1 0.50
J. E. JOLLEY
AND
J. H. HILDEBRAND
the separation of charge in the activated complex is not great. This is confirmed very nicely by studying the effect of adding small amounts of polar substances and of salts on the rates in a non-polar solvent. Such addition has a. very great influence 1 m the equilibrium constant for primary amines m d virtually none for tertiary amines presumably because of interaction with the excess acidic protons in the former case.4 Table I11 shows a comparison of the increases in rate in benzene caused by small additions of ethanol, or tosylate salts, and the corresponding changes in the equilibrium constants for reaction 2. The much smaller changes in the rates show that the transition state while polar is not strongly so. In view of this i t is surprising t h a t triethylamine does not show up as a stronger catalytic base in all of the solvents and, particularly the more basic ones. I n these cases the relative weakness of tertiary amines, as judged by equilibrium studies, was attributed to solvation of the excess acidic protons of the primary and secondary ammonium ions. Such effects should be smaller in the rate studies as demonstrated above. The additional complicating factor seems to be that of steric hindrance in the rate studies (of the F-strain type). The tosylate compound is much more blocked toward proton removal than nitroethane, for example. Thus in 50% dioxane-water trimethylamine reacts twice as rapidly with the tosylate compound as does triethylamine even
TABLE 111 THEEFFECTS OF
-ADDING S M A L L AAMOUSTS O F .AI,COriOI,
k
SALTSTO BESZENEAT 25" ON B f RHOTs --+R
ASI)
+ HH ~'-.
OTs-
n n-Hexylamine Triethylamine
70e t h y l 0,00
Mole
alcohol K(M
4.20 0.00 4.20
-1
hr.
2.19 8. OS 3.18 3.11
-1)
K" *i:j*
1600'' 2700b 2700'
Added n-Iiexylammoniuin p-toluenesulfonate, -11 n-Hexylamine 0.00 2.19 50 3.06 x 10-3 8.80 2300 -%dded di-n-butylammonium p-toliienesulfonate, .'I1 Di-n-butylamine
0.00 4.80
7.04
4.64
x 10-3 x 10-3
7.62 7.88
950 4.500 ..
Ion-pair formation constants using 2,4-dinitropheiiol as reference acid. * In chloroform solvent. Very similar results would be expected in benzene. a
though the latter is a ten times stronger base in water. With nitroethane as a substrate, triethylamine reacts 1.5 times as rapidly as trimethylamine. Bv this argument all of the rates for triethylamine in Tables I and I1 are low by roughly a constant factor because of steric strain in the transition state. EVANSTON, ILLINOIS
[ C O N r R I B U T I O N F R O M DEPARTMEKT O F CHEMISTRY, UNIVERSITY O F CALIFORNIA A T B E R K E L E Y ]
Solubility, Entropy and Partial Molal Volumes in Solutions of Gases in Non-polar Solvents B Y J. E. JGLLEY 4ND J.
H.HILDEBRAND
RECEIVED ACGUST13, 1937
1 critical revim7 of such gas solubilities a s appear t o be sufficiently reliable for our purposes reveals t h e following relations. (a) For a given gas at 1 atmosphere and 25' dissolving in a series of Solvents, log x~ (Y? E mole fraction of gas) decreases iyith increasing solubility parameter, al, of t h e solvent. (b) For different gases in t h e same solvent, log x 2 increases linearly xyith increasing Lennard-Jones force constant, e l k , of the gas. (c) T h e entropies of solution of different gases in the s a n e solvent vary linearly with R In x2, and extrapolate a t x 2 = 1 t o t h e entropy of condensing t o pure liquid t h e vapor of t h e solvent from a hypothetical pressure of 1 atmosphere. T h e temperature coefficient of solubility may thus be obtained from its isothermal value. Solubility increases with temperature for common solvents when x? is less than about and tiice verso. (d) The partial molal entropy of solution of any one gas from 1 atmosphere t o t h e same mole fraction (here 1 0 - 4 ) is nearly the same in all solvents except fluorocarbons, where i t is a little greater. I n any one solvent, it increases in going t o gases with smaller force constant. This is attributed mainly t o increase in freedom of motion of t h e adjacent molecules of the solvent rather than t o change in t h e behavior of t h e gas molecule in a "cage." Partial molal volumes of hytlrogen, deuterium and argon have heen detcrminctl in :L varietJ- of solvents. The results accord with t h e above interpret:ttiun.
Progress toward a satisfactory theory of gas s o h bility has been difficult because of the inaccuracy of much of the published data and the failure to cover a range of temperature sufficient to yield figures for the entropy of solution. -111 outstanding exception has been the broad work of Horiuti,' published in 1931. The need for precise, conipreherlsi\.-e data has recently been partly met by Cook a n d Hanson2 and by Cook, Hamon and Alder3 for (1) J. H o r i u t i , Sci. Papers, Inst. P h y s . Chem. R e s c w r h , T o k y o . S o . 3 4 1 , 17, 125 (1931). (2) 11. W. Cook a n d D. N. H a n s o n , University of California K a d i a tion 1,aboratory R e p < l r t , TTCRI>?15,9 fF!l.j4); Re% .S(i I U S ~, 28 (195;).
hydrogen and deuterium, and by Reeves and Hildebrand? for argon. Clever, Battino, Saylor and C>rossj h:ive kindly put a t our disposal in advance of publication their results for helium, neon, argon and kry-pton. 1 %can ~~ utilize, further, data by for helium, neon and argon in tTTo sol. (3) hl. W.Cook, D. N. H a n s o n a n d B.J , Alder, J . Chem. Phrs.. 26,
,,
J O U R N A L , 7 9 , 1313 7 4 y y 7 ! & Reeves and H. Hildebrand, (1951). ( 5 ) H. L. Clever, R . B a t t i n o , J . H. S a y l o r a n d P. N. Gross, J Phrs. Chem., 61, 1018 f1957). ( h i A I.annurig:, l'rirs J O U R N A L , 62, CS (1930).
GASSOLUBILITIES IN NON-POLAR SOLVENTS
March .5. 1958
10.51
vents; by Gjaldbaek and Hildebrand for nitrogen’ interaction in these cases. The reversal of slope and chlorine8; by Gjaldbaek for carbon m o n ~ x i d e , ~in going t o the more soluble gases is in harmony oxygeng and carbcn dioxidelo; and by Taylor and with the fact that the molecular force field, of, say, chlorine, is nearer to t h a t of carbon tetrachloride Hildebrand for chlorine. l1 Tabfe I gives the figures for solubility that we than to the field of a fluorocarbon. Solubility and Force Constant of Gas.-In Fig. 2 select, expressed as mole fraction of gas, x2, a t 1 atmosphere and 25”. Table I1 gives figures for the are plotted values of log x2 for many cases in the entropy of solution under the same conditions, three solvents for which we have the most data vs. obtained from the slopes of the lines of log x2 lis. -1.5 log T , and the reasonable assumption that Henry’s law holds for such dilute solutions because solutesolute interactions are negligible. Gaps in these tables emphasize the need for additional data. Solubility and Solubility Parameter of Solvent.-Figure 1 shows the relation of the solubility of each gas, plotted as log x2, to the solubility -2
>(”
/
0
0 1
-3
+
*
Y v
CH4
*
-/
L
Kr 0 CpHg
,
0
IO0 FORCE C O N S T A N T , Fig. 2.
\
\
O
1
I
I
I
I
6
7
8
9
IO SOLVENT.
SOLUBILITY
PARAMETER
co
o A
/
-4
N2
OF
Fig. 1.
parameters of the solvents, 61. 1T-e use mole fraction instead of concentration, as in an earlier paper,12 for reasons that will later be apparent. This plot would permit a fairly good prediction of the solubility in a new solvent of any of the gases represented. Such divergent points as the ones for C2Hzand CO, in CcH6 indicate chemical effects, acid-base JOURNAL, 71, 3147 (7) J. C. Gjaldbaek and J H . Hildebrand, THIS (1949). ( 8 ) J . C. Gjaldbaek and J. H. Hildebrand, ibtd., 72, 609 (1950). (9) J. C. Gjaldbaek, A d a Chcm. Scand., 6 , 623 (1952). (10) J. C.Gjaldbaek, ibtd., 8, 1398 (1954). (11) N. W. Taylor and J. H Hildebrand, THISJOURNAL, 45, 682 (1923). (12) J. H. Hildebrand, J . Phys. Chem , 68, 671 (1964).
2 00 Elk4,
the Lennard-Jones force constants of the gases, e/k, as given by Hirschfelder, Curtis and Bird.13 It will be seen t h a t the correlation, except in the case of hydrogen, is excellent. It would appear possible to predict the solubility of another gas in any of these solvents with good approximation. The displacement of the lines corresponds to the solubility parameters of the solvents. Solubility and Entropy of Solution.-Figure 3 is a plot of the entropy of solution, S , - s2g, from gas a t 1 atmosphere t o solution a t the equilibrium concentration, x2,against R In xB. I t shows a remarkably close correlation for different gases in the same solvent, except for the small displacement of the line for the hydrocarbon gases, and relates thc solubility of a gas to its temperature coefficient in a particular solvent. Descent along a line corresponds to chanjging to a gas more like the solvent in force constant, ending a t R In xz = 0 for the solvent itself. The entropy of condensing carbon tetrachloride vayor a t 2.5’ (13) J . 0. Hirschfelder, C. F. Curtis and R . B. Bird, “l\.lolecular Theory of Gases and Liquids,” John Wiley and Sons, N ~ S W York, N. Y.,1954, p. 1110.
J. E. JOI,I,EY
1052
AND
J. H. HILDEBRAND
1701.
SO
IC
8 SOLVENT
6
”
4
2 -
CrFl6
A
t-CeH18
3
CClq
L?
C6H6
0
cs,
9
sj-s, 0
-2 -4
-E -8 -I
c
-20
-i
E,
-12
-14 h’
b-1
x;1
--
I r,
9
Fig. 3.
and 115.3 mm. is -26.3 e u . ; from hypothetical vapor a t 1 atmosphere this would he -22.5 e.u., qgreeing remarkably well, in view of the long extrapolation. with the intercept of the CCI4line a t R In x. = 0, which is -24 1 e u. The agreement is equally good for benzene. The long-puzzling question of the temperature dependence of gas solubilities is answered by reference to Fig. 3. The entropy of solution in benzene, for example, is positive for any gas for which x2 < 8.9 X its solubility would therefore increase with temperature. The reverse is true when X? > s.0 x lo-‘. Entropy of Transferring Gas at 1 Atmosphere into Solutions a t Same Mole Fraction.-Reeves and Hildebrand4 pointed out t h a t the greater entropy of solution of argon in a poorer solvent is mainly the result of the additional entropy of clilution, and that the differences largely disappear if arqori a t 1 atmosphere is transferred into difTerent The solvents Jt the same mole fraction, entropy ol^ dilution from .Qfor gas at 1 atmosphere to lop4 is equal, according to Henry’s law, to the entropy of expanding the gas from 1 atmosphere t o s ~ , / ~ Oatmospheres, -~ which is R In 104x2. Table I11 gives representative values calculated by adding this term to corresponding values given in Table I J The gases and solvents are arranged, as in Table I , in order of increasing force constants and solubility parameters, respectively. One sees t h a t the figures for any one gas in different solvents (lo not differ significantly, except in the fldorocarbons, where they are distinctly larger, but t h a t they fall off
horizontally from left to right for different gases in the same solvent, in accord with their rapidly increasing force constants. The significance of these relations is discussed below. Partial Molal Volumes.--The obvious connection between entropy of solution and partial molal volumes14made it desirable to have reliable vducxs o f the latter quantity for sonic of the solutioris considered in our survey. (a) Materials.-Argon gas was used directly from a cylinder of Linde “Standard Grade” Argon. A inass spectrographic analysis showed it t o be 99.77,argon. The hydrogen and deuterium were 99.7 and 99.47~-pure,respectively. Isoiictane was a Phillips “pure” product, dried with anhydrous magnesium perchlorate and fractionated through a 1.i-plate column. J. T.. Baker “purified” bromoform was dried over calcium chloride and distilled twice over argoii. The remaining solvents were purifed as described previously b y Reeves a n d Hildebrand.4 ib) Apparatus and Procedure.--Tlie apparatus \vas essentially t h a t devised b y Horiuti‘ and consisted of a gas b w e t connected by a loop of glass capillary tnbing to t h e dilatometer irnmersed in a wcll-stirred thermostat, wliose temperature was kept constant t o within + O . O 0 l o . The tlilatotneter consisted of a bu:b of approxitnately 130-nil. capacity entered a t t h e lower end by two calibrated capillary side arms (about 2 cu. piin./cm.). One arm is connected t o the gas buret and t h e other is led upward and left open t o atmospheric pressure. hIercury in the bottom of tile dilatometer serves t o isolate the solvent in the bulb and 3150 indicates its volume b>- the pwition of the mercury tiireads in the sidearms. Sealer1 into the bulb was R small glass enclosed piece of soft iron ~ v h i d could i be agitated from outside hy nieans of a magnet. (14) Cf. J. €1. Hildebrand and R . I,. S c o t t , .I. C - h e n ~ . P h y s . , 2 0 , 1520 (1952); J . H. Hildebrand anti I). S . Glew. .I. Phys. Chem.. 60, C I D (19,ili); I.. W. Reeves and J. 11. I l i l d e l ~ r ~ ~i rb ~f kd, , 60, Ill9 (lU56).
GASSOLUBILITIES IN NON-POLAR SOLVENTS
March 5 , 1955
1053
TABLE I SO1,UBILITY O F
Ne 35
He 10
r/k
GASES,104X2,AT 25" H! 37
AND
1 ATM.
P A R T I A L PRESSURE
co
N! 95
100
0 2
a
118
121
cot
Rr -165
-200
61
14.013
6.0 6.1 6.85 7.3 7 4 7.45
n-C7F16 c-CoF11CFa i-CsHi8' n-CtjH14 ( C2Hd20 n-CJL6 C-CBHIICHJ C-CSI~lZ (Cyclohexane) CCl4 CtjHjCHj
3.105 2.606
4.66 3.75
2.496
3.56
i
8 2 7'85 8.6 8 9
1.216 1 225
6.27l 6.883
1,806 1 .816 3.173 2.5S3
1 . 156 1.5g3
10.0 c/k
65.39
2091° 46.04 29.26 25.36
1 4 .O7 12.47'
CzHt 185
C2H4 200
G . 39' 4.42l 4.537 2.23'
8 631 8 . l5O 6.03l 6.749 3.609
CzNa
25.01 1 8 ,554 14.95 14.86 13.44' 10. 9Fi4 8.778 8.856 4.874
12.0' 8.15l 4.329
252
27.3'
107'0 105'0 97lO
9778
45.31 cc14 28.4' CsHa 20.7' 2.2,4-Trimethylpentane.
115' 1731
14.5' 123l
ENTROPY O F SOLUTION He
Ne
6.3
OF
208l 148'
TABLE I1 GASESAT 25' AND 1 ATM.P A R T I A L
HI
Nz
3.7
-0.0
3.7
3.3
4.4
3.9 8.6
CO
6.2
8.1 4.6 4.2 5.1 5.3
8.9 CH4
n-C7Fis (Cd%)zO CClr CsKo
1650"
7271
1790' 1707'
PRESSURE
A
01
-1.5 -1.8 -1.8
6.2
CD2
Kr
-4
6
1.2
2.1 2.1
1.0
0.0
3.3
1.8
1.2
-1.0 -0 9
-4.2
-
-2 8
.6 - .5 .4 .6
-1.6
-'i.O
4 . 4
1.8 CzH'
CzFIr
CzHe
Cl¶
-11.5 -2.7 -2.4 -1.2
-
-7.7
7.8 -10.3
-7.2
TABLE 111 THEENTROPY OF TRANSFER OF GASESFROM 1 ATMOSPHERE A N D 25" JNTO SOLUTIO?;AT X) = He
csz
7ilo
(CHdPO
-300
n-C7Flo (CZHS)ZO
C7F16 c-CsFi iC Fr c-C61*11CHs C-CsHu CCl4 CsH6CHs C6Hs
46 FS
33'0
e12
SO*
240
78.
10 3'
16.8' 1 7 .3g
7.557
3. 1D3
CH4 148
38.89
7.823
1.1'
cs2
38.77 32.7
Hz
D2
Nz
8.0
8.8
6.G
8.6
8.5
6.9 6.5 7.0 6.2
6.8 6.4 6.9 5.9
5.8 6.3
A
CIZ
2.2 6.1 4.8 4.8 4.7 5 .2 4.9 5.0
2.0
T h e solvent was thoroughly degassed b y boiling for two hours, then sucked directly into the evacuated dilatometer. After being connected t o the gas buret a n d allowed t o come t o equilibrium in the thermostat, t h e initial number of moles of gas in t h e gas buret was determined from six readings of its pressure and volume and simultaneously t h e heights of t h e mercury threads at different pressures read with a telescope. One or more doses of from 2 t o 5 CC. of
-8.8 -7.5
-12.7
gas were pushed over into t h e solvent bulb and dissolved rapidly upon gentle agitation with t h e magnetic stirrer, t h e readings being repeated after each absorption of gas. To eliminate errors due t o changing atmospheric pressure and apparent compressibility of solvent, glass and mercury, the volume expansion of each system was plotted against the pressure acting on the solvent and interpolated at i60 mni. (e) Results are given in Table IV. T h e numbers it] parentheses represent the number of successive additions of gas in one run. I n all b u t a few cases, which 'were rejected, the plots of volume of solution against moles of gas dissolved gave straight lines, whose slopes give values of the partial molal volume of t h e solute, V2. T h e gas is 50 dilute in all these solutions t h a t V2 is independent of x y . V2 g k x 1 2 . Duplicate runs gave values differing in some cases as much as 2 cc. per mole; therefore, we give mean values rounded t o two significant figures. We include tws values for HZobtained b y Horiuti, designated b y ( H ) .
Discussion.-It is t o be seen t h a t the partial molal volumes given in Table IV, like the entropies of solution to x1 = are practically the same for each gas in all these solvents except the fluorocar-
1054
EDWARD C.-\r.ir,,iso . ~ N DKENKETH S.PITZBR
bons and i-CgHlq The increase is strikingly large in the case of H,. It is e\Tident, therefore, that the entropy of solution is mainly determined by tbe dilution, in terms of mole fvactiolz, m f voIainzc f m c tzorr. necessary t o balance the enthalpy. This confiriiis our recent findings for iodine dissolved in solvents of widely different molal volumes.i5 IYe interpret the differences in volume and entropy between different gases and solvents as follows. \Ye reiterate, first a point all too easily forgotten, namely, that what we commonly designate as a partial molal quantity of the solute is in reality what takes place in the system when a differentid amount of solute is added In the case of solutions so dilute as those here considered, these changes represent what happens in the immediate neighborhood of the solute gas molecules. These havt' low attractive fields and small volumes but possess the same kinetic energy as the molecules of solvent hence the latter gain added volume and freedom of motion, the greater the smaller their force fields, such as they would gain at the surface of c~ bubble. Although f, is a little larger for argon than lor hydrogen in CClI, this must be attributed mainly to its greater molecular size. I t s volunie per mole (15) K Shinoda and J H Hildebrand, J (1057)
P h y s C h e m , 61, 769
Vol. 80
from its second virial coefficient is 49 cc., whereas t h a t of hydrogen is 32 cc.13 The solvent around a molecule of hydrogen approaches more marly to the state of a bubble than that around a molecule of argon. The force constants of the gases represented in Tables I11 a n d T I T are much greater than the range in the solubility parameters of the solvents, hence the changes in entropy going horizontally in Table 11. from one gas to another. are much larger than those going vertically, from solvent to solvent. The values of T2for H P and D z in Table I V are so nearly the same as t o fall within the experimental uncertainty, but they differ in the right direction to accord with the slight excess of entropy in the case of H,. This contribution to the entropy of solution accords also with the fact that, in going from gases with larger to those with smaller force constants, the entropy increases faster than ideal as given by -K In xa. The lines in Fig. 3 have slopes of about - 1 .(iinstead of - 1.0. IfTe believe that these findings support an opinion often expressed by the senior authori6 that lattice models are n o t strictly appropriate for liquid solutions. -1gas molecule is not oscillating in a cage with a definite frequency and then jumping t o a new lattice site, but is rather participating with its solvent neighbors in a "random walk" with infinitesiriial steps. The relations revealed in the foregoing survey invite detailed theoretical study and reconciliation with our treatment of liquid-liquid solutions, but they are of such practical use and so suggestive as to model for theoretical treatment that we content ourselves provisionally with this presentation. We express our gratitude to Dr. Berni J. a l d e r for helpful discussions during the course of this investi-. gation, and to the Atomic Energy Commission for its support. (16) J. H. Hildebrand, Disc. F a i a d a y Soc., 16, 9 (1953). BERKELLY.
[ C O S T R I B U T I O S FROM THE r>EPAKTMETT O F CHENISTRY AND C H E M I C A L BERKELEY]
c ALIFORNIB
ESGINEERING, UNIVERSITY
OF
CALIFORSIA,
The Infrared Spectrum, Vibrational Assignment and Spectroscopic Entropy of Carbonyl Chloride BY EDWARD CAT.'IIANO. ~ N DKEKNETH S . PITZER RECEIVED S E P T E X B E R 16, 1957 It had been believed, from correlation with fluorine and sulfur substituted analogs of carbonyl chloride, t h a t the lowest frequency fundamental lay in t h e 220-240 cm.-I region. .Isearch in the far infrared has failed to reveal the existence of this band. It is shown, b y means of the "Matrix Isolatioii" method, t h a t the gas phase 575 cm.-1 band consists of two almost accidentally degenerate vibrational modes of different symmetry species. This leads t o a new vibrational assignment with a calculated spectroscopic entropy which is almost iri agreement with the calorimetric entropy, thus removing what has hitherto been regarded as a major third law discrepancy.
Introduction of which the Nielsen4 work is the most recent and The infrared and Raman spectra of phosgene colnplete. In these investigations, only five Of the have been investigated by a number of \vorkers,?--d six fundamentals were observed. These are a t (1) This research was assisted h y t h e American P e t r o l e u m Ins t i t u t e through Research Project 50. ( 2 ) K . Ananthakrishnan, P r o ( . i,z#!, T , i., SA, 285 (1937). .l
