CRITICAL TEMPERATURE FROM REFRACTIVE INDEX
903
10. The ionic elevation varies directly as the concentration in dilute A J , assuming Aa to be known for a solution, so that Am = C(A, normal solution at 2 5 O ( ’ . 11. The value of A,,, always decreases as the temperature is raised and in a linear manner which is not directly proportional to the absolute temperature. For a binary electrolyte the molecular elevation is lowered by 0.23 rhe for each degree Centigrade, for a ternary electrolyte the lowering is greater and approximately double that amount, and in the single instance of a quaternary electrolyte that we have available, namely, ferric chloride, there is ,t lowering of four times that amount per degree. 12. The decrease in ionic elevation with the temperature rise is very naturally explained by the lessening of the hydration. 13. Since a salt showing positive elevation, such as potassium chloride, raises the fluidity of water, it might seem tempting to regard such a salt in solution as itself a liquid, more fluid than water. This would be an incorrect view. Rabinowitch (4) and the author (2) have independently reached the conclusion that the rise in fluidity must be due to the breaking down of association in thc nater itself, caused by the presence of thc salt.
+
+
REFERENCES (1) HI\c;Hnhr, E c : F l u z d ~ t ya d Pluslicit?/, p 81 et S P ~ lIcGIau--Hi11 Book conipany, Inc , Sew York (1936) (2) Reference 1, p 179 et sep (3) KOLTHOFF, I. ILI : Konduktometrzsche Tztratzonen Steinkopff, Berlin (1923). (4) RABINOWITCH, A I.: J. .im. Chem. Sor. 44, 9.54 (1922). ( 5 ) TAYLOR, H. S : P h y s ~ c ~ C z lh e m s t r y , p 937 D Van Yostrand Company, New York (1932)
T H E DETERlITS-iTIOS OF CRITICAL T E l I P E R b T U R E FROLZ I X D E X OF REFRACTIOS
s. w.W.4K Dcpnrtiwnt o j Chemzstry, Yale-zn-Chzna School of Science, Hua Chung College, Hszchow, Y u n i m n , Chznn
Recezved J a n u a r y 10, 1941
‘The llacleod constant ( 5 ) , C, in the following equation C = s / ( D - d)4‘ (1) where s, D,and d are, respectively, the surface tension of the liquid, the density of the liquid, and the density of the vapor a t the same temperature, is unaffected by temperature for normal liquids, but shows a slight and steady increase with increasing temperature for associated liquids.
904
8. W. WAN
The absolute value of C may be calculated from Fowler's equation (2),
B/4mA2TC = s/(D
- d)4 = C
(2)
where m represents the mass of the molecule,
);(
is a constant for one particular substance,
being the average molecular
density at critical temperature, and B is a function of atomic dimensions and the interaction energy between a pair of molecules. The general application of equation 2 to a complete chemical group is difficult on account of insufficient data for the evaluation of A and B, but the connection between C and T , i s worth considering. Such a connection has been developed independently in different forms by Katayama (2), by Mathias (6) and by Thorpe and Rucker (10). From a survey of available data, Lewis (3) has suggested the following relation as the best representation:
[ ( T o- a)/MKI4 = s / ( D - d)4
(3)
in which M is the molecular weight and a and K are constants for one particular chemical group and are probably configurational or cohesional functions characterizing a particular type of molecule. An empirical equation of the following form has been suggested by Samygin (7):
+ bD/M)' (4) I n this equation r is (n*- l)/(n2 + 2), n being the index of refraction; a s = (ar
and b are constants for one particular chemical group. According to Sugden (9), the parachor, PI is
P = MCv' = Ms'l'/(D
- d)
(5)
and when d is negligible in comparison with D, P iq simply Ms'I4/D. Since, according to Lorena and Lorentz, the mole refraction, R , is M(n2 - 1)/ D(n* 2) or Mr/D, equation 4 may be transformed into
+
P=aR+b
(6)
By combining Sugden's definition of P with equation 3, Lewis has obtained
P = (To
- a)/K
(7)
Hence,
(T,
- a ) / K = aR + b
(8)
905
CRITICAL TEMPERATURE FROM REFRACTIVE INDEX
or
T o = kiR
+ k2
(9)
is hereby deduced as a linear relation between T,and R. It is thus possible to calculate the critical temperature from mole refraction and vice versa when the constants kl and k2 are known for one particular chemical group. The validity of equation 9 has been tested with six different types of compounds. The results of this investigation are given in tables 1 to 6. TABLE 1 Hydrocarbons T, = 7.02R 23.1
+ 1
RTDROCARRON
MOLE
CRITICAL TEMPERATURE ~
I
%-Pentane... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %-Hexane n-Heptane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . n-Octane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TABLE 2
Alcohols
T, = 6.74R + 133.0 I AICOEOL _______.--
1
,
Ethyl alcohol . . . . . . . . . . . . . . . . . . . . . . . . . Propyl alcohol . . . . . . . . . . . . . . . . . . . . . . . . . . Butyl alcohol. . . . . . . . . . . . . . . . . . . . . . . . . . i Isobutyl alcohol. . . . . . . . . . . . . . . . . . . . . . . Heptyl alcohol . . . . . . . . . . . . . . . . . . . . . . . . . . I I Octyl alcohol. . . . . . . . . . . . . . . . . . . . . . . . . . . i
i ~
.I
MOLE REFRACTION
12.90 17.51 22.14 26.73 36.28 40.66
CRlTICAL TEMPERATURE
__
____^____
Calculated
219.9 251 0 282 2 313.1 377.5 407 0
,I--i
Observed
243 1 21i3.7
3%
The values of kl and k2 given in tables 1 to 6 have been determined by the method of least squares. For methyl ethyl ether and ethyl nonylate, the mole refraction is estimated from the constants compiled by Smyth (8). In all other cases, it is obtained from the index of refraction and density data given in the International Critical Tables. The observed critical temperatures are taken also from the latter source. Considering the fact that some of these data certainly need revision, the correlation obtained with equation 9 is remarkable. The close agreement between the experimental and calculated critical temperatures of methyl ethyl ether and
906
S. W. WAN
TABLE 3 Ethers T , = 5.81R 67.1
+
1
UOLE
ETRER
RBFRACTION
--
Calculated
1
197 4 225 0 163 2
I
Diethyl ether Ethyl propyl ether Methyl ethyl ether
1
22 49 27 18 16 54
CRITICAL TEMPERATURE
1
I 1
I
Obaerved
193 8 227 4 164 7
TABLE 4 Carboxylic acids T o = 4.09R 268.5
+
'
ACID
I
Acetic acid . . . . . . . . . . . . . . . . . . . . . . . . . . Propionic acid . . . . . . . . . . . . . . . . . . . . . Butyric acid . , , . , . . . , . . , . . . , I Valeric acid.. . . . . . . . . . . . . . . . . . . . . . . . . . . ~
,
, ,
,
,
,
,
, ,
,
~
MOLE REFRACTION
13.00 17.59 22.21 26.77
1I
,
I 1
CRITICAL TEMPERATURE
Calculated
321.7 340.4 359.3 378.0
I
1 ~
~
1
Observed
321.6 339.5 355.0 379.0
TABLE 5 Esters T, = 4.61R 150.8
+
ESTER
Observed
Ethyl Butyl Ethyl Ethyl Ethyl
.I
acetate.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . acetate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . butyrate.. . . . . . . . . . . . . . . . . . . . . . . . . . . . I propionate. . . . . . . . . . . . . . . . . . . . . . . . . ,1 nonylate.:. . . . . . . . . . . . . . . . . . . . . . . .
22.19 31.56 31.54 26.81 54.44
1 1
,
250.1 306 293 273 400
253.1 296.3 296.2 274.4 401.7
TABLE 6
Nitriles T , = 4.02R 228.4
+
Acetonitrile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Propionitrile.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.20 15.76
273.5 291.8
!
274.7 291.2
CRITICAL TEiMPERATURE FROM REFRACTIVE INDEX
907
ethyl nonylate indicates the possibility of predicting the critical temperature of a substance even without knowing its index of refraction, provided the constants of equation 9 have been established for the particular chemical group concerned. Lewis (4)has expressed the idea that the cohesive force between molecules is probably governed to a large extent by the arrangement of electrons around the neutral molecules taken as a whole, and that the major part of the cohesive effect is exerted by those electrons which do not participate in forming a true valence bond. Since mole refraction is a measure of the electronic polarization in a molecule, its rble in equation 9 is not inconceivable. Although, a t the present stage, no exact theoretical explanation can be offered for this relation, it is sufficiently interesting to stimulate further investigation. SUMMARY
1. A linear relation between critical temperature and mole refraction is derived. 2. The relation is tested with six different types of organic compounds for which critical temperature data are available; the agreement between calculated and experimental crit'ical temperatures is good. REFEREXCES (1) FOWLER:Proc. Roy. SOC.(London) 19, 38 (1923). (2) KATAYAMA: Science Repts. T6hoku Imp. Univ. 4, 373 (1916). (3) LEWIS: J. Chem. SOC. 1938, 261. (4) LEWIS: S a t u r e 146, 551 (1940). (5) MACLEOD: Trans. Faraday SOC.19, 38 (1923). (6) 1\fATHIAS: Le Point Critique des Corps Purs, p. 164 (1904). (7) SAMYGIN: J. Phys. Cheni. (U.S.S.R.) 10, 455 (1937). (8) SrryTH: Dielectric Constant and Molecular Structure, American Chemical Society Monograph. Reinhold Publishing Corporation, New York (1931). (9) SUGDEN:Pnrachor and Valency. Routledge, London (1930). (10) THORPE A N D RDCKER: J. Chem. s o c . 46, 135 (1884).
