DAVIDHART
202
Vol. 56
THE PERIODICITY OF CHEMICAL THERMODYNAMIC FUNCTIONS BY DAVIDHART Chemical Research Laboratory, Picatinny Arsenal, Dover, New Jersey Recebed December 18, 1960
An extensive study of the periodicity of chemical thermodynamic functions has developed definite relationship between atomic number and equivalent heat of formation, entro y, oxidation-reduction potential, ionization potential and electronegativity for oxides. Halides and sulfides also have gee, studied.
I. Introduction
show. a very definite and interesting periodicity. By the equivalent heat of formation of oxides is Ever since the time of Berthelotl attempts have been made to determine whether a more.or less meant the value obtained by dividing the heat of general relationship exists between the heats of formation by the number of equivalents of oxygen. In Fig. 1, only those values were taken for the formation of inorganic compounds and the periodic oxides which correspond to the predicted valence system. While the results of these attempts showed a definite relationship within each periodic given by the periodit table. Solid lines were group, it was not until recently, when Trombe2 con- drawn between points obtained from the heats of sidered the heat of formation per gram atom of formation values available in the literature. The halogen instead of the molecular heat of formation values were taken from Bichowsky and Rossinilg of the halide, that any general relationship was in- Latimer,'O Thompson," Kelley,12J3and the National dicated. An excellent summary of these attempts Bureau of Standards.14 By following the pattern is given by Sue3 who, like Trombe, plotted that the indicated, dotted lines were drawn from which the heat of formation per gram atom of the electroneg- approximate values of the equivalent heats of formaative element as a function of the atomic number tion of oxides can be estimated for which there are of the less electronegative element in the compound. at present no data in the literature as to their heats However, Sue applied this method to oxides, sul- of formation. From the estimated equivalent fides and nitrides as well as to halides aEd obtained heats of formation taken from the figure, the cora series of saw-tooth curves. He also tried to re- respon'ding heat of formation can be calculated. late the heats of formation of inorganic compounds The curves obtained are a series of approximately to the average ionization potentials, i.e., the energy parallel straight lines with some deviations for the required to separate all the valence electrons of oxides of the elements at the beginning of a period. an element divided by the number of these elec- Thus, for the first period, all except lithium oxide fall on a straight line. For the second period, sotrons. Using the concept of electronegativity, Pauling4 dium oxide does not fall on the straight line and introduced a certain amount of order into inorganic magnesium oxide is also somewhat off. The thermochemistry. The electronegativity, which is maxima of these curves occur with lithium oxide directly related to the heat of formation, was plotted for the first period, the divalent element oxides for the second and third periods, and the trivalent as a function of the atomic number. As a result of a systematic investigation, begun element oxides for the other periods. in 1942, of a number of inorganic oxidation-reduc- 111. Equivalent Free Energy of Formation of tion reactions between finely divided solid parOxides and Atomic Number t i c l e ~ , ~the - ~ existence of a more or less general Although the standard heat of formation, -AH!, relationship between a number of thermochemical as well as thermodynamic functions and the periodic of the oxides a t 298.160K.15 has been considered a system was recognized. Some of these functional rough measure of the stability, the true measure of relationships have not yet appeared in the litera- this property is considered to be the standard free ture. It is the purpose of this paper, therefore, to energy of formation, -AF: a t 298.16"K. In a show that a careful consideration of these relation- series of publications beginning with 1932, Kelley12 ships will reveal the existence of considerable of the U. S. Bureau of Mines, gives the most probamount of order in the field of inorganic thermo- able values of the standard free energies of formation at 25". In 1942 Thompsonll published a chemistry.
Equivalent Heat of Formation and Atomic Number If the equivalent heats of formation of the oxides of the elements are plotted as a function of the atomic number, a series of curves is obtained which 11.
(1) Berthelot, "Thermochemie," Vol. I. p. 284. (2) C. R. Trombe, Acad. Sei., 218, 457 (3) Pierre She, J . Chim. Phya., 48, 45 (1945). (4) Linus Pauling. J . A m . Chcm. Soc., M, 3570
(1944). (1932).
(5) George C. Hale and D. Hart, U. S. Patent 2,461,544 (1949). (6) Georgs C. Hale and D. Hart, U. S. Patent 2,467,334 (1949). (7) George C. Hale and D. Hart, U. S. Patent 2,468,061 (1949). (8) D. H4rt, Unpublished Results and Picstinny Arsenal Technical Reports.
(9) F. R. Bichowsky and F. D. Rossini, "The Thermochomistry of the Chemical Substances." Reinhold Publishing Corp., New York N. Y., 1936. (10) W. M. Latimer, "The Oxidation States of the Elements,' Prentice-Hall, Inc.. New York, N. Y . , 1938. (11) M. deKay Thompson, "The Total and Free Energies of Formation of Oxides of Thirty-Two Metals." The Electrochemical Society. Inc., New York, N. Y., 1942. (12) K. K. Kelley, U. 8. Burtaii of Mines. Bull., 350 (1932). (13) K. K. Xelleyand C. T. Anderson, U.S. Bureau of Mines, Bull., 384 (1935). (14) F. D. Rossini, D. D. Wagman, W. € Evans, I. L. Levine and I. Jaff. "Selected Values of Chemical Thermodynamic Properties " N. B. S. Circular 500. U. S. Govt. Printing Office, 1951. (15) G. N. Lewis and M. Randall, "Thermodynamics and the Fre Energy of Chemical Substances," McGraw-Hill Book Co., Inc., New York, N. Y., 1923.
Feb., 1952
THEPERIODICITY OF CHEMICAL THERMODYKAMIC FUNCTIONS
10
I
I
20
30
1
I
I
40 50 60 70 ATOMIC NUMBER.
I
I
80
90
208
1
IC
Fig. 1.
comprehensive critical survey of free energy relations for thirty-two metallic oxides. More recently the National Bureau of Standards,13 with the aid of the U. S. Navy Department, Office of Naval Research, is compiling “Tables of Selected Values of Chemical Thermodynamic Properties.” However, many values for the free energy of formation of oxides still are not available. I n Fig. 2 the equivalent free energies of formation of the oxides, calculated from available free energies of formation, were plotted as a function of atomic number. The curves obtained were a series of approximately parallel straight lines, similar to those in
Fig. 1 for the equivalent heats of formation. The corresponding decomposition potentials were calculated and an appropriate scale placed on the righthand side in Fig. 2. Here, too, solid lines were drawn between points obtained from the literature values and dotted lines were drawn to follow out the pattern. In this manner approximate valws for equivalent free energies of formation were obtained from which approximate values for the corresponding free energy of formation could be calculated which are not available in the literature. A tabulation of the values used to obtain Figs. 1 and 2 is given in Table I. Included in this table
Fig. 2.
DAVID HART
204
Vol. 56
TABLEI CHEMICAL THERMODYNAMIC PROPERTIES OB THB ELEMENTS AND O m s s Entropy of Atomelsmenb et ic 298.WK. So, c a l . 1 Periodic num- Elenient der. mole group ber 1 Ii 31.2" 3 1.i 6.7 IA Ne 11 12.2 19 K 15.2 Rb 37 16.6 CS 55 19.8 87 (22 * 5) cu 29 IB 7.96 47 10.21 Ag Au 11.4 79 Be IIA 4 2.28 12 7.77 Mg Ca 9.95 20 Sr 12.516 38 Ba 56 16.216 Ra (19.9) 88 En IIB 30 9.95 Cd 48 12.3 18.5 80 Hg B 5 IIIA 1.7 AI 13 6.75 21 ac 11.0" 10.516 39 Y 13.7 57 La (Rare Earths) Ao 89 10.2 IIIB 31 Ga 12.5 In 49 15.4 TI 81 7.24 IVA 22 Ti 9.18 Zr 40 Hf 13.1 72 Th 13.6 90 C 6 1.36d IVB 14 Bi 4.47 32 10.14 ee Sn 12.3 50 15.51 Pb 82 V 23 7.05 VA Cb 41 8.471' Ta 73 9.9 91 Pa 45.77" VB 7 N 15 P 10.6' AB 33 8.4 Sb 51 10.5 13.6 Bi 83 Cr 24 5.68 VIA Mo 6.83 42 74 8.0 W 92 U 11.1 0 49.003" 8 VIB 16 S 7.62' Se 10.0 34 11.88 Te 52 Po 84 Mu 7.61 25 VIIA 43 8 Re 75 93 F VIlB 9 48.6' 17 Cl 53.294 Br 35 36.4b I 53 27.9' 86 a Value for diatomic gas. Rhombic. Red.
Oxide Ha0 Lit0 Na:O
KaO RbrO Car0 cuzo Agio Aut0 Be0 M go CaO SrO BaO RaO ZnO CdO
H . 0 BaOi Ah01 ScaOi
YZOi Lax08
Entropy of oxide et 298.16OK. Sa. cel./ der. mole 16.72 (5.9) 17 (22.9) (25.7) (32.1) (37.5) 24.1 29.09 (34.8) 3.37 6.55 9.5 13.0 16.8 (19.9) 10.5 13.1 17.2 ( 2.4)
12.6 (15) (20) (26.4)
Into: TlaOi Ti02 ZrOa HfO: ThOi
c0; Si02 GeOt
suo; PbOa
vror CbiOb TsrOr Par06
24 29 (35.4) 12.01 12.03 19.6 19.6 51.06 10.00 (13) 12.5 18.3 31.3 (32.5) 34.2
uoi
36.6 (29.7) 25.2 29.9 (35.7) (17.2) 18.68 19.90 (22.6)
80: SeOi TeO,
17.7 (20.1) (22)
NiOr Paoh AmOr BbaOa BirOr CrOi
MOO:
woi
-
Standard heat of formation AHfQ. kcal./mole 68.3 -142.3 99.45 86.2 82.8 82.1 ( - 81) 39.84 7.31
-
-139 -146.1 -151.7 -140.8 -133
-
- 83.17 - 60.86 - 21.68
AS",
sal./deg. 39.0 ( - 32) 31.9 ( - 32) ( - 32) ( - 32) ( - 32) 16.3 15.8 (- 12.5) 23.4 25.6 25.0 24.0 23.9 ( - 24.5) 24.1 23.7 26.4 ( - 74.5) 74.5 (- 74.5) ( - 74.5) ( - 74.5)
-
-
-
-
-
-
-
-
(-
AcaOi Gat08
Entropy of formetion of oxide
-339.8 -399.0 -410 -440 -457
74.5)
(
- 69.9
-258 -222.5 120 -22517 -258.2 -271.5 -293 94.05 -205.4 -128.3 138 3 66.12 -373 -463.2 -499.9
- 73.5 74.5) - 43.2 - 46
-
(-
- 42.5 - 43.0
-
- 43.77 (-
-490)
46)
-
- 48.8
- 46.21 -105.3 ( - 107) -108.1
-
(-114) -114.1 -113.6 (-114) ( -62)
- 61.65
- 61.6 (-
62)
- 63.4 ((-
63.4) 63.4)
E uivalent Standard free Equivalent %eatof formation AHP. kcal. -34.2 -71.2 -49.7 -43.1 -41.5 -41.1 (-40.3) -19.92 3.66
kceL/mble 56.7 -132.8 89.91, 76.7 73.4 78.6 ( - 71.5) 34.98 2.59
-69.5 -73.1 -75.9 -70.4 -66.5
132 -138.5 -144.2 -133.6 -125.9
-
-41.59 -30.43 -10.84 -56.6 -66.5 -68.3 -73.3 -76.2 (-82) 43 -37.1 30 -56.3 -64.6 -67.9 -73.3 -23.51 -51.35 -32.1 -34.7 -16.53 -37.3 -48.32 -49.90
-
-
energy of formation
A m
-
-
-
-
-
- 76.05 - 53.79
free energy of formation AFrO
n.
kcd -28.4 -66.4 -45.0 -38.4 -36.7 -36.3 (-35.8) -17.49 1.3
-
-66 -69.3 -72.1 -66.8 -63.0
13.99 -317.6 -376.8 -387.8 -417.8 -434.8
-38.0 -26.9 7.0 -52.9 -62.8 -64.6 -69.6 -72.5
(-468) -237 -200.5 98.1 -212.1 -244.4 -258.8 -280.2 94.26 -192.4 -114.5 -124.2 62.34 -344 -431 -470.6
(-78) -39.5 -33.4 -16.4 -53.0 -61.1 -64.7 -70.1 -23.74 -48.1 -28.6 -31.05 -13.09 -34.4 43 -47.06
-
-
-
-
-
-
10 -367.0 -218.6 -234.4
- 1 -36.70 -21.86 -23.4
-333 -184.6 -200.5
-33.3 -18.46 -20.05
-138.4 -180.33 -200.16" -291.6
-23.1 -30.06 -33.36 -48.6
120 -161.95 -182.47 -273
-
20 -27 -30.4 -45.5
-105.2
-17.5
-
86.3
-14.5
- 83.0"
-13.9
-
04.6
-10.8
-
Elsctronegetivities of the Elemente 2.1 1.0 0.9 .8 .8 .7 .7 1.8 1.8 2.3 1.5 1.2 1 .o 1.0 0.85 0.8 1.5 1.5 1.9 2.0 1.5 1.3 1.2 1.1 1.0 1.6 1.6 1.9 1.6 1.6 1.3 1.1 2.5 1.8 1.7 1.8 1.8 1.8 1.6 1.4 1.4 3.0 2.1 2.0 2.1 1.8 2.1 2.1 2.1 3.5 2.5 2.3 2.1 2.0
2.3
MnzO7
-297.5
Rea07
-21.3 4.0 3.0 2.8 2.6 2.4
clzoi
Value for diatomic liquid.
(16) V. Kireev. Acta Phyeicochim., U. R . 9. S.. 21, 55 (1946). (17) B. Neumsnn, C. ICroger and H.Kunz. 2.anorg. allgem. Chsm., 932, 335 (1937).
e
Value for diatomic solid.
Graphite. * White; red = 7.
(18) C. Hub, E. Squitieri and P. E. Snyder, J . Am. Chem. Soc., 70, 3380 (1948~. (19) V. A. Kiren, "Zhurnal fisicheskoi khimie Leningrad." 22, 847 11948).
Feh., 1952
THEPERIODICITY
OF
are other chemical thermodynamic functions such as the entropies of the elements and oxides, the entropies of formation for the oxides, ionization potentials and electronegativities. The values in parentheses were estimated from the figures given in this paper. The following conclusions may be drawn from Table I: (1) Any oxide of an A family has a greater heat of formation and free energy of formation than any oxide of the corresponding B family. (2) In Groups IA, IB, IIA, IIB, IIIB and IVB, the heats of formation of the oxides decrease with increasing atomic number except for the following: (a). The first two oxides of Group IIA, Be0 and MgO, have lower heats of formation than the other oxides of this group. (b) I n Group IVB the first oxide, COZ, a gas, has a lower heat of formation than the other oxides, which are solids. (3) In Groups IIIA, IVA, VA, VIA and VIIA, the heats of formation and free energy of formation of the oxides increase with increasing atomic number. (4) In Groups VB, VIB, and VIIB, the heats of formation fluctuate alternately beginning with a relatively low value, then high and then low again. Similar conclusions may be drawn for the equivalent heats of formation and equivalent free energies of formation. The oxides were then arranged in the order of decreasing equivalent heat of formation as in Table 11. This same order is obtained for the equivalent free energies of formation. From this table it appears that the equivalent free energies of formation rather than the free energies themselves are a measure of the relative stabilities of the oxides a t ordinary temperatures. Of course, these values do not afford a true measure of the relative stabilities a t themuch higher temperatures employed in metallurgical practice. To determine these, calculations would have to be made of the free energies of formation at different temperatures, using the standard equation given by K. I
