428
R . T. LAGEMASZ; AXD W. S. DUSBAR
(13) >\ICBAIS,J . .4su STEWART, -1. : J. Chexn. SOC.1927, 1392. (14) MCBAIS,J . IT.,T;OLD!R . D . , ASD JOHSSTOS, S.:J . Im.Chein. SOC.63, 1000 (1911) (15) MALKIS,T . : Ber. 63, 1807 (1930). L. H.: J. Phys. Chem. 26, 21T (1922). (16) MILLIGAS, (17) ~ ~ I L L I G A SW. , O., . ~ S D WEISER:€1.B.: J . Phys. Chem. 41, 1029 (1937). (18) OUDEJIASG, .I.c.: J . prakt. Chem. 89,206 (1863). (19) THIESSEX, P. A , , ASD ST'ICFF,J . : Z.physik. Chem. A176, 397 (1936). (20) WEISER,,H . B., A X D MILLIGAS, W .0 . : J . Phys. C'heiii. 38, 513 (1934). (21) WEISER,H. B . , .~SDMILLIGAS, I T . 0.: Chem. R e v . 25, 1 (1939). (22) WEISER,H . 13., .is11NILLIGAS, W .0 . : J . .lm.Cheiii. SOC.59, 1456 (1937).
RELATIOXSHIPS B E T W E E S T H E T'ELOCITY OF SOUTU'D AND OTHER PH'T'SICAL PROPERTIES OF LIQCIDS R . T. LAGEMASS
AND
W. S. D U S B A R
Depaltment of Physics, Emory Un,iveiszt~,Emory Cniversaty, Georgia
Received June Y, 1946
I n the past the chief use of measurements of the velocity of sound in liquids has been in the determination of the adiabatic compressibility from which the ratio of the specific heats may be found provided the isothermal compressibility is known. At the same time certain qualitatire facts relating the sound velocity t o structure ha\-e become well known. These shon-ed that the velocity of sound itself was not an additive and constitutive property, and little application of measurements of the velocity of sound to the elucidation of molecular structure seemed possible, until Rao discovered a function of the velocity which was independent of the temperature. Rao (15, 16) shoTyed that in any one liquid the density and the velocity of sound are connected by the relation v"% /d = T', TI-herev is the velocity of sound, d the density measured a t the same temperature as the velocity, 31 the molecular weight, and 'c' a constant independent of the temperature. It is the purpose of this communication t o draw attention t o the very simple relationships esisting between the quantity T-, which vie choose to call the molecular sound velocity, and certain other physical properties. These relations hare been applied only to the lower members of some homologous series. Aismore data are accumulated the relations will probably be more generally applicable. L I S E A R RELATIONSHIPS O F MOLECULAR SOUND VELOCITY
For the members of each homologous series for which data are available, it has been found that a linear relationship exists between the molecular sound velocity and the following physical properties: molecular refraction (Jf,,), parachor ( P ) ,Souders' viscosity constant ( I ) , van der Waals' b ( b ) , molecular magnetic rotation ( T ) , and the critical volume (17c). I n a graphical plot of any of these properties against T', the slopes of the straight lines obtained for
129
VELOCITY OF SOCXD I S LIQCIDS
the series of homologues are very nearly identical, hut the intercepts vary. In most cases the curves for all the series are almost coincident, and t o a good approximation a single line would represent the data for all compounds. TO make suck graphs, d u e s of 1- were taken from Rao (1G), values of MD from Herz ( 7 ) , Eisenlohr ( 5 ) , and the Landolt-Bornstein tables (lo), values of P , b. and 1’, from the Landolt-Bornstein tables (lo), values of I from Souders (19), and values of T from Perkin (14). The plots show a typographical error in Souders’ data (19), where the 1-alue of I for ethyl alcohol should be 171, not 117.
W
800
$00
600
300
400
200
$j I
v) (L
0 U
W P
a
2
3 0 v)
100
200
0
0
0
400
800
1200
1600
2000
MOLECULAR SOUND VELOCITY
FIG.1. Relation of molecular sound velocity t o the parachor and Souders’ 1
Figure 1 shows the relationship betrTeen the molecular sound velocity and the parachor and Souders’ I for four homologous series. Plots of T’ against the other properties mentioned above have a similar appearance. On the assumption that a linear relation holds for each homologous series, the constants il and B of the relation T’ = A B X have been evaluated by the method of least squares and are listed in table 1. X may be any of the quantities: mole refraction, parachor, van der Waals’ b. Souders’ I , critical volume, or molecular magnetic rotation. Table 2 shows how ne11 the data are fitted by these equations. Here values of the observed molecular sound velocity are listed in the third column. I n column 4 appear values of the molecular sound velocity calculated from the mole refraction values of column 2 hy use of the appropriate constants taken from table 1. The a\-erage error of about 0.5 per cent between the calculated and observed values of T‘ is characteristic of
+
430
R. T. LAGEXAKV A S D W. S. DUNBAR
the small error involved in connecting any of the other physical properties with the molecular sound velocity. It is obvious that the constants recorded in table 1 may be used t o find values of T' for higher members of the series from known values of any other of the TABLE 1 Constants of the h e a l , eqzialzons relatzng m o l c c n l a ~sound velocity a n d other phusical propertaes
'
SERIES
1 ' i A
1
Monohydric alcohols
_ R
_ _ __
Paraffins 101.4 Esters of acetic acid 172 2
I
P
'11
41.89
I
I
b
I
_
T
~
-__
~
16 67 4 935, 150.3
38.611 46 S i ' 4 551
81.63 41 701-27 38, 5.072
I
150 71 140,1001
46
I
I
31 57 3 454 -313 6 247,3001
Benzene hy- 1 I I drocarbons -59 101 39 61 -41 31 4 930 -27 751 4.035
281 31 169.4 123 4 180.9
195 8 147,3001-1117 i 186.9
TABLE 2 Obserred a n d calculated LmZiies o j the molecular sozind celocity ______
COXPOUND
1
ji, (OBSERVED)
1
T.
~
I
(OBSERTED)
v (C~LCL'LATED)
P E R CENT DIFFERESCE
I
0.0 -0.1 0.3 -0.2
851 1037 1211
854 1031 1214
0.3 -0.6 0.2
421 624 806 1004 1198
425 615 812 1005 1197
1.0 -1.5 0.8 0.1 -0.08
979 1170 1731
97s 1171 1731
-0.1 0.09 0 0
25.26 29.91 34.57 39.19
1160 1356 1545 1746
Methyl acetate Ethyl acetate Propyl acetate
17.65 22.25 26.98
Methyl alcohol Ethyl alcohol Propyl alcohol Butyl alcohol Amyl alcohol
8.23 12.78 l i . 52 22.13 26.74
Benzene Toluene Cymene
I
..
26.18 31 06 45 18
1
i
1160 1355 1550 IT43
Pentane. . . . . . . . . . . . . . . . . . . . . Hexane. . . . . . . . . . . . . . . . . . . Heptane . . . . . . . . . . . . . . . . . . . . Octane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
I
constants (and rzcc 1 c ~ s n ) amin-ing . the linear relation to hold. Thi. procedure would appear to he better than summing additive and constitutive factors, wliich ~ i a not y consider w c h effects a? exaltation a. one goes to higher members. The fact that the other quantities are linear 71 ith l7 means that they are linear n i t h one another. Eqiiationq connecting t n o a t a time can he set up from 144,400b table 1. For exmple. .ince 7 = 1G.67 4.935P and 1- = 220.6
+
-+
431
VELOCITY O F SOUSD IS LIQCIDS
+
for the paraffins, i t follows that P = 41.32 29,260b. Although a few isolated examples of such linear relations are recorded in the literature (6, 8, 11, 17), it now appears that t u enty-one linear relations exist among the seven properties considered here. I t should he stated that several norkers (1, 4, 7, 20, 21) have indicated that the ratio of t u o of the above-mentioned properties yields it constant for a great numlier of compounds. While this mav lie useful as a rough working rule, it ~ o u l dgenerally he niorc exact t o cay they are lineally related. For example, Buehler (1) state< that the ratio of Souders' I to tlie parachor ii 1.22 for about tnenty-five compounds (1 2; for parafhns). I-se of the conitants of table 1 give* I = I .39P - 3T.6 for paraffins, tliii i q a inore accurate statement of the facts, a': can be qeen fioni a plot of I i'ersiis I-'. The ncitlition of CHZ groups in a Iiomologous seriei: does not, in general, c a u v a conitant ratio to exist between the physical properties, h i i t inqtearl :idti> constant amounts to the previous \ alue. This lead> to a linear cur\ e ivhich a < a rule does not pass through zero. I t i< interesting i o notc that from the equation 1. = -4 B P and from the definition- of l7 and P , it nlay be qhov n that
+
a iclation bet\\ e m velocity oi s x i i i d . buritlee tension (-,), and density, inwhich .I and I: are constants for a11 coiiipoiintis of a single series. Similar relations may be set up by using the refi.:icti\-c iiidcs, T-iscoqity, x i d T7eidet'i constant in addition to thr. suif'acc tenyion anti ~ o i i n d\-elocitv. VELOC'ITY O F S O U S n . \ S D R O I L I S G .\SD CRITICAL FOISTS
Examination of the data on nornial boiling points ( T B )and critical temperaiures ( T c )reveals that they :ire connected with the nicdecular sound velocity by cquatioiis of the form TB = -4 R log 1- and Yc = C D log ,'I where A , B, C, and D :ire constants for each homologous series. The boiling point is plotted against the log of the molecular sound 1-elocity for four series in figure 2. It may be seen that straight line:: rcsult for series of unassociatcd compounds. Ai similar plot can he made for 7', ~ ' c i ' s ~17. i ~ Imvis (11) has found that T c and TB are linear functions oi thc log of the p:trachor. its would tie expected t'roin the linearity het\\-ecn 1- arid 1'. U-an (2?), hon-ever, stat'es that' T c = k,Jl, k?, whereas the consideration$ t1liO\.(T favor the relation T c = lil lcg JID 1 ~ : . On the basis of t h e data giI-en hy IViiii on t\vo series of unassociateci conipoimds;, the t\vo equations appcnr to possess ~thoiit equal merit. \\-:in's \-due of k: for pnrnffins, incidentally, ,dioiild be 267.5, not 268.5.
+
+
+ -+
\Yhen considwing t h c ~i~orriiieiitioiie(t phy,sical properties :is udc!itive antl constitutive, i t is custoinary to separate the molcculnr constant; icto atomic increments anti T ( ' ilic vulues to dci11:k I)oncls, triple lionds, and othw constitutil-e f:ictois;. T a h h li lists soi1i.c ot' tlicrc \ - d i i e ~ along . Jvith i,ei'erences
432
R. T. LAGEM.\?;?;
. I S D W. S. D U S K I R
I 0 B e n z e n e Hydrocarbons 0 Esters o f Acetic Acid X Monohydric Alcohols 0 Paraffins
140
-
-
p i-
E
100-
0
a.
(3
-
z
2
0
m
60
-
I
I
I
I
I
e .a
2.6
LOG ~ ' I G .2.
I
1
I
I
3.0
3.4
3.2
V
Relation of the boiling point t o the molecular sourid veiucity
Atomzc increments
,
PARACHOR
(12)
(5)
I
1 I
S 0 F ('1 ur I CH, Double bond Triple bond
I
2 i 50 2 37 29 i
1
I
60 79 110 55.6 -15.5
I
15.4 9.2 17.5 20.0 255 55 69 90 -10.0
1
I
O F SOUKDI C O b A L E N T RADIUS
(16)
I
~~
H C
_ _
UOLE REFRACTIOS \=LOCITY
1.100 2 41s
1
92.5 10
(13)
1
0.30 0.77 0.70
1
'
1.525 100 5.967 5 565 13.900 5.618
19.0
1,733
35
2.398
71 1
227 245 304 195
I
0.66 0.64 0 99 1.14 1.33
110 I
t u the literature from which they were obtained. In a column of the Periudic Table, the atomic increments for all the properties listed increase with increase i n the principal quantum nurnher. Except for Souders' I . the contributions
433
VELOCITY OF S O C S D I S LIQUIDS
of bonds increase with their multiplicity. Figure 3 is a plot of the covalent radii of the halogens versus their atomic increments as found from four molecular constants. ,4 smooth curve can be drawn in each case. Likewise, for atoms of a column of the Periodic Table, a similar relation exists betveen the atomic increments of any two of the properties. & i nalternative procedure (2, 3, 9, 18, 24) in synthesizing molecular constants is to sum bond increments. Such a scheme is particularly useful xhen comparison is made with interatomic distances and dissociation energies. Values for some frequently occurring bonds and also the sources of the data are compiled in table -1. To obtain the values given for the bond velocities (9) and for 220 1.4
20
Iodine
1.2
260
I
300
1
I
--.
60
P
100
-
-
v)
2 a a
B
1.0
-
0.8
-
0.6
-
3 0
I
I
-
z
Bromine
Chlorine
-1 W
30
u
0 I
I
4
i
Fluorine
8
MD I
16
12
I
I
I
FIG 3 . Graph showing the relation between the covxlent radius and atomic increments for elements from a column of the Periodic Table.
the bond parachors. the best values for the C-C and C-H bonds were obtained by least squares from the paraffins, following which, these values were used on single molecules to find other bond values. Improved values could no dovl 116 obtained by taking for the IJoncl parachors and bond velocities the iiiean values from measurements on a number of similar molecules. From table 4 it may be seen that the bond increments, except for bond lengths, of all the atom pairs increase 113th increase in the bond multiplicity. Figure 4 shons the relation of bond length to bond refraction and is reprehentative of the curves obtained by plotting any of the columns of table 4 against any other column for bonds of the same niultiplicity. For bonds of an atom with a series of atonis from a r o or ~ from a column of the Periodic Table, a I
434
______.
.
C-H . . . . . . I C-F. . . . . . . . .
c-c1..
.
.
.
'
. . . . ..I . . . . . . . . . . . . . . . .. I ... , I . . . . . 1 ........ H-H. . , . . ' H-CI.. . . . . . .
C-Br..
c-I.
c-s.. c-x c-0. c-c..
~
1.705 1.60 6.51 9.47 14.51 4.59
1.51 1.425 1.209 2.0s
~
H-0 . . . . . . . . . , CI-CI . . . . . . j C-C.. . . . . . . i
c=s. . . . . . . . . . c=o. . . . . . . . .
j
CzN . . . . . . . . . h C .. . . . . . .
.I
1
1.73 4.15 10.61 3.42 4.77 6.025
17 26 A: 08 82
-
.
7
95 2
0 Q 1 7
7 2
35
"0
a
24T 305 I
7 0 34 5 4 6 4 25 35 2 67,s 26 4 99 L11 5 28 7 129 72 1 319 37 4 186 63 3 1 28.5 53 2 ________~
18 2
5.55 $1 3
66 0 30 2
36 8
/
c-I d
1 0; 1.41 1.76 1 91 2.10 1 81 1 47 1.43 1 54 0 60 1 29 0.99 1.98 1.33 1 61 1 22 I 15 1 20
_- ____ -
VELOCITY OF 5 0 L T D I S LIQUIDS
435
smooth curve is obtained. This graph, of course, enables one to estiaiate bond incremenls -\yhich are not as yet knon-11. It is apparent that the bond increments for the various properties beiir a close relationship to one mother, provided the mi ant1 coliiiiin~oi the Periodic T,d)lc w e taken into :iccomt.
-
coscLusIoss It should I ~ G Xbe clear thnt nimsurenients on the \-elocit;; of sound can aupplement and replace nieasiiremcnIs on other physicnl propei?i,,s in studies of molecular structure. .4lthough the soiintl i-clocit,?. ma>- not he so conveniently nie:isured as the :ei'r;ictiye indcs oi a 1ic;uicl. it' is coniparnhlc in ease of measuyenient to the other propertics dixiiswl. n-itli tlie cl(1fiiitt. clrnviBac!i, however, that, relatively lwge amounts of !iquitl arc required i v i t h the interferometer method. At preseiir , values :?rc usii:illy cluotetl -,vliich incliicie four ani1 someas good :is> and tiiyles five signiiicant figurri~. 1I-+ yields ;in accuracy :it le in *sonic crises better than, that for sny oC tlie othei. p h y i c d propertics except rcf'r:icti~,ity. I
7
(11) (12)
LEWIS, D. T . : J. Chem. SOC.1938, 1056. h l U M F O R D , 8..%., A N D PHILLIPS, J . Jv. c . :,I.
('belli. sot. 1929, 211%. (13) PAULISG,I,. : The Il'alicre of thc Che,riiccii Bond. Cornel1 Cniversity Press, Ithsca, h7ew York (1940). (14) PERKI?;, W.H.: J. Cliem. SOC.69, 1026 (18961. (15) RAO,h l . 11.: Indian J. Pliys. 14, 109 (1940). (16) ILio, AI. It.: J. Chein. Phys. 9, 652 (1041). (17) SAUYGI?;, 31. AI.: J. Pllvs. C'helli. ( C . S.P.1i.110, 455 ( 1 9 3 i , . (18) SMYTEI, C. P . : Phil. hlag. 60, 361 11925). (19) SOTDERS, XI., J R . :J. *%iii.Cheni. SOC.60, I54 (1938). (20) S I G D E N , S . : T h e I'nrachor a n d 17a/encg, p . 31. Alfred 'Knopf, l.o~icion (1930). (21) TROGTON: Phil. Mag. 18, 54 (1884). (22) \VAS, S.W.: J. Phya. C'hem. 45, 903 (1941). (23) W.4NG, s.: J. Cilem. I'hyS. 7 , 1012 (1939). (24) v o s STEIGER. A . I,.: Ber. 54, 13S1 (1921;.
EFFECT OF' SI:I?FAICE-.1CTIT7E AGESTS t - P O S DISPERSIOXS SILIC=\ I S SYLEYE I-.R. DALIERELL, IC. GAYER, Department o j
011'
H. LAUDENSLAGER Chemisfry? Western R e s e w e I:niz'ersity, Clepeland, Ohio AND
Received February 9 , 1946
Tliis \\-ork is a continuation (1, 2) of the study of the eft'ect of surface-active agents upon particle-size distribution in organosols. This paper describes results obtained with finely divided silica dispersed in xylene. CHElIIC1LS
purified grade of xylene \vas redi,5tilled, and the fraction boiling between 137" and 138.5'C;., a niixture of 0- and vi-xylenes, was used in the research. A sample of Iiahlbaum silica was used. This contained 16 per cent' of water and 0.01 per cent of material not volatilized ivith hydrofluoric acid. It was heated in a furnace at 900°C. for 24 hr. in a stream of dried air, then ball-milled for 45 min. and screened through a 200-mesh seive. It finally had a water cont,ent of 0.4 per cent,. The surface-active agents used are shown in table 3. These were all of the purest grade obtainable. P R E P A R I T I O S O F S1LIC.I-XTLESE
SjTBTEMS
T o 500 nil. of xylene in a n-ide-mouth Dewar flask was added 0.500 g . of silica poivder. The surface-active agent (about 0.001 mole) \va3 added to this mixture, and the ivhole vas then mixed for 45 min. at 25'C., {wing a stirrer witmha threehlatle propeller operating a t 500 I t . P . i r . Loss of xylene \\-its diminished by riiising in a draftless:. enclosed compartment. 'The temperature inside the flask was held a t 25°C. =k 0.5" by a glass U-tube coniiected t o 3 variable-texnperature xater line. The L7-tube also served 3s a baffle.
