Jesse Elson
Delaware Valley College Doyiestown, Pennsylvania 18901
1
1
A Bonding- Parameter and Its Application to Chemistry
single hond dissociation energies (SBE's) were used by Pauling ( I ) to calculate ionic resonance energies (IRE'S) from which electronegativity values were estimated. In the present study the SBE's are combined with the associated bond distances (BD's) to yield additional information about chemical honding Many sets of diatomics (Sic, SiBr, AsCI; SeH, CBr; HTe, CI; PI, Pz; SiI, S2, SBr, OF, Se,; BrI, Siz; 02,Tea) have nearly equal SBE's, whereas they differ significantly in BD's. Therefore both measurements (SBE and BD) are combined into a bonding parameter, b, that measures average bond energy per unit of bond distance. Other bond properties (force constants and vibrational frequencies) are not used here because of fundamental difficulties in their measurement and paucity of data. The form of the honding parameter, b, is determined by a statistical analysis of 109 diatomic molecules (3-4) divided into three categories: homonuclear, alkali halogenides, and heteronuclear (excluding alkali halogenides). Figures in parentheses represent number of molecules in each category. Linear Regression Coefficients for BE versus BD for 109 Molecules Linear
Diatomic Molecules Homonuclear (17) Alkali halogemdea (20) Heteronuclear (72) (excluding alkali haloeenides)
Regression Coefficient
--0 74 -0 78
-0 33
The summary in the table shows that linear regression does not adequately explain the inverse relation hetween bond energy and hond distance because only 74 and 78%, respectively, of the variability between BE and BD for the stratified data (homonuclear diatomics, and alkali halogenides) are accounted for linearly. The remaining data variahility requires a large order polynomial, which use would he unwarranted because the mathematical accuracy would be greater than that of the experimental measurements. Therefore the BE/BD ratio is plotted more simply on a logarithmic scale as shown in eqn. (1). BE/BD = 1IY (1) where BE is in ergs/molecule, BD is in cm, and b is the bonding parameter. The b values are calculated from SBE's (1) and associated BD's (5) and are shown in Figure 1 for 21 homonuclear diatomics as a function of the periodic group. The features of Figure 1 are as follows: (a) 564
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PERIODIC GROUP Figure 1.
Bonding parameter versus periodic group.
in general all series increase in 6 value from left to right while the lithium series peaks at carbon; ( b ) only hydrogen has a larger b value than carbon; (c) the b value of oxygen is greater than that of sulfur and of selenium, although the latter two have larger SBE's, which likewise applies to nitrogen and phosphorus and to fluorine and bromine. A Ab value for the heteronuclear molecule (AB) is calculated by eqn. (2) for which a positive Ab value means that the hond energy per unit bond distance is greater for AB than the mean of ASand Bz. AKAB) = b(AB) - Ib(Ad b(B;)l/2 (2 1 Panling (6) used a similar relationship to calculate I R E values from SBE's of heteronuclear and homonuclear molecules. However, while the IRE value has to be positive a przori, the Ab value can have any sign.
+
Periodicity of the Ab Values of the Hydrides
The Ab values for 18 hydride bonds are plotted in Figure 2. The plot shows periodicity in the Ab values with maxima in the curve at the halogenides. The latter Ab values will he used in subsequent discussions Ionization of Hydrohalogenic Acids
In an explanation of the small ionization constant of hydrogen fluoride in comparison with those of the other hydrohalogenic acids, it was pointed out by McCoubrey (7) and Pauling (8) that the strength of an halogenide acid in aqueous solution depends upon the difference in free energies of the hydrated ions and the undissociated molecules The free energy changes showed that
"
ATOMIC NUMBER Figure 2.
Ab value of hydride bond versus atomic number.
the values for hydrogen iodide, hydrogen bromide, and
for the formation of hydrogen halogenide moleculegin aqueous solution and the formation of hydrogen ion plus halogenide ions in aqueous solution as a function of the Pauling electronegativity values for the halogen atoms, and showed a linear plot for the halogenide ions and a quadratic plot for the hydrogen halogenide molecules. However, the latter plot did not pass through the experimental points, and there was no basis to express the free energy change of the undissociated molecules as a quadratic function. In Figure 3 the energy changes as described above (for ions and molecules) are plotted as a function of the Ab values (from Fig. 2) of the hydrogen halogenide bonds. The plot for the halogenide ions shows linearity only between bromide and fluoride, and not for the four ions as shown by Pauling. The plot for the molecules in Figure 3 is of the same general form as that for the ions, although the two curves do not parallel each other. Melting Points and Boiling Points of Alkali Halogenides
The observed mp's and bp's of alkali halogenides show large irregularities. It would be expected that crystals with t h e smallest cation, with each anion, would have t h e largest mp because of the stronger attraction. However, the lithium salts (chloride, bromide, and iodide) have the smallest mp's of all the alkali halogenides. Pauling (10) attributed the irregularities to a radius-ratio effect and calculated "corrected mp's
0.6 0.8 1.0 1.2 1.4 1.6 1.8 (A) IONIC RADIUS OF ALKALIES 0.7
0.8
0.9
1.0
1.1
1.2
A
1.3
f
(B) TETRAHEDRAL COVALE T RADIUS OF NON-METALS Figure 4. Range in boiling points between \A) Fluoride and iodide; bromide and fluoride versus (A1 ionic radius, (81 covalent radius.
\B)
and bp's that vary in a regular manner throughout each sequence and correspond closely in qualitative behavior to the interionic distances, except for a small deviation shown by the cesium salts." In view of the large differences in bp's and the large range in hp between fluoride and iodide for some of the five alkalies, the range is plotted as a function of the alkali's ionic radius in Figure 4a. Although the range decreases linearly with increase in alkali ion size, that for the sodium halogenides is greater than would be expected from its ionic radius in comparison with the other alkalies. The odd behavior of the sodium halogenides is also evident in Figure 5 where the mp's and bp's of the salts are plotted as a function of Ab value of the M-X bond. The small Ab values of the sodium salts are unexpected, and cause the sodium bp and mp curves to be out of position with respect to the other alkali curves. Further examination of Figure 5 shows that all of the bp curves are convex and decrease in slope from sodium to cesium The mp curves are irregular with those for potassium and cesium concave in shape. The concavities in the latter curves occur a t the chloride position which correlates with the small crystal energies of potassium and cesium- chlorides. Since the Ab values are calculated from dissociation energies of the diatomic alkali molecules in the gas phase when dipole contributions would be greatest, the hp curves should also reflect the dipole effects, while the symmetry of coordination in the crystal would tend to reduce such contributions. Boiling Points of Covalent Molecules
b b OF HX BOND Figure 3. Standard freeenergy change to form HX molecule and Xu s Ab of HX bond.
Some covalent halogenides are studied similarly to the ionic molecules. The range in bp between bromide and fluoride for the trihalogenides of boron, phosphorus, and arsenic, and for the tetrahalogenides of Volume 45, Number
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Ab VALUE OF M-X
BOND
Figure 6. Boiling point of hydrogen halogenide and of molecular halogenide versus Ab value of H-X and of M-X bond.
Ab VALUE OF M-X BOND Figure 5.
(A) Melting point and (6) boiling point of alkali hologenide
versus Ab value of M-X bond.
carbon and silicon, is plotted as a function of the tetrahedral covalent radius of nonmetal. Figure 4h shows that the range decreases nonlinearly with increase in covalent radius, hut that the horon halogenide range is less than would he expected from its covalent radius in comparison with the other nonmetals. The odd behavior of the horon halogenides is also evident in Figure 6 where the hp's of hydrogen halogenides and of molecular halogenides are plotted as a function of the Ab value of the H-X and M-X bond, respectively. The b value of diatomic boron is estimated from Figure 1 in order to calculate the Ab values of the horonhalogenide bonds from eqn. (2). The latter have the largest Ab values in Figure 6, which is associated with their small bp's, and with the small hp range as shown in Figure 4b. In comparison the carbon halogenides have the smallest Ab values, and the largest range of hp's of the molecular halogenides. Figure 6 shows that the fluorides have the largest
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Ab values (similarly to the alkali halogenides), but that there is negative correlation between Ab values and hp's (unlike the alkali halogenides), except for hydrogen fluoride. The latter's relatively high bp is associated with its hydrogen bonding power. The molecular halogenides are bonded by directional covalent forces so that the large A6 values of the fluorides indicate strong intramolecular and weak intermolecular forces as exhibited by low bp's of the fluorides. Substitution of more easily polarizable halogens for fluorine results in increased deformahility associated with the larger atoms yielding cohesion energies of the van der Waals type that are nondirectional and cause greater intermolecular attraction. This results in higher hp's of the other halogenides as compared with the fluorides. Literature Cited ( 1 ) PAULING, L., "The Nature of the Chemical Bond," (3rd ed.), Cornell University Press, Ithaca, N. Y., 1960, p. 85. (2) HERZBERG, G., "Spectra of Diatomic Molecules," Van Nostrand, New York, N. Y., 1950, Table 39. ( 3 ) COTTRELL, L. T., "The Strength of Chemical Bonds," (2nd ed.), Butterworths, London, 1958. (4) SUTTON, L. G., (Editor) "Interatomic Distances," Special, Publication No. 11. The Chemical Society. London. 1958. ( 6 ) PAULING, L., (in. cit., p. 83. (7) MCC~UBREY, J. C., Trans. Faraday Soc., 51, 743 (1955). ( 8 ) PAULING, L., J. CHEM.EDUC.,33, 16 (1956). ( 9 ) PAULING, L., op nt., p. 619. (10) PAULING, L., op. a t . , p. 530.
