KOTES
3900
Vapor ization Energy and Density Relations in Nonpolar Liquids
P
/‘
by A. A. Miller General Electric Research Laboratory, Schenectady, New Yorlc (Received J u l y 3, 1964)
-
The vaporization energy is important for the interpretation of liquid-vapor equilibrium. Also , the derived quantities, “cohesive energy density,” e / v , and ‘(solubility parameter,” ( E / V ) ‘ / I , have been suggested as empirical measures of intermolecular attraction in liquids. This paper presents a simple relationship between vaporization energy and density which apparently has not yet been reported, and certainly not emphasized, in the literature.2 The examples of nonpolar liquids which are considered are benzene, carbon tetrachloride, and six normal alkanes in the Cg to Clz range. Liquid densities were taken from A.P.I. Tables3 and from T i n ~ n e r m a n s . ~ The latter was also the source of the orthobaric vapor densities. For benzene and n-heptane, the vaporization energies up to the boilihg points, TB, were computed from Haggenmacher’s5 values of the heat and external work of vaporization: e = h - pAv. Between TB and T c , the Clapeyron equation was used E
= P ( V , - VI)
[(T/p)(dp/dT) - 11
with the dp/dT = yc values reported by Rowlinson.6 For carbon tetrachloride, the vaporization energies tabulated by :\Ioelwyn-Hughes7 between 0’ and TC were used directly. Figure 1 shows that for each of these three liquids, the vaporization energy is a linear function of the liquid density over the entire liquid range. Extrapolation to E = 0, the critical point, gives the proper values of the critical densities, pc.8 Hence E
= k(P
-
Pc)
(1)
--
t,
I I
/
I
/
/--
/’
,
/
I * < $
05
I
I
I
I
I
I
,
I
io I5 LIQUID DENSITY, p ,9m I c c
I
I
c
I
I 20
I
,
, -
Figure 1. Vaporization energies us. liquid densities for benzene, carbon tetrachloride, and n-heptane. Arrows indicate boiling points.
By an additional semiempirical term, Frost and KalkwarflO extended the K-R equation to the critical point. The I?-K constants have been reported by Thodos and co-workers for saturated aliphatic’’ and aromatic hydrocarbons,12 and for CCl,. l 3 As should be expected, the F-I< and the K-R9 constants have similar values. In the present context, the derivation of the K-R vapor pressure equation differs somewhat from the conventional m e t h ~ d . Starting ~ with the exact Clapeyron equation, dp/dT = h/TAv, with h = E pAv and with the usual simplifications, applying up to approximately the boiling point (Av = v, and pv, = RT), we obtain d In p/dT = e/RT2 1 / T , but dJdT = (de/dp)(dp/dT) = k(dp/dT) by eq. 1. Plots of p us. T show that with nonpolar liquids for the small
+
+
~~~
~
~~
~
(1) J. H. Hildebrand and R. L. Scott, “The Solubility of Nouelectrolytes.” Reinhold Publishing Corp., New York, N. Y., 1950. (2) J. R. Partington, “Advanced Treatise on Physical Chemistry.” Vol. 11, Longmans, Green and Co., London, 1951. (3) F. D. Rossini, “Physical and Thermodynamic Properties of Hydrocarbons,” A.P.I. 44, Carnegie Press, Pit,tshurgh, Pa., 1953. (4) J. Timmermans, “Physico-Chemical Constants of Pure Organic Compounds.” Elsevier Publishers, New York, N. Y., 1950. (5) J. E. Haggenmacher, I n d . E n g . Chem., 40, 436 (1948). (6) J. S. Rowlinson, “Liquids and Liquid Mixtures,” Butterworths, London, 1959, Tables 2.3 and 2.4. (7) E. A. Moelwyn-Hughes, ”Physical Chemistry,” Pergamon Press New York, N. Y . , 1961, Table XVI-10. (8) K . A. Kobe and R. E. Lynn, Jr., Chem. Rev., 52, 117 (1953). (9) See E. A. Moelwyn-Hughes, ref. 7, p. 696 ff. (10) A. A. Frost and D. R. Kalkwarf, J . Chem. Phys., 21, 264
where k = de/dp. The values of k (cal. cc./g.2) are 169, 43.5, and 185, for CeHe, CC14, and C ~ H Mre, spectively. When extrapolated in the direction of higher densities, the lines in Fig. 1 should terminate a t eo, pa for the hypothetical liquid at OOK., where eo = ho, the heat of (1953). vaporization. The latter can be’derived froin accurate (11) N. E. Sondak and G. Thodos, A.I.Ch.E. J., 2, 347 (1956). vapor pressure equations, such as the IGrchoff(12) D. L. Bond and G. Thodos, J . Chem. Eng. Data, 5, 288 (1960). Rankine (K-R) equation, of the form: log p = A (13) E. C. Reynes and (3.Thodos, I n d . Eng. Chem. (Fundamentals), BIT C log T , where ho = - 2 . 3 R B / M ~ a l . / g . ~ 1 , 127 (1962).
+
T h e Journal of Physical Ch,emistry
+
NOTES
3 901
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expansions up to Z'B, p is very nearly linear in T . Under these condition^,'^ E = eo aT. Substitution in the Clapeyron equation and integration gives the Kirchoff-Rankine equation
+
In p
=
A
-
eo/RT
+ [l + a/R1 In T
(2)
talline solids. 18 However, they are consistently 2% higher than values given by the Doolittle relation,lg - l O / M , which, in turn, are about 1% above values PO = e derived by Riedel.20 I n an earlier papcr,l6 the liquid viscosities of CsH6 and CCl, were related to the free volume fraction, defined as f = ( v - v O ) / u = ( p o - p ) / p o . E'roni the present work, f / f c = (eo - e)/eO, where fc refers to the critical point. For the nonpolar liquids considered here, p,/po 'v 0.25 and fc N 0.75, with the values differing slightly for each liquid.
For C6H6, cI) (cal./g.) = 140, 153 (K-R),9 144 (F-K),12 and 150, from latent heats determined in the 20-50' rangels and extrapolated linearly to O'K. A mean value, 147 (+=6) cal./g., gives, by Fig. 1, po = 1.'17 (=k0.04) g./cc. For CCL, eo = 73 (K-R)9 and 70.5 (14'-K)13 giving po = 2.15 (-10.04) g./cc. These values (14) Direct e 5s. IT plots of the Haggennmcher values. up to 7 ' ~show are consisteni with po e 4pc = 1.22 and 2.22 g./cc., very little curvature. Since h = B 4- E T , for the conditions cited, respectively, which were found to apply in a free volunie h is also linear in T , which is the basis for usual derivation of the treatment of liquid viscosities for C6Hs and cc1*.J6 K-R equation. (15) See J. It. Partington, ref. 2, p. 315. For C7H16, eo = 126 cal./g.,I' and by Fig. 1, po = 0.92 (16) A. A. Miller, J . Phys. Chem., 6 7 , 2809 (1963). g./cc. (17) G. Allen, G. Gee, and G. J. Wilson, Polymer, 1, 458 (1960). By eq. 1 and Fig. 1 we obtain the further relations E2
-
€1 :=
k(p2 - p1) ; E
k = =
- Po) ;
Ell/(PO
€0
(18) See E. A. Moelwyn-Hughes, ref. 7, p. 320. (19) A. K. Doolittle, J . A p p l . P h y s . , 22, 1471 (1951). (20) L. Riedel, Chem.-Ingr.-Tech., 26, 257 (1954)
+ (dE/dp)(p
PO>
(3)
The parameters for six normal alkanes are listed in Table I. Thlc slopes, de/dp, were derived from the linear E 11s. p plots based on the Haggenmacher values.6 The B constant in the F-K equation'l was used to obtain eo. Ai3 a convenient reference point, the 'E, p data a t 20' are 1 i ~ t e d . l ~ With these data and eq. 3,
The Conductance of Some Quaternary Ammonium Electrolytes in Hydrogen Cyanide
by R. H. Davies Table I : Vaporization Energy-Density Parameters for +Alkanes, C,H2,+2
cs Ce
c7 cs c,o Ci2
de/dp, cal.
€0,
t,
cc./g.*
cal./g.
cal./g.
200 193 185
133 129 126 124 121 120
80 0 81 6 82 0
181 174 162
Department of Chemistry, University College, Swansea, Walee
and E. G. Taylor
-----200-
82 5 83 0 83 0
PI
PO,
eom,
g./cc.
g./cc.
cal./cc.
0 0 0 0 0 0
626
660 684 703 730 749
0 0 0 0 0 0
891 906 922 941 948 977
Thompson Chemical Laboratory, W i l l i a m s College, Williamstown, Maasachusetts (Receii-ed Julg IS, 1964)
118 117 116 117 115 117
the values of po were derived. For this series of nalkanes, the "cohesive energy density" a t OoI cal./cc. For the same series a t 20°, the c.e.d. increaseci regularly from 50.2 to 62.1 cal./cc.17 The critical densities, p., calculated by eq. 1, are within 3% of the literature values,a and the ratio pa/po decreases slowly froni 0.260 for C5Hlz to 0.243 for Cl2H2,, paralleling the trend in the critical compressibility factor, ( P V / R T ) C . ~The , ~ po-values in Table I are within 1% of the zero-point densities for the crys-
The fact that earlier work in hydrogen cyanide' indicated unusual behavior of salts containing large ions has led us to reopen the investigation. Furthermore, the recent ex tension of the Onsager conductance equation, in addition to providing a reason for the anabatic behavior previously observed, may be applied to conductttnce data at higher concentrations than formerly used. We have also, therefore, talteii the opportunity to show that the long-chain quaternary ammonium salts behave as normal electrolytes in hydrogen cyanide.
Experimental MateriaZs. Hydrogen cyanide as supplied (Imperial Chemical Industries, Ltd.) contained up to 1.8%:, ( I ) J. E. Coates and E. G. Taylor, J . C h e m SOC.,1245, 1495 (1936)
Volume 68, Number 12 Decemher, 1964
