380
J.
n.
SIMONS AND ROBERT KINYEL SMITH
(3) HORIBA, S.: Mem. Coll. Sci. Eng. Kyoto Imp. Univ. 3, 63 (1911). (4) KONO,M.:J. Chem. SOC.Japan 44, 406 (1923). (5) MILLER, W . L., AND RICPHERSON, R . H . : J. Phys. Chem. 12, 706 (1908). (6) TAYLOR, S. F.: J . Phys. Chern. 1, 461 (1897). (7) VARTERESSIAN, K. A , , AND F ~ K S K M. E , R . : Ind. Eng. Chem. 28, 928 (1936). E. R., HSIZD.A,V., A N D VOLD,R. D.: J. Am. Chem. SOC.63, 3237 (1931). (8) WASHBURN, R. M.,AND CORRET, A . S.: J. Chern. SOC.,1926, 2461. (9) WOODHAN, (10) WRIGHT,C. R. A , : Proc. Roy. SOC. (London) 60, 372 (1892).
T H E EXTROPY OF VAPORIZATIOS ASD DESSITY OF LIQUIDS AT T H E I R BOILISG POISTS J. H . SIMOSS
AND
ROBERT KISSEL SMITH
School of Chemistry and Physics, The Pennsylvania State College, State College, Pennsylvania Received November 13, 1941
The nearly constant entropy of vaporization of liquids a t a definite pressure is a useful property and one that has been given extensive theoretical consideration. Hildebrand (4)modified Trouton’s rule (9) in order to reduce the drift with boiling temperature by considering it for constant vapor concentration. Kistyakovskii (6) formulated an expression for the entropy of vaporization which gives a reasonably good agreement with experimental data,-
A S = R In V in which V is the gas volume.
(1)
For a perfect gas this can be rewritten as follows:
AS = R In ( R T )
(2)
Other empirical equations have been given (1, 2, 7, 8) to express the same property. These equations use either a logarithmic function or a power series in temperature. By making use of experimental data, Huffington ( 5 ) established for a number of substances the expression
A S = 1.8 R In V,/V,
(3)
where V , and VI are the molar gaseous and liquid volumes a t the boiling temperature. This and similar equations do not and cannot be expected to hcld for all liquids. This would require the force fields surrounding the molecules in the liquid to be either the same or related in a simple manner for all liquids. By employing a picture of the vaporization process which involves two steps, we have found that it is possible to separate the total entropy of vaporization per mole a t the boiling point a t 1 atmosphere pressure into two parts. We first consider that sufficientliquid to form 1 mole of gas is converted to a perfect gas
ENTROPY OF VAPORIZATIOPU'
a t its boiling temperature and a t constant volume. expand to 1 atmosphere pressure.
A S = ASc
381
This gas is then allowed to
+ ASz
(4)
A S is the total entropy of vaporization per mole a t the boiling point a t 1 atmosphere pressure, A S , is the entropy involved in the conversion process from liquid to perfect gae a t constant voliime, and A S z is the entropy of expansion from the liquid to gas volumes. AS, = R In V a / V l= R In D,/Da
(5)
If the perfect gas assumption is used for the vapor a t 1 atmosphere, AS, = R In RT D l / M = R In D l / M
+ R In ( R T )
(6)
D l is the density of the liquid a t its boiling point, and M is the molecular weight in the gas. In producing the vapor from the liquid a t constant volume any order existing in the liquid must be destroyed, and those forces responsible for the existence of a liquid must be overcome. Both of these are dependent upon the properties of the molecules under consideration. Empirically, we can state,
AS, = nR (7) leaving n, a pure number, to carry the burden of the molecular properties and complexities. The complete equation for the entropy of vaporization is
A S = nR
+ R In D , / M + R In ( R T )
(8)
In table 1 are given DL, the density of the liquid at the boiling point; OK., the boiling temperature at 1 atmosphere pressure; ASz, the entropy of expan-. sion; AS,, the measured entropy of vaporization; and nR. It is observed that ASz is an approximate constant for most substances with a value of about 11.5. I t is at least as constant as AS,,. I t has, however, a drift with molecular weight for any one homologous series of compounds or series of compounds in which one element is varied in one column of the periodic table. This is readily seen in figure 1. I t is also observed that the values for certain series appear to fall on a straight line. For most series AS, decreases with increasing boiling temperatures, although for series coming higher in the temperature scale the values of A& are higher. For very high boiling series, the reverse is true. This could he rxpcctrtl from equation G . In a series D J M decreases more rapidly than RT increases, hut for different series of compounds having st)ronger intramolecular forces (higher boiling points for the same molecular weight, in the gas) RT will have increased more than D,,/M decreased. Olmrvntion of the experimental values in figure 1 suggests a curve above which no points appear and which should intersect the lower-molecular-weight ends of the lines representing the homologous series (Le., the value for the
382
J
. H . SIMONS
AND ROBERT KINSEL SMITH
TABLE 1 Densities and entropies o j vaporization and expansion of liquids at the boiling temperature SUBSTANCE
Di
as,
AS=
BOILING POINT
isrn. ASz . .
rams per I
Helium . . . . . . . . . . . . . . . . . . . . . . . . . . . Neon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Argon . . . . . . . . . . . . . . . . . . . . . . . . . . . . Krypton . . . . . . . . . . . . . . . . . . . . . . . . . . Xenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radon . . . . . . . . . . . . . . . . . . . . Hydrogen . . . . . . . . . . . . . . . . . . . . . . . . . Riitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . Chlorine . . . . . . . . . . . . . . . . . . . . . . . . . . Bromine . . . . . . . . . . . . . . . . . . . . . . Mercury. . . . . . . . . . . . . . . . . . . . . . . . . . Zinc . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sulfur . . . . . . . . . . . . . . . . . . . . . . . . . Bismuth . . . . . . . . . . . . . . . . . . . . . . . CFI . . . . . . . . . . . . . . . . . . . . . . . . . CzFa . . . . . . . . . . . . . . . . . . . . . . . . C3Fs . . . . . . . . . . . . . . . . . . . . . . . . C4Flo. . . . . . . . . . . . . . . . . . . . . . . . . CsFlo . . . . . . . . . . . . . . . . . . CsFla . . . . . . . . . . . . . . . . . . . . . . . . . . . . C, Fi, ......................... Methane . . . . . . . . . . . . . . . . . . . . . . . . Ethane . . . . . . . . . . . . . . . . . . . . . . . . . . Propane . . . . . . . . . . . . . . . . . . . . . . . . . . . n-Butane . . . . . . . . . . . . . . . . . . . . . . . . . 2-Methylbutane .................... n-Pentane . . . . . . . . . . . . . . . . . . . . . . . . . Seopentane . . . . . . . . . . . . . . . . . . . . . . . Diisoprapyl . . . . . . . . . . . . . . . . . . . . . . . . n-Hexane . . . . . . . . . . . . . n-Heptane . . . . . . . . . . . . . . . . . . . . . . . . n-Octane . . . . . . . . . . . . . . . . . . . . . . . n-Xonane . . . . . . . . . . . . . . . . . . . . . . . n-Decane . . . . . . . . . . . . . . . . . . . . . . . . . 2,6-Dimethyloctane . . . . . . . . . . . . . . . . n-Undecane . . . . . . . . . . . . . . . . . n-Tridecane . . . . . . . . . . . . . . . . . . . . . . . n-Tetradecane . . . . . . . . . . . . . . . . . . . . n-Pentadecane . . . . . . . . . . . . . . . . . . . n-Hexadecane . . . . . . . . . . . . . . . . . . . . n-Heptadecane . . . . . . . . . . . . . . . . . . . . . n-Octadecane . . . . . . . . . . . . . . . . . . . Benzene .................. Toluenc . . . . . . . . . . . . . . . . . . . . . . . m-Xylene . . . . . . . . . . . . . . n-Propylbenzene . . . . . . . . . . Naphthalene . . . . . . . . . . . . . . . . . . . Hydrogen cyanide.,. . . . . . . . .
0.1% 1.204 1.402 2.155 3.06 4.40 0.071 0.808 1 . 557 3.09 12.64 6.1 1.375 8.75 1.96 1.85 1.45 1.55 1.67 1.51 1.68 0.415 0.516 0.586 0.600 0.6317 0.6108 0.613 0.6289 0.613 0.5996 0.612 0.610 0.608 0.610 0.600 0.608 0.597 0.594 0.590 0.595 0.577 0.805 0.777 0.759 0.693 0.797 0.683
calrrirr
$19
degrrs
4.77 9.72 11.05 11.15 11.62 11.72 8.12 10.4 12.1 12.5 16.2 13.5 13.44 17.26 11.15 10.72 9.9 9.9 10.1 9.75 9.80 10.9 11.25 11.08 10.86 10.70 10.70 10.51 10.6 10.6 10.4 10.5 10.2 10.1 10.01 9.96 9.85 9.75 9.66 9.58 9.50 9.40 11.4 11.2 1 0 .8 10.9 11.1 12.9
raloricr )GI
dcgree
5.7 15.3 17.30 19.53 20.52 10.6 17.3 20.0 21.6 20.1 20.1 19.0 26.7 20.3 20.5 20.9 20.9 20.9 21.3 20.9 18.2 19.7 18.8 19.4 21.1 20.7 20.3 20.3 m.5 20.5
20.0 20.1 20.2 20.3 19.6 19.0
QK.
4.2 27.2 87.4 120.2 164 211 20.4 77.3 239 332 630 1180 718 1723 145 195 235 268 296 324 353 112 185 119 274 301 309 282 331 342 371 398 424 447 432 470 507 426 544 561 576 581 353 384 412 431 491 299
(nR)
0.93 5.6 6.25 7.9 8.8 2.5 6.9 7.9 9.1 3.9 6.6 5.6 9.4 9.1 10.2 11.0 11.0 10.8 11.5 11.1 7.3 8.3 7.7 8.5 10.4 10.0 9.7 9.7 10.1 10.0
8.6 8.9 10.0 9.4 8.5 8.1
383
ESTROPY OF VAPORIZATION
TABLE 1-Continued DI
SUBSTANCE
ASz
~
ASm
~
~
BolLUic
mm
1 ASm - ASz '
1
Acetonitrile Propionitrile Butyronitrile Benzoni trile Benzyl cyanide Formic acid Acetic acid Ethyl chloride Ethyl bromide Ethyl iodide Propjl iodide Isopropyl iodide Fluorobenzene Chlorobenzene Bromobenzene Iodobenzene Methyl formate Ethyl formate Methyl acetate Ethyl acetate Methyl propionate Methyl n-butyrate Methjl isobutyrate Ethyl propionate n-Propyl acetate Ether Ethyl alcohol Glycol n-Propyl alcohol Isopropyl alcohol Cs clohexanol Phenol Benzyl alcohol m-Cresol E t h j lamiiie Aniline Dlpropylamine Benzylamine Rfcthylaniline o-Toluidine Water Hydrogen chloride Hydrogen bromide Hydrogen iodide Sulfur dioxide Sulfur tiioxide H j drogen sulfide 4mnionia -
__
__
1
1
I
'
1
~
~
- -
0 712 0 701 0 698 0 850 0 845 1 123 0 940 0 915 1 429 1 811 1582 1 563 0 939 1 143 1 319 1 570 0 954 0 874 0 885 0 835 0 845 0 802 0 792 0 792 0 792 0 697 0 7379 1 020 0 740 0 735 0 840 0 941 0 898 0 893 0 687 0 882 0 655 0 846 0 836 0 847 0 958 1 193 2 142 2 790 1 460 1 856 n 963 0 697
12.5 11.9 11.5 11.5 11.4 12.6 12.4 12.2 11.4 11.6 11.3 11.3 11.2 11.6 11.3 11.2 11.9 11.6 11.7 11.1 11.1 11.1 11.1 11.2 11.2 11.3 12.0 13.0 11.9 11.8 11.2 11.9 11.6 11.6 11.9 11.8 11 4 11.4 11.1 11.7 14 7 12 4 I2 2 11 9 12 5 11 3 12 3 12 7
- __..
20.1 20.0 20.3 20.3 22.8 25.0 20.5 20.6 a
22.2 21.5 21.3 25.7 21.7 21.7 21.8 21.9 21.9 20.3 26.3 21.1 26.6 25.8 27.2 25.2 22.6 22.7 21.1 20.1 21 8 21 7 26 0 20.6 20.8 18.2 23.1 23.8 21.1 23.2
,
355 370 391 464 507 374 391 385 311 345 375 363 359 405 429 462 305 327 330 350 353 375 367 372 375 308 351 471 371 353 434 455 479 476 289 457 384 457 469 474 373 188 206 238 263 318 213 240
(nR)
7.6 8.1 8.8 8.8 10.2 12.6 9.1 9.0
10.3 9.9 10.4 14.6 10.6 10.6 10.7 10.7 10.7 9.0 14.3 8.1 14.7 14.0 16.0 13.6 11.0 10.8 9.3 8.7 10.7 10 0 11.3 8.2 8.6 6.3 10.6 12.5 8.8 10.5
___
384
J
. H . SIMONS AND ROBERT XINSEL SMITH TABLE 1-Concluded ..
BOILING
Di
porn
Lsn
.as.
..
ram
Phosphorus trichloride . . . . . . . . . . . . . Hydrogen selenide . . . . . . . . . . . . . . . . . Hydrogen telluride . . . . .... Arsenic trichloride . . . . .... Antimony trichloride . . . . . . . . . . . . . . . Antimony tribromide . . . . . . . . . . . . . . . Silicon hydride . . . . . . . . . . . . . . . . . . . . . SitHs . . . . . . . . . . . . . . . . . . . . . . Silicon tetrabromide . . . . . . . . . . . . . . . . Titanium tetrachloride., . . . . . . . . . . . GelHs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GesHs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lead chloride., . . . . . . . . . . . . . . . . . . . . Lead bromide . . . . . . . . . . . . . . . . . . . . . . Lead iodide . . . . . . . . . . . . . . . . . . . . . . Mercuric chloride . . . . . . . . . . . . . . . . . . Mercuric bromide . . . . . . . . . . . . . . . . . . Mercuric iodide . . . . . . . . . . . . . . . . . . . . Lithium fluoride . . . . . . . . . . . . . . . . . . Lithium chloride . . . . . . . . . . . . . . . . . . . Lithium bromide.,. . . . . . . . . . . . . . . . Sodium fluoride.,. . . . . . . . . . . . . . . . Sodium chloride . . . . . . . . . . . . . . . . . . Sodium bromide . . . . . . . . . . . . . . . . . . . Sodium iodide . . . . . . . . . . . . . . . . . . . . . Rubidium fluoride . . . . . . . . . . . . . . . . . Rubidium chloride . . . . . . . . . . . . . . . . . Rubidium bromide . . . . . . . . . . . . . . . . Rubidium iodide . . . . . . . . . . . . . . . . . Cesium chloride . . . . . . . . . . . . . . . . . .
per 66
.
cdoriss par degree
cdoriss per degree
'K
11.5 12.4 12.2 11.7 12.1 11.7 11.1 10.8 10.8 11.4 11.3 11.1 14.7 14.3 14.0 13.3 12.9 12.6 17.7 16.0 15.9 17.4 16.1 15.6 14.0 16.0 15.0 14.7 14.3 14.8
21.8 20.9 20.1 23.8 23.9 23.8 18.8 20.1
347 231 271 393 493
1.60 2.12 2.57 1.940 2.437 2.8(7) 0.66 0.68 2.407 1.500 1.7(?) 1 .8(?) 4.29 4.85 5(7) 4 . 346 4.852 4.92 1. 075 1.177 2.01 1.545 1.223 1.811 2.06 2.28 1.56 1.99 2.13 2.05
20.8 20.4
25.3 24.6 23.9 26.7 22.9 23.6 26.4 26.7
26.0 28.5 24.4 23.7
553 161 258 426 408 302
383 1223 1189 1227 577 595 627 1943 1626 1538 1973 1686 1663 1573 1683 1663 1613 1573 1563
(SR)
10.3 8.5 7.9 12.1 11.8 12.1 7.7 9.3
9.5 9.3
12.0 11.7 11.3 9.0 6.9 7.7 9.0 10.6
10.0 13.5 9.7 9.4
member of the series of zero molecular weight) . If the limiting value of Dz/M as M decreases to zero were a constant for all series of compounds. then equation 6 becomes
ASz = A
+ R In T
(9)
in which A is a constant . This should be the equation for the curve . In figure 2. -log D i / M is plotted against molecular weight for a number of series of compounds Straight lines are thus obtained which apparently meet in a common point a t zero molecular weight . It should be pointed out that D i / M is the reciprocal of molecular volume a t the boiling point and that an additive law with molecular weight is to be expected However. an interesting equation is obtained from the graph .
.
.
log V I = U M
+K
(10)
385
ENTROPY OF VAPORIZATIOS
In thiq equation VI is the molar volume of the liquid a t its boiling point, JI is the molecular weight in the vapor, I< is a universal constant (1.42i), and a is a parameter which is constant for a series of like compounds but which varies from w i e s to series. I n general, it changes in one direction as the intramolecular I
I
I
I
14 12 IO
a S, (e.u) 6
4
2
0
100
200 300 400
500 600
700
T E MPERATURE FIG.1. Entropy of expansion of a gas from its volume as a liquid to that of a perfect gas a t 1 atmosphere pressure as a function of boiling temperature. Curve I, Buorocarbons, curve 11, hydrocarbons; curve 111, hydrogen halides; curve IV, aromatic hydi ocarbons; curve V, mercuric halides.
attractive forces (dipole, etc.) increase and is apparently related to these forces. From figure 2, log D , / M = -1.427, D J M = 0.0372 cc.-', and
ASx = R In T
+ 2.225
(11)
+
The equation for a straight line in figure 1 is ASz = cT b. If this is equated to the value of AS, in equation 6, the following equation for the boiling temperature results:
eT = R In R T D J M
-b
(12)
Egloff, Sherman, and Dull (3) used, with considerable success, the following empirical equation to correlate the boiling points of hydrocarbons:
T = a log (n
+ 6) + h
(13)
386
J. H. SIMONS AND ROBERT KINSEL SMITH
In this equation n is the number of carbon atoms and a and b are constants for all hydrocarbons, whereas h varies with different series of hydrocarbons. For straight-chain hydrocarbons the equation becomes
T
= 745.42' log (n f 4.4)
- 416.31'
(14)
If c and b of equation 12 are evaluated from figure 1 (c = -0.006 calorie per degree'; b = 13.0 calories per degree), and D Iand In T assumed constant, which
-
MOLECULAR WEIGHT FIQ. 2. Logarithm of the molecular volume at the boiling temperature as a function of molecular weight.
are approximately (0.6 and 6.25) for hydrocarbons then equation 12 becomes
T
= 766" log (n
bf
higher molecular weight,
+ 0.143) - 454"
(15)
This equation is seen to be not greatly different from equation 14, and it is obtained as a consequence of a straight-line relationship for a series of compounds in figure 1. A number of additional observations may be made. The points for hydrogen and the inert monatomic gases fall on or near the curve of equation 11, in figure 1. For two different series of compounds the one having compounds with higher boiling temperatures for the same molecular weight (higher intramolecular forces) is represented by a straight line that has a smaller slope and a higher intercept with the logarithmic curve. For salts the slope has apparently the
.
RELATIVE VISCOSITIES O F YON-AQUEOUS SOLUTIONS
387
opposite sign; but this is to be expected, as in liquid salts the chief attractive force is electrostatic, and as the size of the ion increases, the attractive force decreases. Salts of higher molecular weight have, frequently, lower boiling points than similar salts of lower molecular weights. The value of nR in the table seems to be approximately constant for like molecules. For normal liquids with large polyatomic molecules this number is about 11. For certain other substances with monatomic molecules,-such as argon, neon, mercury, and zinc,-this number is about 5. For fused uniunivalent salts, n is approximately 9. For associated liquids in which the vapors are not polymerized, such as the alcohols of lower molecular weight, n is larger, being 14 or greater. REFERENCES (1) BINGHAM, E.C.: J. Am. Chem. SOC.28, 723 (1906). (2) DEFORCRAND, R . : Compt. rend. 166, 1493 (1913). (3) EQLOFF, G.,SHERMAN, J., AND DULL,R . B . : J . Phys. Chem. 44,730 (1940). J. H . : J. Am. Chem. SOC.37, 970 (1915); 40,45 (1918). (4) HILDEBRAND, (5) HUFFINGTON, J. D . : Phil. Mag. [7] 19, 836 (1935). V.A,: J. Russ. Phys. Chem. SOC.6.9, 256 (1921). (6) KISTYAKOVSKII, (7) MORTIMER, F . 6.: J. Am. Chem. SOC.44, 1429 (1922). (8)NERNBT, W.: Nachr. kgl. Ges. Wiss. Gottingen (1906). (9) TROUTON, F . : Phil. Mag. 151 18,54 (1884).
STUDIES OF RELATIVE VISCOSITY OF NON-AQUEOUS SOLUTIONS' H . T . BRISCOE
AND
WILMER
T. RINEHART
Department of Chemistry, Indiana University, Bloomington, Indiana Received November 15, 1941
This investigation has to do with the effect of temperature upon the relative viscosity, 70, of non-aqueous solvents containing electrolytes and non-electrolytes. Consideration has also been given to the Griineisen effect in solutions containing an inorganic salt, namely, potassium iodide dissolved in a non-aqueous solvent. EXPERIMENTAL
Exactly 5 ml. of liquid was measured into Ostwald-type viscometers at 25'C. As a check, two viscometers used for each determination always contained a solution of the same concentration. The liquid inside the viscometers was protected from the atmosphere by means of soda lime tubes. The viscometers were suspended in a constant-temperature bath by means of rigid glass supports Presented by Wilmer T. Rinehart to the Faculty of the Graduate School of Indiana University in partial fulfillment of the requirements for the degree of Doctor of Philosophy, October, 1940.
