tenaciously electromotive force of cells containing cadmium retained water. All solutions were made up by weight or sulfate. Activity coefficients of cadmium sul- by the dilution of a more concentrated solution that had fate determined by the isopiestic vapor pressure been made up by weight. The experimental procedure and the method for determethodg differed appreciably from the values of mining the value of the heat effect accompanying a diluLa Mer and Parks, but were in good agreement tion were the same as previously described.6s10*11,1a with activity coefficients calculated from freezing Experimental Results point measurements and corrected to 25’ with The first two columns of Table I give the inithe aid of then available thermal data. The tial and final concentrations of a dilution, rerelative partial molal heat contents and heat spectively. The remainder of the table indicates capacities determined in this investigation are the number of duplicate runs, the average value just the quantities required to correct freezing of the intermediate heat of dilution (AH)I5and These thermal quanpoint measurements to 25’. the probable error, exclusive of systematic ertities may also be computed from e. m. f . data so that our measurements should be of some rors, a t each temperature. Although the abvalue in locating the source of the discrepancy solute values of the probable errors are larger than those observed in the study of sodium chlomentioned above. ride solutions,” the percentage errors are of the Experimental same magnitude. It is estimated that systematic The apparatus was essentially that used by Gulbranerrors are not greater than 1%. sen6,10a11 with the following modifications. Extrapolation to Infinite Dilution.-The data New gold-plated brass pipets were constructed.12 Their in Figs. 1 and volumes were 6.285 and 6.293 * 0.002 ml. a t 20’. The of Table I are plotted against m’/’ 2 by the point to point method previously de(1) From a thesis submitted by Mr. T . H. Dunkelberger in partial fulfillment of the requirements for the degree of Doctor of Philosophy, scribed.l’ The lowest point on the 15’ curve August, 1937. was obtained after a smooth curve had been (2) Present address, Department of Chemistry, University of Idaho, Moscow, Idaho. drawn through the other experimental points a t (3) E. Lange, J. Monheim and A. L. Robinson, THISJOURNAL, 66, that temperature by placing the m = 0.0125 4733 (1933). (4) E. Plake, Z.OhysiR. Chem., 16!2A, 257 (1932). point on the smooth curve. 66, 2637 (5) E. Culbransen and A. I.. Robinson, THISJOURNAL, Lange and his collaborators have found that (1934). (6) T . F.Young and W .I.. Groenier, i b i d . , 68, 187 (1936). in very dilute solutions the relation between the (7) P . Debye and E. Hiickel, Physin. Z . , 84, 185 (1923). heat of dilution and m’/’is linear within es(7a) H.Bjerrum, 2.physik. Chem., l l S A , 145 (1926). (8) V. K. La Mer and W. G. Parks, THISJOURNAL, 66, 4343 (1933). (9) R.A. Robinson and R . S. Jones, ibid., 68,959 (1936). (10) E:. Gulbransen, Thesis, University of Pittsburgh, 1934. (11) Ts. Langeand A. I,. Robinson, Chem. Reo., 0, 89 (1931). (1’2) T H.Dunkelberger, Thesis, University of Pittshurgh; 1937.
(13) E.Lange and J. Monheim, Z . physik. Chrm., 140A, 51 (1930). (14) Thanks are due to Dr. Mary Warga and Mr. Marcus Morgan for making this examination. (15) Where possible the nomenclature of Lewis and Randall “Thermodynamics,” McGraw-Hill Book Co., Inc., New York City, 1923, is used.
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T. H. DUNKELBERGER AND A. L. ROBINSON TABLE I - A H , cal./mole CdSO, Runs 10" Runs 1.5' 4 515 + 4 ,01003 4 415 * 6 .002516 4 568 * 4 4 868 * ,005015 6 500 * 2 4 762 * ,001258 4 610: * 4 4 896 * ,002508 4 546 * 6 6 796 * .0006289 4 667 * 8 4 820 * .001254 6 587 * 3 4 731 * .0003144 4 818 * 6 4 785 * .0006269 6 569 * 7 4 711 * 0001572 8 562 * 7 4 638 * ,0003134 6 529 f 10 4 653 * .00007861 6 592 *
m2
Runs
0 005031
6 6 6 4 4 4 2 4 4 6 4 6
1111
0 8 8 4 4 2 2 1 .1
05 .05 ,025 ,015
0125
14 8 11 5 8
8 11 15
6 10
20°
968 * 8 837 * 8 987 * 4 852 5 992 i8 874 f 10 994 i1 889 * 5 879 f 10 813 * 10 763 5 719 t 9 f
f
16
Vol. ti0
The situation with cadmium sulfate and other 2-2 type salts3is complicated by the fact that the curves a t the lowest measured concentrations have slopes that are considerably greater than the limiting theoretical slopes (for 1-1, 2-1, and 1-2 type salts the situation is reversed). This may be due to incomplete dissociation, complex ion formation or some other factor. In any case, agreement with theory a t infinite dilution demands that the curves of Fig. 2 show inflection points a t some very low concentration. Ap-
timated experimental error and have extrapolated to infinite dilution accordingly.ll This was the procedure adopted with the sodium chloride measurements,6although some curvature a t the greatest
0
0.25
0.5 m'/f.
0.75
1.0
Fig. 1.-Integral heats of dilution of cadmium sulfate. The region to the left of the broken line is shown in Fig. 2.
dilutions was noticed. l6 The chord-area method of Young and Vogell' is undoubtedly better fordetermining the initial slopes of the heat of dilution curves provided that a suitable analytical expression for the results can be found. The extrapolation to infinite dilution with our method of plotting is somewhat more uncertain and limiting slope values obtained in this manner are not of high accuracy, but our procedure is adequate for determining values for the thermal quantities desired.'& (16) T h e choid-area method applied t o these d a t a by Young and Groeniers gave limiting slopes in excellent agreement with theoretical values. Similar treatment of the results obtained with 8 other 1-1 type and 17 salts of t h e 1-2 and 2-1 valence types by Lange and his collaborators gave limiting slope values t h a t in most cases are in better agreement with t h m r y t h a n t h e values obtained by linear extrapolation. Professor T. F. Young has kindly communicated this information. (17) F.Young and 0. G . Vogel, THISJ O U R N A L , 64,3025 (1932). (181 Lzvalues for sodium chloride solutions a t 25' calculated by t h e point t o point method [A. L. Robinson, ibid., 54, 1311 (193211 and t h e chord-area method IT.F. Younn and 0. G. Vogel, {bid., 54, : W J O (1032) 1 are i n excellent agreement although thc limiting slopes rc1)orted differ considergbly.
T.
0.04 0.08 na'/?. Fig. 2.-Integral heats of dilution of cadmium sulfate. The 15 and 20" curves have been displacd 100 and 200 calories, respectively. 0
parently our measurements have not been extended to sufficiently low concentration to reveal this effect. Although the unusually great length of our chords is a disadvantage in using the chord-area method, a plot of the chords showed no indication of a maximum slope a t low concentrations. Since earlier measurements with zinc and copper sulfates3 a t 25' extending to 4.6 X m also showed no evidence of a maximum slope,1° we feel that a linear extrapolation (19) Professor T. F. Young (personal communication) h a s found evidence for a maximum slope in the case cf calcium sulfate [E. Lange and J Monheim, 2.p k y s i k . Chcm., MOA, 349 (1931)Ja t about 0.001 7% and suggests t h a t if t h e maximum is due t o incomplete dissociation it might I J C expected to occur a t still smaller concentrations wit11 wrakcr sults.
Julie, 103s
I-IEATSOF DILUTION AND HEATCONTENTS OF CADMIUN SULFATE
of the experimental results will introduce no large error into the integral heat of dilution values, although it will not give a correct value for the limiting slope. This is evident from an inspection of Fig. 2 where several extrapolations fusing into the theoretical limiting curve are shown. We have arbitrarily added 15 cal./mole to the values for the integral heats of dilution obtained by linear extrapolation, to include probable approach to the theoretical limiting slope; this introduces a further uncertainty, of not more than 10 cal., into the values of Table 111. The values of the slopes used for the linear extrapolation are given in Table 11, together with theoretical values20s21 for the limiting slopes. TABLE I1 b AH,/dm'/2 t, "C.
10 15 20 25
Theor.
Lin. extrap.
-2840
-6330 -8320 -8800 - 10800(8)
-3144 -3472 -3816
Integral Heats of Dilution.-An attempt to find an empirical equation to fit the curves of Fig. 1 over their entire range was unsuccessful. The section of the 10' curve above m1l2= 0.05, however, was well represented by an equation of the type AH, = A The same type of equation fitted the 15" curve reasonably well but was quite unsatisfactory for the 20' curve. The equations are
-+
10' 15'
- AH- = 881.4 - 852.4e-7.36'n'/2 cal./mole - A H , = 1260.7 - 1173.9e-6.60m1/2 cal./mole
This type of equation has one serious defect; it has an asymptote a t or near the upper concentration limit of these experiments and therefore fails to follow the experimental trend at higher concentrations, where another inflection point and sharp rise3:22are indicated for the curves of Fig. 1. For this reason graphical rather than analytical values were used in obtaining derived quantities for the highest concentrations of these experiments. Table I11 lists values for the integral heat of dilution a t rounded concentrations read from the experimental curves of Figs. 1 and 2 (extrapolated as indicated above) and also, for 10 and 15', values calculated from the empirical equations for m"' > 0.05. The mean deviations of the (20) 0 . G a t t y , Phil. Mag.. 11, 1082 (1931). (21) G . Scatchard, ' h I S JOURNAr.. 65, 2037 (1931). ( 2 2 ) 11. U.Ilolhbocr, Z.p i r y ~ i l i Chcm., . 39,691 (19LIl).
1308
experimental points from the graphical values are 7.5, 10.8, and 8.0 cal. for the 10, 1.5, and 20' curves, respectively; mean deviations of calculated values from graphical values are 5.5 and 12.7 cal. a t 10 and 15'. There is little to choose between the two sets of values. Relative Partial Molal Heat Contents.The relative partial molal heat contents of the solvent and solute (E1and z2) were evaluated from the equations of RossiniZ3
The slopes necessary for these calculations were obtained by applying the differentiated form of Lagrange's interpolation formulaz4to the curves of Figs. 1 and 2 or by differentiation of the empirical equations given above. Values for El and ZZso obtained are given in Table IV. TABLE I11 INTEGRAL HEATSOF DILUTIONOF CADMIUMSULFATE SOLUTIONS - AH,, cal:/mole cadmium sulfate 111
Calcd.
0.0001 .0005 ,001 .005 .01 .05
48 127 185 365 473 717 798 850 873 880
.1 .2
.4 .8
100
Graph
Calcd.
48 127 185 367 467 718 816 845 887 882
68 171 248 47 1 590 924 1061 1162 1232
150
Graph
68 171 248 495 594 907 1020 1171 1257
20 0 Graph
73 182 263 556 088 1035 1179 1302 1435 1524
Relative Partial - Molal Heat Capacity.-To evaluate - C,o? values of 1 2 were plotted against t for each of a number of round concentrations and the slopes of the resulting curves were determined. Values for ZZa t 25' were taken from the results of Lange, Monheim and RobinFigure 3 shows some typical plots. For the short temperature range of these studies (10-25') a linear variation of with temperature was assumed and the straight lines best representing the results were derived by the method of least squares. The dilution measurements of although made with a less sensitive calorimeter and under less carefully controlled conditions, are of some
cp2
(23) F D. Rossini, B w . Slaiidards J. Rzseavch, 6, 799 (1931). (24) 1'.R . Running, "l?rni,irical Formulas," John Wiley and Sons, Iuc , New York, N Y . , 1017.
T. H. DUNKELBERGER AND A . L. ROBINSON
1304
Vol. GO
slope25,26for 25', 106 cal. mole-' degree-l, is also shown. Values for C,O, read from the smoothed curve are given in Table V.
cfi2 -
TABLE V RELATIVE PARTIAL MOLALHEATCAPACITY OF CADMIUM SULFATE cpz
-
cal./mole OC.
I17
5 12 15 26 31
0.uo01 .0005 ,001 ,005 .Ol
Zp* - e,"*
cal./mole O C
VI
0.05 .I .2 .4 .8
41 46 55 G6 79
Discussion 0
10
20
t , "C. Fig. 3.-Zz us. t . 0 , Plake; %, Lange, Monheim and Robinson; 0, this investigation.
interest for purposes of comparison. At about 21.3' Plake measured heats of dilution between 0.25 and 0.0002 M ; a few measurements were made a t about 12.2 and 0.3' between 0.1 and 0.005 iM. These results were plotted by the point to point method and after extrapolation to infinite dilution E2 values were calculated as indicated above. These values are shown in Fig. 3 although they were not used in computing the vs. t slopes. It is interesting to note that the most reliable of Plake's values (21.3') are in good agreement with our results. The values for 12.2 and 0.3" are uncertain to about 100 cal./mole because of the long extrapolation to infinite dilution so that the departures from linearity indicated in Fig. 3 cannot be taken seriously.
Calorimetric values for integral heats of dilution and relative partial molal heat contents may be compared with values obtained electrometrically by La Mer and Parks.* Evaluation of E2 values from calorimetric data involves a differentiation of experimental results with respect to concentration ; hence, values for integral heats of dilution should be more reliable. Evaluation of Z z from e. m. f . measurements similarly requires a differentiation of the experimental results with respect to temperature, while the determination of integral heats of dilution requires the subsequent integration of these values over a range of concentrations; hence, the integral heats of dilution should be less reliable than the values. Therefore, a comparison of ZZvalues is made, in Table VI, although our AH, values should be somewhat more reliable.
zz
TABLEIV RELATIVE PARTIAL MOLALHEATCONTENTS O F CADMIUM SULFATESOLUTIONS Lz,cal./mole cdpo4 LI, c a l . / m ~ l eH20 m
0.0001 ,0005 ,001 ,005 .01 .@5 .1
.2
.4 .8
100
67 168 254 486 588 851 893 902 908 913
150
92 225 316 639 780 1129 1234 1295 1357
zn
101 239 337 765 890 1259 1387 149b 1612 1716
15
100
-0.0435 -0.0439 - ,0338 - ,0343 - ,0011 - ,0012 - ,010 - ,013 - ,027 - ,032 - ,120 - .187 - .174 - ,318 - .188 ,437 - .262 - ,722 - .483
-
200
-0.0479 - ,0387 - ,0025 - ,019 - ,036 - .188 - ,475 - .765 -1.64 -4.23
The slopes of the curves of Fig. 3 are plotted against m'/' in Fig. 4. The theoretical limiting
0.4
0
Fig. 4.-Epz
-
0.8 vs. m'/?.
It is noted that the agreement is excellent a t the lower concentrations listed but the differexices a t higher concentrations are greater than ( 2 5 ) M. Randall and F. D. Rossini, THIS J O U R N A L , 61, 323 (1929). (26) V. K. La Mer and I. A. Cowperthwaite, i b i d . , 16, 1004 (19331
A THERMODYNAMIC STUDY OF THE CADMIUM-ANTIMONY SYSTEM
Julie, 1938
the estimated experimental errors. The most dilute solution used in the e. m. f . measurements was 0.0005 m, while our measurements extend to about 0.0001 m; La Mer and Parks extrapolated to infinite dilution with the aid of the extended Debye-Hiickel theory, while our somewhat shorter, semi-empirical extrapolation has been described above. Since the agreement is excellent a t the lowest concentrations it is evident that the discrepancies a t higher concentrations are not due to the different methods of extrapolation. Since La Mer and Parks have indicated the existence of certain experimental difficulties with their cells and since activity coefficients calculated from their data do not agree well with those found by Robinson and Jonesg it seems likely that some part of the discrepancy is due to unreliability of the e. m. E. measurements. Moreover, Harned,27by recalculating similar data obtained by La Mer and Cowperthwaite28with zinc sulfate cells, has found that the method of calculation used by La Mer and Cowperthwaite introduces uncertainties aside from those inherent in the experimental work. TABLE VI L?,cal./mole
111
0.0001 ,0005 .001 .005 .01 .02
Cal.
1ooc. E. m. f .
67 168 254 486 588 730
147 234 475 568 849
Cal.
CdSOd
15OC. E. m. f .
92 225 316 639 786 943
182 276 522 650 981
200C.
Cal.
E. m. I.
101 239 337 765 890 1037
239 327 581 740 1148
J O U R N A L , 69, 360 (193i). (27) H. S. Harned, THIS (28) V. K. La Mer and I. A. Cowperthwaite, ibid., 63, 2040 (1931).
[CONTRIBUTION FROM THE
1305
We have not recalculated activity coefficients for cadmium sulfate solutions a t 25" by correcting freezing point data with the 1 2 and - tit values reported here. Our measurements may be combined with the earlier, and probably less reliable, heats of solution measurements of Holsbeer,?? which extended from about 0.2 m to saturation a t several temperatures, to compute relative heat contents and heat capacities for the entire concentration range from infinite dilution to saturation. Values for also could be obtained by utilizing Holsboer's data. It is hoped to carry out these calculations in the near future. We are grateful to the National Research Council for two grants in aid which made possible the construction of the apparatus used in this investigation.
Summary Intermediate heats of dilution of aqueous cadmium sulfate solutions have been measured over the concentration range from 0.8 to 0.0001 m a t 10, 15, and 20' and have been extrapolated to infinite dilution to obtain integral heats of di1u'tion. No definite approach to the limiting law of Debye and Hiickel is indicated a t the lowest concentrations measured. Relative partial molal heat contents and heat capacities have been calculated for the temperature and concentration ranges of the rneasurements and have been compared with values obtained from e. m. f . measurements by La Mer and Parks. PITTSBURGH, PENNA.
DEPARTMENT O F CHEMISTRY O F THEC A R N E C I E
RECEIVEDMARCH 2, 1938
INSTITUTE O F TECHNOLOGY]
A Thermodynamic Study of the Cadium-Antimony System BY HARRY SELTZ AND B. J. DEWITT The phase equilibrium relations in the cadmium-antimony system have been studied by several investigators.' Thermal, microscopic, Xray and conductivity methods have been employed. Hansen,2 from a critical review of these data, accepts the diagram of Murakami and (1) Kurnakov and Konstantinov, %. anorg. C h i n , 58, 1 (1908); Treitrchke, 2 . anorg. allgem. Chrm., SO, 217 (1906); hlurakami and Shinagawa. Kineoku *to Kenkyu, 6,283 (1928). (2) A t . Hansen, "Der Aufbau der ZweistoWegierungen." Verlag von Julius Springer, Berlin, Germany, 1936.
Shinagawa which will be used in several calculations in this paper. Two intermetallic compounds are formed, CdSb and CdrSbz. The former is stable to its melting point, 4 5 5 O , while the latter is metastable a t all temperatures and melts at 420'.
I n pursuance of a program of investigation of the thermodynamics of metal systems, this paper describes the results of an electromotive force study of liquid cadmium-antimony solutions.
