NOTES
202 1
tion. This expression can be simplified further since (dW/dr) = 0 and (d2W/dr2) = k , when r = re, the equilibrium internuclear distance. Substituting (2) in (1) and differentiating eliminates A , and we will have the following expression for thle binding energy,
wo.
sublimation of the oxide may be calculated. The calculated results are compared with the best available experimental data8 in Table I. Except for the magnesium oxide, the agreement with the experimental values seems reasonable. This indicates that the bonding in MgO is not as ionic as the other three, or the molecular parameters available are in gross error.
Table I : Dissociation Energies for Alkaline E a r t h Oxides
Oxide
(4)
MgO CaO SrO BaO
- Wo, the binding energy, is the energy required to separate the two ions from equilibrium position to infinite distance apart. Though p , the repulsion force constant, can be calculated for each molecule utilizing the reported force constants, it is calculated for BaO(g) only and the same value for p is assumed for others. This approximation is necessitated by the fact that the reported force constants for all but BaO(g) are for the excited states. The polarizabilities for cations are taken from the paper of Tassman and Kahn4 and a value of 2.75 X cm.3 for 0-2 (the best available data); p for BaO(g) was calculated to be 0.31 8. The re values (A.) used are BaO = 1.94, SrO = 1.92, CaO = 1.82, and hlgO == 1.75, taken from the recent compilation by Brewer and R o ~ e n b l a t . ~ Once Wo values are calculated, a simple Born-Haber cycle would yield the dissociation energies
LXO(g)
-2 LI+2(g) + 0 - 2 ( g )
iD0 nf(g)
+ O(g)
-
- Wa, kcal./ mole 684 649 639 643
Dissoci&tion energy, -kc&l./mole-This work Ref. 8
Heat of sublimation a t -29S°K., kcal./moleThis work Exptl. data Ref.
102 234 f 15 163 f 10 10 f 10 83 f 10 5 9 9 169 f 15 147 f 15 102 f 10 5111 143 i 15 126.7 141 :-t 10 132 95 i 15 104 i 4
a b
8 2b
'
a R. L. Altman, J . Phys. Chem., 67, 366 (1963). T. P. J. H. Babeliowsky, A. J. H. Boerboom, a n d J. Kistemaker, Physica,
28, 1155 (1962).
Even though the model assumes a completely ionic bonding, which certainly is an approximation, a reasonable estiniate of the djssociation energy of a diatomic molecule may be made based on such a model for the highly electropositive metal oxide. (4) J. R. Tassman and A. H. Kahn, P h y s . R e t . , 9 2 , 890 (1953).
(5) L. Brewer and G. M.Rosenblat, private communications. (6) D. F. C. Morris, Proc. R o y . Soc. (London), A242, 116 (1957). (7) (a) National Bureau of Standards, Circular 500, 1952; (b) 0. E. Krikorian, J . P h y s . Chem., 67, 1586 (1963). (8) R. J. Ackermann, R. J. Thorn, and G. H. Winslow, Planetary Space Sci., 3, 12 (1961).
Evidence of Validity of Amagat's Law i n Determining Compressibility Factors for Gaseous
I
.Iff2(g)
+ O(g)
I is the total energy required to remove two electrons from metal atoms, and E is the electron affinity for O(g) for two electrons. The values for I are known better than a few tenths of a per cent. The same is not true of E , and the best reported value ( E = + l 5 3 kcal./mole) is by ?vIorris.6 The d,issociation energy for BaO(g) calculated, based on this model, is 141 f 10 kcal./mole, which is in fairly good agreement with the best thermochemical value of 132 d: 4 kcal./mole caiculated using the best heat of sublimation data.2b Combining the dissociation energies with heats of sublimation for heats of formation for oxideslVb and the dissociation energy for oxygen, the heats of
Mixtures under Low and Moderate Pressures
by Philip S. Ton Sacramento County Department of Public Health, Sacramento, California (Received February 8, 1964)
The compressibility factor, z, defined as pvlnRT, is the most common term used to express the compressibility deviation of a real gas or gaseous mixture from its expected behavior if it were an ideal gas. Experimental values of z, calculated from density measurements or from isothermal volumetric measurements a t varying pressures, have been determined for many Volume 68, Number 7
J u l y , 1964
2022
NOTES
pure gases aiid a few mixtures. Experimental values of variously expressed compressibility deviations have been the basis for determining constants for the many more or less accurate equations of state for real gases. When the critical constants are known for a pure gas, x values may be estimated by recourse to the law of corresponding states and graphs showing x values us. reduced temperatures and pressures. Methods for determining equations of state for gaseous mixtures have been developed by combining constants of equations for the pure components in various ways. Another method of determining compressibility deviations for mixtures, generally easier to apply, involves direct usc of the x factors of the pure components. When the molar composition of a mixture is known, the expression 2,iX
=
21x1
+
22x2 .
.... .
+ znxn
(1)
(where xl, 5 2 , etc., equal the mole fractions of the components, and a, x2, etc., equal the compressibility factors of the components) may be used to estimate the compressibility factors of a mixture, where all components exist as gases a t the applicable pressures and temperatures involved. The question arises in using eq. 1 as to what x values to use for the individual components; that is, whether they should be those of the pure components a t their respective partial pressures in the mixture, or those of the pure components each at the total pressure of the mixture. I n Gibbs’ interpretation of Dalton’s law of partial pressures,* and as advocated by G i l l e ~ p i e , ~ calculations based on partial pressure conditions should give valid results. If Amagat’s law of partial volumes is considered valid,* however, it would appear that total pressure conditions should be used. Amagat’s early data5 on compressibilities of nitrogen, oxygen, and air at elevated pressures were used by him to justify his law. It has been found since, in general, that use of total pressure x factors for components results in z values for mixtures which are in better agreement with experimental values at high pressures than those which would result from use of partial pressure factors. Where low pressures are considered, compressibility deviations of mixtures are often small enough to be ignored for many applications, and few experimental data have been published. The assumpt’iorlhas Often been made that Dalton’s law would be valid under these conditions, and component z values used should be those ullder partial pressures, The of both the partial pressure and the total pressure met,hods in obtaining z values for mixtures is tested herein by use of x values for air and for the three principal conT h e Journal 0.f Physical Chemistry
stituents of air. Iralues of x for air were calculated by both methods using eq. 1 and are compared with experimentally derived x values for air. The x factors of the pure components do not differ greatly a t like temperatures and pressures. To compare the two methods, however, it would appear that the necessary and sufficient condition would be only that the x factors vary significantly with pressure. Table I gives Compressibility factors for nitrogen, oxygen, and argon at 1 atm. and 1OOoK.,and 1, 10, 40, and 100 atm. a t 200 and 3OO0K., and also z factors
Table I : Compressibility Factors for Principal Constituents of Air Pressure, Temp., etm. OK.
--Oxygen-At
At p
p
Compressibility factorsa---
I
-Kitrogen-0.78~
Aip
100
1
0.981
0.986
200
1
0.99788 0.9788 0.9185 0.844
0.99834 0.9970I 0.9834 0.90956 0.9354* 0 . 8 7 3 4 0.863b 0.6871
10 40 100 300
1
10 40 100
0.99982 0 . 9 9 9 8 6 0.99838 0.99870 0.9982 0 9962 1 . 0 0 6 4 0 9998
0,9772
-Argon--. Ai 0.21~
At p
Ai 0.01~
0.9954
0.9782
0.9998
0.99937 0.99370 0.974Zb 0.930b
0.99704 0.97023 0.8778 0.6917
0.99997 0.99971 0.99882 0.99706
0 99939 0.99987 0.99937 0 . 9 9 9 9 9 0.99402 0.99873 0.99382 0.99994 0 . 9 7 7 3 0 . 9 9 5 0 0 . 9 7 7 3 0.99975 0 . 9 5 4 1 0 . 9 8 7 4 0 , 9 6 3 3 0.99937
a Ref. 8. The values shown are z factors for partial pressures slightlydifferent from 0 . 7 8 ~or 0.21p, to adjust. for the considerable difference in z factors. The final result in Table 11, however, is not affected by these adjustments within the number of significant figures given.
for these gases at the applicable partial pressures involved. For purposes of this study, air is considered to consist of 78% N,, 21% 02,and 1% Ar (where the molar values are, respectively, 78.08%, 20.95%) and 0.93YG6’~.Table I1 gives the compressibility factors for air as calculated using eq. 1 and using x values of components both under the partial pressures and under the total pressures involved, aiid compares these values with experimental values for air itself. The latter values were derived from compressibility measurements of many investigators, and closely follow the Beattie-Bridgeman cquat>ionof state.’ (1) See, for example, J. A. Beattie, W.H. Stockmayer, and H . G . Ingersoll, J . Chem. P h y s . . 9, 871 (1941); J. 0. Hirshfelder and W. E. Roseveare, J . Phys. Chem., 43, 15 (1939). (2) J. m‘, Gihbs, Papers, 1, 155 (1906). (3) L. 3 . Gillespk Phys. Rev., 36, 121 (1930). (4) E H. Amagat, Compt. rend., 127, 88 (1898). (5) E. H . Amagnt, Ann. chim. p h y s . , [ 5 ] 19, 345 (1880). (6) “G. El. Standard Atmosphere,” G. S. Government Printing Office, Washingtor), D. c.,1962, p. 9.
NOTES
2023
Table I1 : Comparison of Calculated and Experimental Compressibility Factors for Air Compressibility faciors----Calcd. from Calcd. from t o t d pressure partial pressure From equations z factors z factors of statea
law a t low pressures, the partial pressure method cannot be presumed in general to be more accurate. (7) J . A. Beattie and 0. C. Bridgeman, Proc. Am. A c a d . A r t s S c i . , 6 3 , 229 (1928). (8) J. Hilsenratz,. et al., "Tables of Thermal Properties of Gases," National Bureau of Standards Circular KO. 564, U. S. Government Printing Office, Washington, D. C., 1955.
_ _ I -
Temp.,
Pressure,
OK.
atm. p
100
1
0.980
0.9813
200
1 10 40 100
0 0 0 0
99769 9768 9086 810
0 0 0 0
99856 9857 9441 878
0 0 0 0
99767 97666 9080 8105
1 10 40 100
0 0 0 0
99972 99741 9920 9941
0 0 0 0
99986 99872 99130 9972
0 0 0 0
99970 99717 99135 9933
300
a
0.9809
Ref. 8
(9) C. W. Solbrig and R. T . Ellington, A.I.Ch.E. Chern. E n g . Progr. Series, 5 9 , 127 (1963).
A Color Reaction between Trinitrobenzoic Acid and Acetone
by John E. Neufer, Rloshe H. Zirin, and Dan Trivich D e p w t m e n t of Chemistry, W a y n e State University, Detroit 8. Michigan (Received February 1 4 , 1964)
A review of the results of comparison in Table I1 will show that, in all cases presented, the use of component x values a t total mixture pressures will give results closely approximating the experimentally derived values, and in most (if not all) cases within experimental accuracy. The use of the partial pressure method is converse1:y shown to be apparently much more unreliable iii estimating compressibility factors for air, and in most cases gives results considerably outside experimental error. If it is assumed that the total pressure method is more valid for pressures down to 1 atm., the rather theoretical question may be raised as to whether or not that method would also be more valid for pressures under 1 atm. This (question can be answered by considering the low pressure isothermal x curves for air, and the components of air, vs. pressure. These isothermals at all except extremely low temperatures are found to be essentially linear, converging as expected to unity a t zero pres~,ure.~''The deviation from unity of an isothermal would then be essentially proportional to pressure. Therefore, if the total pressure x values of components were used and were more valid in determining the z values for a gas a t l atm., they would also be more valid a t any lower pressure down to zero. The foregoing analysis does not prove, of course, that use of total pressure component x values would always give answers closer to experimentally derived z values for mixtures than would the partial pressure method, for moderate and low pressures. For example, mixtures of hydrogen and ethane under moderate pressures apparently do not follow Amagat's law.g It would appear, however, that lacking more experimental data which would contradict Amagat's
We have found that dilute solutions of 2,4,6-trinitrobenzoic acid (TH) in acetone, which are nearly colorless when freshly prepared, develop green to red colors on standing in the dark. Exposure to strong visible light bleaches the color and the darkening-bleaching cycle can be repeated a large number of times. This suggests that TH forms a complex with acetone since solutions of TH in water, alcohol, and dioxane do not produce similar colors. A number of color-forming reactions have been reported involving nitro compounds and acetone, e.g., by Willgerodt,l Janovsky, and others. 3--6 An extensive study of this field has been reported by C a n b a ~ k . ~ I n contrast with the present reaction between T H and acetone, the previously reported methods for the development of color invariably required the presence of base and, further, the colored solutions obtained were not reported as being sensitive to exposure to light. Extensive tabulations of complexes formed by nitro compounds are included in reviews by Andrew8 and Briegleb.9 It is pointed out that usually nitro aromatic ~
~~
(1) C. Willgerodt, Ber., 14, 2451 (1881); 2 5 , 608 (1892). (2) (a) J. V. Janovsky and L. Erb, ihid., 19, 2155 (1886); (b) ihid., 2 4 , 971 (1891).
(3) M . Jaffe, Z. physiol. Chem., 10, 390 (1886). (4) C. L. Jackson and R. S.Robinson. Am. Chem. J . , 1 1 , 93 (1889). ( 5 ) V. Meyer, Ber., 2 9 , 848 (1896). (6) R . W. Bost and F. Nicholson, I n d . Eng. Chem., A n a l . Ed., 7 , 190 (1935). (These authors mention in a table that T H forms a color with acetone in the presence of alkali.) (7) T. Canbick, F a r m . Revy, 48, 153, 217, 234, 249 (1949). ( 8 ) L. S.Andrews, Chem. Rev., 54, 713 (1954). (9) , G . Briegleb, "Elektronen-Donator-Acceptnr-Komplexe," Springer-Verlag, Berlin, 1961.
Volume 6 8 , *Yurnher 7
Julu, 1964
