400, and a t 425' the reaction rates were determined for the principal primary reaction. Evidence is presented concerning the other reactions involved. 2. The principal primary reaction is skowri to be HCOO&Hs
+CzHa
+ HCOOH
This is followed by the decomposition of formic acid
+ +
IlCOOH +CO HZ0 HCOOH +COX HP XHCOOH ---+ COz HCHO
+
+ HzO
3. Evidence is presented that minor primary
reactions occur, and the nature of these reactions is suggested. 4. Calculated from the present data, the energy of activation of the reaction producing ethylene is 40,010 cal. HOUGHTON, MICHIGAN
RECEIVED AUGUST10, 1939
{CONTRIBUTION FROM THE RESEARCH LABORATORY OF PHYSICAL CHEMISTRY, MASSACHUSETTS INSTITUTE OF TECHNOLOGY No. 4273
Vapor-Liquid Equilibrium. IV. Carbon Tetrachloride-Cyclohexane Mixtures1 BY GEORGE SCATCHARD, S. E. WOODAND J. M. MOCHEL The gas heater for the equilibrium still was replaced by In the third paper of this series,2 we showed that benzene-cyclohexane mixtures have an en- an electrical heater with a Variac control which greatly the accuracy of the regulation of the boiling. tropy increase on mixing which is larger than that increased To prevent direct radiation t o the thermometer, the of an ideal solution even at constant total volume, bottom of the glass still is painted with black stovepipe and which we attributed tentatively t o some lack enamel which is renewed when necessary. A hood of of randomness in at least one of the pure liquids. aluminum foil is placed over the top of the still, and for Since earlier calculations3 had given no indica- temperatures of 60" or higher a shield of aluminum foil is placed around the still. This protection prevents the tion of such an effect for benzene-carbon tetra- increase of material in the inner boiler during the runs a t chloride mixtures, and since cyclohexane has high temperatures, but does not affect the decrease during an unusually small entropy of fusion, we have the low temperature runs The thermocouple was recalibrated from 60 to 100' as next studied carbon tetrachloride-cyclohexane mixtures. Although there is a slight excess en- before by measuring the vapor pressure of water and determiaing the temperature from this pressure by the tropy of mixing at constant total volume, i t is equation of Smith, Keyes and Gerry,4 and the low temless than a tenth of that for benzene-cyclohexane perature calibration was checked by a determination of mixtures. Mixtures of cyclohexane with carbon the transition point of sodium sulfate decahydratc tetrachloride agree with simple theory in every Measurements of the vapor pressure of cyclohexane respect more closely than do those with benzene. agreed with those with the gas heated still except at 30 The cyclohexane was purified as in 111. Muck c. P. carbon tetrachloride was refluxed for eleven hours with an aqueous solution 10% in potassium permanganate and 10% in sodium hydroxide. The carbon tetrachloride was distilled off, dried with calcium chloride and rectified in the column described in Paper 111. The boiling points of the products and of the rejected portions were measured in a small Cottrell apparatus with a five-junction thermocouple. The n o m 1 boiling points, which should be used €or relative values only, are: CCli
Product
76 69
Tops Bottoms
75 93 76 54 76.67 76.69 76.72 76.68 76 68
Tops Bottoms
79.29 80 41 80.69 80.68 82.64 80.99 80 74
CsHir
Product
80 73
(1) Presented before the Division of Physical and Inorganic Chemistry of the Atneriean Chemkd Society, September 14, 1939 (2) I and 11 are published in THISJOVRNAL, 60, 1275, 1278 (1938). and 111 in J . Phys. Chern., IS, 119 (1939). (3) George Scatchard, Trans Poraday SJC, 89, 160 (1937)
and 35'. Apparently there had been radiation from the flame t o the thermometer which cancelled out a t those temperatures a t which the calibration had also been carried out in the still. So the measurements for benzene at 30, 35 and 40" were repeated, and new equations were derived foi cyclohexane and benzene. The equations are CCL: log pi = 6.68148 - 1045.022/T CeHii: log p z 6.65859 - 1040.641/T CsHtj. log pa = 6.66457 - 1007.742/T
-
99,577/T2
- 104,865/Te - 116,197/P
+
(2' = f 273.16.) Thestandard (root mean square) derespectively. The viations are 0.5, 1.3 and 1.5 X normal boiling point of carbon tetrachloride is 76.68,". Timmermans and Martin6 give 76.75. The new boiling points of cyclohexane and benzene are 80.738 and 80.106', which are 0.004 lower and 0.005°higher than our former values. The values of the vapor pressures of these three substances at rounded temperatures are given in Table 11. (4) I,. B. Smith, F. G. Reyes and 13. T.Gerry, Proc. A m . Acad. A r l r and Sci., 69,137 (1934). i.5) J . 'I'immermens and F. Martin, J . ckim. fihrs., I S , 747 (1926).
Nov. , 1939
EQUILIBRIA OF CARBON TETRACHLORIDE-CYCLOHEXANE MIXTURES
3207
The compositions were determined from the densities at 2 5 O , which are given by the equation
+
d = (0.77383 0.81031 ~ i ) / ( lf !&%z/150) (1) = 1 - e2 = 1/(1 wzdl/wldz) (2)
21
+
in +hich WI is the weight of carbon tetrachloride, dl its density, and z1 its volume fraction, and W Z , dz and zz are the corresponding quantities for cyclohexane. In Table I are given the weight fractions and mole fractions of carbon tetraTABLEI DENSITIESOF CYCLOHEXANE-CARBON TETRACHLORIDE AT 25" MIXTURES Weight fraction CClr
Mole fraction cc14
Density
0.0000 .2053 .3744 .5177 .6369 ,6434 .7530 .7530 ,8458 .9268 1.0000
0.0000 .1238 ,2466 .3699 .4897 .4968 .6251 .6251 .7500 ,8738 1.0000
0.77383 .86401 .95609 1.05106 1.14605 1.15162 1.25638 1.25646 1.36199 1.47019 1.58414
Deviation from eq. 1
..... -0.00003 .00008 .00011 .00016 .00006 - .00018 - .00010 - .00009 .00010
+ + + + +
.....
100VM/Vo
... 0.069 ,108 .140 .151 .161 .175 .168 .139 .078
...
chloride, the measured densities, the difference of these densities from those calculated by equation 1, and the measured values of 100VM/Vo. V is the volume of the mixture, Vothat of the unmixed components, and VM = V - Va. From equation 1, it follows that VM/vQ = 2122/150
0.50 0.75 1.0 Xl . Fig. 1.-Vapor pressure os. mole fraction for carbon tetrachloride-cyclohexane a t 40'. 0
0.25
and the liquid composition as abscissa. The curve just below it and the flagged circles have the vapor composition as abscissa, and the two lower curves are the derived partial pressures with the liquid composition as abscissa. The broken lines are the Raoult's law lines for the total and partial pressures os. liquid composition.
(3)
There is a systematic error in these results which corresponds to a loss of 2 4 mg. of the component first weighed out, and which we confirmed later as the approximate loss by evaporation between the two weighings. Since this corresponds to only 0.01-0.0270 in the composition, it was not considered worth while to repeat these measurements with a different technique, but we have used equation 1 to determine the equilibrium compositions. Vapor-liquid equilibrium measurements were made a t intervals of approximately one-eighth in the mole fraction a t 40 and 70' and for a single mixture, about 50 mole per cent., at 30, 50 and 60'. For mixtures containing more than 4Oy0 carbon tetrachloride, nitrogen replaced helium as the confining gas. The measurements at 40' are shown in Fig. 1, in which the curves are determined from equations 6,7,14 and 15 and the circles are the individual experimental points. The top curve gives the equilibrium pressure as ordinate
TABLEI1 VAPORPRESSURES OF PURESUBSTANCES Temp.,
OC.
30 40 50 60 70 80
Carbon tetrachloride, mm.
141.55 213.34 312.04 444.28 617.43
....
Cyclohexane, mm.
Benzene, mm.
121.60 184.61 271.80 389.29 543.95 743.27
119.16 182.70 271.34 391.6fi 551.03 757.56
The measurements are reported in detail in Table I11 as mole fraction of carbon tetrachloride in the liquid and in the vapor, equilibrium pressure, and the derived excess free energy of mixing. After each of the last three is given the deviation of the corresponding quantity from that calculated by equations 6, 7, 14 and 15. After the measurements with mixtures there was a distinct odor of phosgene which was stronger from the condensate than from the liquid and which increased after each measurement. Therefore three approximately equimolal mixtures
GEORGE SCATCHARD, S.E. WOODAND J. M. MOCHEL
3208
0 . 1 2 6 2 0 . 1 5 1 5 -0.no06 ,3822 - ,0008 ,2453 ,40G6 - , 0 0 0 8 ,3669 ..?lo3 - ,0010 ,4739 .3474 - ,0029 ,5151 ,5116 - .ooin ,4753 ,6341 - ,0008 .606l ,7642 . 7 7 m - .a004 ,8786 ,8822 - ,0002 ,1455 -- ,0002 70’ ,1248 ,2787 ,0002 ,2468 .3640 .3981 - ,0003 .5150 - ,0003 .4836, .?I473 ,001; ,5153 4796 .5113 i= .00lKl , 6074 . li320 .0004 ,7535 .oom ,7880 ,8757 .851S - ,0001 500 .4728 .:114 - ,0010 ,5173 - ,0006 Coo ,4829 .5137 -- ,0006 60’ ,4810
40’
+
+ -
190.62 185.62 2oo.m
203.40 204.~ 203.45 206.97 210.15
212.04 558.78 571.59 582.59 591.57 594.42 501 . 7 3 600.52 m3.79 ti13.!37 154.73
298.44 425.34
i-0.00
8.77 11.50 .02 1 4 . 6 2 - .06 15.61 1 - . 0 5 15.90 - . 0 5 15.65 - .O6 1 5 . 1 6 - .05 1 2 . 0 1 - .03 7.10 .06 5.58 .n5 1 0 . 1 9 .17 1 3 . 0 3 . l l 13.89 := .00 13.90 .06 13.92 .(I9 1 3 . 4 8 ,435 1 0 . 7 9 . l 0 6.50 * .OO 16.38 .01 1 5 . 2 3 .04 1 4 . 5 7
+ .ni
+
+0.05
+ + + -
.IO .18 .13 .09 .07 .I1 .OF
- .09
+ + +
-c . i n 4- .04
-+ + +
+ + + +
-
-
+
.n2
- .lo - .15 - .06
- .os
equations of the deviations from equation 4 is entirely negligible, and the effect of deviations from equation 5 may probably be neglected. For p1 and 6 2 we have used 0.9 the value calculated by the theory of corresponding states from the equation of Keyes, Smith and Gerry’ for water vapor. The values for carbon tetrachloride are one-sixth to one-third larger than those measured by Eucken and Mayer,8 but their measurements with carbon tetrachloride do not seem consistent with those on other gases. These results may be expressed by the equations F = (1.3333 - O.oOB916T) I/,OZ~ZZ (11) in which V,”= xllil xZTV2 = ‘Ip/(Nl Nz)
+
.O6
+
ICV = I3335 ‘v,oZ,z.2 S,” = 0.0022916 L’~ZI,ZJ pf = (1.3335 - 0 . 0 0 2 2 9 1 6 T ) V ~ ~ ~ ~ p t = (1.3335 - 0.0022916T) Vzz12
.I? .10 .07 = .00
were studied a t 40 and a t 70”. The first was the last of a series which included all those preceding it, the third was the last of a series which included all those following it run in the order opposite to that of the table, and the second was made up fresh from the components. The first and third check extremely well, and the deviations of the third are in opposite directions at the two ternperatures. A test with #-dimethylaminobenzaldehyde6 indicated less than 0.005% phosgene. This confirms the evidence from the equilibrium measurements that the effect of the phosgene is negligible. In I1 it was shown2that, if the liquid and vapor volumes are given, respectively, by
Vol. 61
(12) (13) (14) (15)
The calculated results from which the deviations in Table I11 are calculated are from equation 11 for F f , and from the combination of equations 6, 7 , 14 and 15 for P and y1. The constants are chosen to give the average at 40 and 70” and a linear variation of of F f with the temperature. The average deviation is 0.07% in y 1 and about 0.01% in P. Although the equation is simpler than that of 111, the agreement is considerably better than in that paper. There is no indication that a more complicated function of the composition or of the temperature would be preferable. The solutions are far from regular. The ratio of the temperature l - / ( N l f N 2 ) = T’,r, + t;r* (4) coefficient of equation 11 to the constant term I”,’(Ni + N?) = R T / P Piyt 4- 8 2 ~ ( 5 ) is 0.0017. The corresponding coefficient for the excess chemical potentials and other excess benzene-cyclohexane mixtures is 0.0019. thermodynamic functions are given by For theoretical purposes we are interested in the mixing process a t constant total v01ume.~ We pf = RT In PyllPtxl .t (PI -- S‘l)(P - PI) ((7) will designate the functions calculated for this p.,“ = R T In Pyz/P~r2 (& - VZ)(P- Pz) ( 7 ) process with a subscript >., and the values measF,” FE,’(iV, + iv,) = t, ,$ + l.2 ,f (8) ured a t constant pressure with a subscript p . .TF = -(dF,E/dT),,\ (9) We apply the equations as in 111, using for the 31; = Elf = Ff +- TS; (10) coefficients of thermal expansion and of comin which NI and NZ are the numbers of moles of pressibility and their ratio a t 25’ the two components, x 1 and xz are the mole fraca0 = 1.228(1 - 0 . 0 1 8 ~ )X tions in the liquid, y1 and ya the mule fractions in do = i . i o ( i + o.oo9z2) x 10-4 the vapor, P is the vapor pressure of the solution, (aa/@o) = 11.16(1 - 0.0272~) PI and PZare the vapor pressures of the com(d In @/dT = 0.0076, which is its value for ponents, VI and VZare the molal volumes of the carbon tetrachloride as well as for benzene. liquid components, and PI and & are functions of V: = 97.111/(1 - 0.1070622) cc./mole the temperature, each characteristic of one of the (7) P. G . Keyes, L. B . Smith and H.T.Gerry, Pro6. A m . Acad. components. The effect on the subsequent Airs ond Sci , 70, 319 (1936)
e
+
+
E
(6) L.Rosenthaler, Pharm. 4cm Reln , 14, 8 (1937)
(81 A. E u c h and L Mapar, 2 physk. Chrm.,
BI, 462 (1929).
Nov., 1939
EQUILIBRIA O F CARBON
Then at 25' d: - F," = (Va/2P)(VM/V0)' (dt - F:), 0.004891 X 97.111 ~
TETRACHLORIDE-CYCLOHEXANE MIXTURES
3209
+
i ~ ~ p ~ / 0.00922) ( l (1 0.10706~~) cal./mole (16) S l - S: = - VMao/po ( V0/2p)(V M / V Q )d2 In p / d T (S: - Sf)* = -0.001802 X 97.111(1 - 0.027Zz)ZiZz/(1 0.10706~~) -I- 0.0076(A: - F:) cal./mole ' C . (17) (18) = T(S? - S:)= (A: - F:)= (E:
+
-
+
-
In Fig. 2 are shown Ffx at 25' and at 70' from equation 11, HZ from equation 12, and EE a t 2 5 O , calculated from HZ and equation 18. The difference between A t x and a t 25' is less than half the width of the line, so the same curve may serve for both. TStx is the difference between the top curve and the third, and TStx is the difference between the second curve and the third. This second difference is less than a quarter of the first, so three-quarters of the deviation from regularity is accounted for by the change in volume on mixing. These mixtures are so nearly ideal that we should expect the deviations from random distribution to have a very small effect. Using, as in 111, Kirkwood's equationg for this effect for a mixture of spheres of equal radii, each with eight nearest neighbors, and with the same value of E 2 for an equimolal mixture as for carbon tetrachloride-cyclohexane, 20.7 cal./mole, we obtain
ex
E,M, =
BizXiXZ
-
(Biza/4RT)~1%z2
20.7 = B n / 4 - Biia/64RT Biz = 84 E$ - d ! % = (- S ~ Z / ~ R T ) X I % ~ ~ ~ = -0.09 cal./mole, when X I = 0.5
(19)
(20)
This effect is very small compared to the measured difference of +4.0 cal./mole. The difference of 4 cal./mole is so small that it is well to consider the corresponding difference in the more familiar quantities which are directly measured. The effect on y1 is very small and may be neglected. In an equimolal mixture the measured pressure is 2.63% greater than that calculated by Raoult's law at 40°, and 2.17% greater a t 70'. This decrease of 0.46% would be only 0.18y0 if the solutions were regular. Of the remaining 0.28%, 0.22% is accounted for by the volume change on mixing, and there is only O.O6y0 left unexplained. However, our measurements are so precise that we believe that the uncertainty of this figure is less than 0.0270 or less than one-third its value. (9)
J. 0. Kirkwood, 1.Phys. Chrm., U , 97 (1B99).
0.25
0
0.50
0.75
1 .o
x1.
thermodynamic functions for carbon tetrachloride-cyclohexane.
Fig. Z.-Various
We are particularly interested in the comparison with benzene-cyclohexane mixtures, for which the unexplained difference is 50 cal. per mole, or thirteen times as great as for carbon tetrachloride-cyclohexane. If the explanation is to be sought in incomplete randomness in one of the component liquids, not more than one-thirteenth is contributed by the cyclohexane unless there are compensating effects in the mixtures of cyclohexane with carbon tetrachloride. However, earlier measurements indicate that benzene-carbon tetrachloride mixtures are almost regular. We are a t present making further measurements on this system. With the assumptions that the cohesive energy density, a = ( E - E,J/V, is equal to -(dE/bV), and that Sf is zero, E? may be computed from VMand /3 by the equation E: = V'/p
(211
This leads to a value of 41 cal. per mole for an equimolal mixture, which is approximately twice as great as the directly determined value of 21 cal. per mole and is even larger than the heat of mixing at constant presstire, which is 34 cal. per mole. The absolute difference is not, however, so very great. From the equations for the vapor pressures of the components, the equations for the deviations from the perfect gas laws, and the densities of the components at 25', the cohesive energy densities of the components are calculated as all = -72.96 and &a = -66.54. The assumption
3210
A. JOHNSTON EVELYN LAINGMCBAIN,WALTERB. DYEAND STEWART
Vol. 61
Summary The vapor-liquid equilibrium pressure and compositions of carbon tetrachloride-cyclohexane E,"I = --(\',G - daG)~v:zlz2 (22) For an equimolal mixture this yields E% = mixtures have been measured at 40 and 70" over 3.8 cal. per mole instead of the measured 20.7. the whole composition range, and a t 30, 50, and However, if we calculate -UIZ from the relation 60" for approximately equimolal mixtures. The densities have been determined at 25'. E Z = (2a12 - all - (1.22) i'O2,ZZ (23) These measurements have been expressed and the measured 20.7 for equimolal mixtures, we analytically, and corresponding equations derived obtain -as = 69.34, which is only 0.5% less than for the thermodynamic functions, including the 4 7 2 . 9 6 X 66.54 = 69.67. So, quadratic combi- energy and entropy of mixing a t constant total nation gives a very good approximation for uf2, and volume. the small error is in the direction predicted by the The dependence upon composition agrees with quantum theory. The treatment of solutions the predictions of the simple theory. The deviamakes too drastic demands for a simple theory tion from regularity is relatively large but most of in requiring a small difference between large it is explained by the volume change on mixing. numbers. On the other hand, measurements on The unexplained entropy increase on mixing solutions afford a correspondingly accurate meas- is only one-thirteenth as large as for benzeneure of one of these quantities if the others are cyclohexane mixtures. known. CAMBRIDGE, MASSACHUSETTS RECEIVED AUGUST29,1939 that the mutual energy per unit volumes, equal to -2 leads t o the result
[CONTRIBUTION FROM THE
a12,
is
DEPARTMENT O F CHEMISTRY, STANFORD UNIVERSITY]
Solutions of the Paraftin-Chain Sulfonic Acids as Colloidal Electrolytes BY EVELYN LAINGMCBAIN,WALTERB. DYEAND STEWART A. JOHNSTON Colloidal electrolytes since their first recognition by McBain in 1913 have received steadily increasing attention, because of their interesting departures from the behavior of ordinary electrolytes and because they embrace such large groups of substances. The soaps originally studied do not lend themselves to precise examination in very dilute solution on account of the prominent effects of hydrolysis. It remained therefore for Lottermoser and Piischell to show that in great dilution many non-hydrolyzable salts of alkyl sulfuric acids conform to the behavior of the Debye-Huckel theory, rather suddenly departing from it a t a very low concentration designated, by Bury and collaborators, the critical concentration for micelles. This has been confirmed by many subsequent investigators, and necessitated a modification of the original formulation to conform more dosely to later conceptions of interionic attraction. Different authors, however, differ in their sirable to have exact different properties of a non-hydrolyzable pure (1) Lottermoser and Puschel, Kolloid 2 , 68, 175 11933)
material of simple chemical composition sufficiently soluble that it may be studied over a wide range of concentrations. The present communication comprises measurements of lowering of freezing point, conductivity, viscosity and density of straight chain sulfonic acids with special emphasis upon dodecyl sulfonic acid. The results for diffusion have been published2 and a provisional discussion is being given elsewhere,aalthough it is not until our measurements of transport number are completed that a sufficient number of equations will be available for a deiinitive solution of the problem, except in its principal outlines which are already generally known, Experimental An especially pure preparation of laurylsulfonic acid was made by M. E. Synerholm by the method of Noller and Gordon4; its equivalent weight by titration was 100.05% of the theoretical, the excess probably being water. The other sulfonic (2) Evelyn Laing McBaio, Proc. Roy. SOC.(London). A178,415 (1939). (3) Van Rysselberghe, Colloid Symposium, 1939. '4) Noller and Gordon, THIY JOURNAL, 55, 1090 (1933).
