NOTES
3190
parison with the data. The agreement is good for methemoglobin, but there are noticeable deviations for oxyhemoglobin that are undoubtedly partly explained by some monochromator slit width averaging of the peaks (2-mm. slits were used and the monochromator dispersion was 6.6 mp/mm.).
Table I : Gaussian Fit of Spectra eo
Methemoglobin 630 500 406 388 369 300 265
15870 20000 24650 25800 27100 33300 37750
576 540 450' 416 394 349 2 75
17355 18540 22200 24050 25400 28670 36363
1060 4000 1400 1300 5400 5100 3200
4.2 9.5 125 30 27.0 16.0 31.5
Oxyhemoglobin 550 1100 3200 1400 1200 6200 4220
16.0 15.0 11.0 118 17.0 28.4 35.8
Volume-Energy Relations in Liquids at O O K .
by A. A. Miller General Electric Research Laboratory, Schenectady, N ~ wYork (Received March 16, 1966)
By a special (nonlinear) extrapolation of measured liquid densities, Doolittle' derived the relation, In vo = 10/M, for the specific volumes of n-alkanes in the hypothetical liquid state at 0°K. These values were shown to agree with several earlier, independent estimates.'J Additional confirmation by more recect methods willbe presented later. For ethane, which consists of only two methyl groups, 2ro = 1.396 cc./g. or 21.0 cc./mole of CH3. For the infinite polymethylene chain, uo = 1.00 cc./g. or 14.0 cc./mole of CH2. Comparison of these molar volumes shows that YO(H)= 7.0 cc./mole, with no contribution by the internal carbon atom. Thus, the minimum volume at O'K., where (dE/dv)* = 0, can be attributed entirely to the attraction-repulsion of the peripheral H atoms. By comparison, the van der Waals volumes are u,(CH3) = 13.67, (CHJ = 10.23, (H) = 3.45, and I
(-C-)
= 3.33 c~./mole.~
I
Discussion Earlier result^^^^ gave 104b = 33-36 for other nonheme globular proteins, a significantly higher range than the hemoglobin results reported here. Farultraviolet or infrared transitions of the heme groups would cause greater dispersion in the visible and therefore predict an opposite difference. The peptide chains must therefore be responsible for the difference observed. Variations in amino acid compositionwere considered, but a rough calculation suggested that this effect would not account for the magnitude of the difference. A hypochromic effect in the 19O-mp peptide was also considered (hemoglobin is considerably more a-helical than the other proteins), but the predicted reduction in slope was only a fraction of the observed difference. We have therefore observed a significantly lower dispersion in the globin as compared to other proteins that have been studied, but have not established a quantitative explanation. (15) I. Tinoco, Jr., A. Halpern, and W. T. Simpson in "Polyamino Acids, Polypeptides, and Proteins," M. A. Stahmann, Ed., University of Wisconsin Press, Madison, Wis., 1962,p. 167. (16) K. Rosenheck and P. Doty, Proc. Natl. A d . Sei. U. S.,47. 1775 (1961).
The Journal of Physicd Chemistry
The vaporization energy, BO, for the hypothetical liquid at 0°K. is given by the B constant of the FrostKalkwarf vapor pressure equation: eo = -2.3RB cal./mole.46 Thodos and eo-workers have reported the F-K constants for saturated aliphatic,8 olefinic,7 naphthenic? and aromaticg hydrocarbons, and miscellaneous compounds including CCL.'O It was shown that B is an additive function of the chemical structure. For the n-alkanes,6 following ethane (B = - 1070"),the slope of the linear plot of B us. the number of carbon atoms gives AB = -340"/methylene unit. Hence, BO(CH3) = 2.45 and eo(CH2) = 1.55 kcal./mole, and the ratio is 1.58, which is close to the ratio of the number of H atoms in the two groups. For the eoheaive energy densities, (~/v)o = 117 cal./cc. for CHa ~
~~
-
(1) A. I(.Doolittle, J . Appl. Phys., 22, 1471 (1951). (2) A. P. Mathews, J . Phys. Chem., 20, 554 (1916). (3) A. Bondi, aid., 68, 441 (1964). (4) See E. A. Moelwyn-Hughes, "Physical Chemistry," Pergamon Press, Inc., New York, N.Y., 1961,p. 696 ff. (6) A. A. Miller, J . Phys. Chem., 68, 3900 (1964). (6) N.E.Sondak and G. Thodos, A.1.Ch.E. J., 2,347 (1956). (7) C. H.Smith and G. Thodos, ibid., 6, 569 (1960). (8) G.J. Pasek and G. Thodos, J. Chem. Eng. Data, 7, 21 (1962). (9) D.L.Bond and G . Thodos, &id., 5, 288 (1960). (10) E.C. Reynes and G. Thodos, Ind. Eng. C h m . Fundamatals, 1, 127 (1962).
NOTES
3191
and 110 cal./cc. for CH2, using the Doolittle vo values. By linear extrapolation of vaporization energy us. liquid density plots, it was found earlier that (E/V)O N 117 cal./cc. for the C5 to CIZn-alkane~.~ The following new relationship between EO and vo and the van der Waals constants a and b is proposed ab/vo2 (1) This originates from the equation EO = a’/vo, for a van der Waals liquid,’l with the argument that the a’ applying at 0°K. and the van der Waals a applying at the critical point are related as a’ = a(b/vo). It will be recalled that, in terms of the critical constants, a = 27R2Tc2/64Pcand b = RTc/8P,. By structural additivity, Thodos has derived a and b values which give excellent agreement with the observed critical constants for olefinic, saturated aliphatic, naphthenic, and aromatic hydrocarbons.12 By eq. 1, using the Thodos eo, a, and b values, we may compute VO. Table I compares several estimates of vo for nalkanes. For the van der Waals rule,2 vo = zcv, where zo = (PV/RT),, the critical constants reported by Kobe and Lynn were used.13 Although the methods of Riedel14and Pitzer are similar, the latter’s equationls with reported “acentric factors”l6 and critical densities13gives vo values which are 5% lower. After methane, the other four methods show agreement to within 2%. Above CgHl3, however, vo = elO/M and eq. 1 give diverging values, and for CZ0H42,va = 1.036 and 0.976 cc./g., respectively. The zero-point volumes of the crystalline solids17 are 2 to 3% lower than the values in the first column of Table I. EO
=
Table I : Specific Volumes of n-Alkane Liquids at 0°K. (ab/sa)’/2
CH4 C& CaHs C4&0 C5Hi2 c~H14 c~Hi6 CsHls
... 1.396 1.256 1.189 1.150 1.123 1.105 1.092
1.88 1.40 1.27 1.19 1.15 1.12 1.10
1.08
zovc
Riedel“
Pitrerls
1.78 1.40 1.26 1.20 1.16 1.13 1.10 1.10
1.75 1.335 1.235 1.180 1.150 1.130 1.116 1.105
1.64 1.28 1.17 1.12 1.09
... 1.05
...
The vo values, computed by eq. 1, for four compact symmetry, are ‘Ompared in molecules with ‘I with “hard-core volumes,” ’*, derived by Flory and Abe from thermal expansion coefficientsat 2 5 O . 18 Based on Thodos’ Eo-values, the cohesive energy at ‘OK* js ‘Ompared with the F1Ory ’* energy parameter.
Table II : Volume-Energy Parameters for Spheriodal Molecules VO,
cc./g.a
CeH6
0.880
ccI4
0.492 0.980 l.i4
c-C~H~Z C(CH&
*,
u co./g!
0.885 0.485
1.00 1.19
4%
oal./cc.
p*, cal./oc.b
Ratio
150 136 127 95
0.92 0.93 0.95 0.93
163 146 133 102
By eq. 1. ’See ref. 18, at 25”.
By the van der Waals rule, vo = z,v,, and eq. 1, we obtain Eo(cal./mole) = (0.0527zc-4)RTc
It may be noted, in passing, that if vo = xcvc, b = v , ~ / ~ v orather , than*b = v,/3, a well-known discrepancy in the van der Waals equation.
Discussion The scope of the simple relation, go = ab/vo2,requires further empirical examination, particularly since its theoretical basis is not immediately apparent. The Frost-Kalkwarf vapor pressure equation, in a reduced form, has been shown to apply to a broad range of polar and nonpolar, organic and inorganic liquids, where hydrogen bonding is absent.Q For such liquids, the empirical constants of the F-K equation can be calculated from a single reduced vapor pressure point. Thus, the critical pressure and temperature and the normal boiling point, for example, are sufficient to define vo via eq. 1and also vc via the van der Waals rule: vc = ( V ~ R T ~ / P ~ ) ~ ~ * . A thermochemical interpretation of the F-K equation, in terms of AH’o and AC,, has been discussed.20 The present work, together with the e p relations reported previou~ly,~ may be useful for deriving an alternate interpretation, with the liquid volume as an explicit parameter. ~~
(11) See ref. 4, pp. 378, 379. (12) G. Thodos, A.I.Ch.E. J., 1, 165, 168 (1955); 2, 508 (1956);3, 428 (1957). (13) K. A. Kobe and R. E. Lynn, Chem. Rev., 52, 117 (1953). (14) L. Riedel, Chem. Ingr.-Tech., 26, 257 (1954). (15) See G. N. Lewis and M. Randall, “Thermodynamics,” McGrawHill Book Go., Inc., New York, N. Y., 1961, p. 621. (16) K. S. Pitzer, et al., J . Am. Chem. SOC.,77, 3433 (1955). (17) See A. Bondi, J. Phz/s. Chem., 58, 929 (1954), Table V, eq. 2. (18) P. J. Flow and A. Abe, J. A m . Chem. SOC.,86, 3563 (1964). (19) see D. G. Miller and G. Thodos, I&. EW. Chem. Fundumatala, 2, 78, 80 (19631, for the reduced F-K equation in terms of the Riedel ac-parameter. (20) A. Bondi and R. B. McConaughy, Proc. Am. Petrol. Inat., Sect. III, 42, 40 (1962).
Volum 68,Number 9 September 1966
