R. H. STOKES 645

A REVISION O F SOME BOND-ENERGY VALUES A N D T H E VARIATION OF BOND-ENERGY WITH BOND-LENGTH

BY H.. A. SKINNER.

Received 9th April 1945.

In his book “ The Nature of the Chemical Bond “, Pauling 1 has given a table of bond-energies for a large number of bonds. Pauling’s values are derived, practically entirely, from thermochemical data compiled by Rossini and Bichowskyg and published in “The Thermochemistry of Chemical Substances,” in 1936. Since that date, several new thermo- chemical and spectroscopic measurements have appeared, in consequence of which it now seems opportune to review the bondenergies as given by Pauling, in the light of more recent data.

L. Pading, The Nature of the Chemical Bond, 1939, chap. 2. a Bichowsky and Rossini, Thermochemistry of Chemical Substances, 1936.

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646 REVISION O F SOME BOND-ENERGY VALUES

1. Single -bonded Diatomic Molecules. Bond-energies in single-bonded diatomic molecules are directly ob-

tainable from thermochemical or spectroscopic estimations of the heats of dissociation. Herzberg 8 has recently compiled an extensive and critical List of the molecular constants (including dissociation energy) of a large number of diatomic molecules : from Herzberg's quoted values the bond- energies (at room temp.) of H2, the halogens, and the alkali-metals are as follows :-

104.1 Li-Li 27-2 63'5 Na-Na 18.5

c1-c1 58.1 K-K I 2-8

36.4. CSAS 11-3 Br-Br 46.3 Rb-Rb 12.2

(all values in k.ca1. mole-1).

These values are practically identical with the corresponding figures quoted by Pauling.

2. Bond -energies Derived from Polyatomic Molecules. To derive the bond-energies of single covalent bonds linking multi-

valent atoms (e.g. P-P, N-N, 0-0) i t is necessary to use data obtained on polyatomic molecules. If i t can be assumed with reasonable certainty that the M-M bonds in a molecule M, are all normal single bonds, then it follows that the M-M bond-energy is given by the heat of formation of M, (gas) from the gaseous atoms (aa) divided by the number of M-M bonds in the molecule M,. The bond-energies P-P, As-As, S-S, Se-Se, and C-C may be computed by this method.

(a) The P-P Bond-energy.-Pauling quotes the value 18.9 k.cal. for the P-P bond energy. The derivation involves, a t one stage, a knowledge of the dissociation energy of the P, molecule, for which Bichowsky and Rossini quote :

P2k) -+ 2P(g) - 42'2. A recent spectrosoopic examination of the P, molecule by Herzberg shows the above value to be considerably in error, the recommended value now being 116.9 k.cal. Using Herzberg's value, the P-P bond-energy is derived as follows :

( I ) P(c) --f P,(g)- 13.2 (Ref. : B. and 12:) (2) P,(g) --f 2P2(g) - 30 (Ref. : B. and R.)

L3, Pz(g) + 2P(g) - 116.9 (Ref. 4) whence :

P ( C ) --f P(g) - 69-25 P,(g) -+ 4 W ) - 263.8

from which, since the P, molecule contains 6 P-P bonds, the P-P bond- energy is 44 k.cal. mote -l. *

3 G. Herzberg, Molecular Spectra and Molecular Structure, 1939, p. 483. 4 See ref 3, and Herzberg, Herzberg, Milne, Can. J. lies., 1940, 18, 139. * It should be noted that tfis value (44 k.ca1.) refers to the P-P energy in

the molecule P4, in which the P-P-P angles are all equal to 60'. In compounds in which the P-P bonds are directed at the normal angle of

goo (for 9 bonds), we might expect &he P-P bond-energy to be greater than 44 k.cal. Using the method of Pauling which relates bond-strength to the overlap of the radial parts of the wave-functions #9,, #pv, where

eZ = 4 3 sin 8 cos 4 p,, = 4 3 sin 8 sin PI = 4 3 COS 8 [Footnote contirtued on opposife page.

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H. A. SKINNER 647

(b) The As-As Bond-energy.-Pauling's value of 15.1 k.cal. for the As-As bond-energy uses the value of 35 k.cal. as quoted by Bichowsky and Rossini for the energy of dissociation of As,@). More recent spectro- scopic measurements by Kinzer and Almy 6 yield 92-2 k.cal. for this quantity, from which we re-estimate the As-As bond-energy as follows :

((I) As(c) -+ As4(& - (2) As4(g) --f zAs,(g) - 21 ((3) As,(g) --f zAs(g) - 92-2 (Ref. : 6)

- 30.4 (Ref. : B. and R.) (Ref. : B. and R.)

whence : As(c) AS(^) - 58-95 ,As,(g) -+ 4As(g) - 205.4

and the estimated As-As bond-energy = 34-2 k . c d mole-'.* (c) The S-S Bond-Energy.-The bond-energy of the S-S bond may

be derived from thermal data involving the molecules S,, s6, and S,. The value estimated here differs from that of Pauling, in that we have chosen the recent value obtained by Olsson 7 for the heat of dissociation of the S, molecule, i.e. 84 k.cal., in place of the value 102.6 k.cal. quoted by Rossini.

(I) 3S,(g) --f 4S6(g) - zg (Ref. : B. and R.) (2) S,(g) + 3S2(g) - 64 (Ref. : B. and R.)

{(3) Sdg) -+ zS(g) - 84 (Ref. : B. and R.)

The relevant thermochemical data are :

from which :

giving for the S-S bond-energy, S-S = 53.9 k.caZ. mole-l. quotes the value 63 k.cal.

for the heat of dissociation of the molecule Se,(g) : combining this with thermal data quoted by Bichowsky and Rossini, we have :

{ (2) Se,(g) --f 2Se(g) - 63 (Ref. : 3)

S 8 k ) -+ 8S(g) - 431

(d ) The Se-Se Bond-energy.-Herzberg

(I) Se6(g) + 3Se,(g) - 56 (Ref. : B. and R.)

from which

and the bond-energy Se-Se = 40.8 k.cal. mole-l. (e) The C-C Bond-energy.-The C-C bond-energy has been derived

from the heat of sublimation of diamond, to which i t is simply related and given by +L (where L = sublimation heat). There has been much controversy concerning the value of L, and a t the present time apparently good, but conflicting evidence points to each of the three values, L = 125,

and 8, t$ are the angles used in spherical polar co-ordinates, the relative strength of two bonds with bond-angle go", and with bond-angle (go - 2 4 ' is given by :

Se6(g) --f 6Se(g) - '45

or E(,,-,,) = E,, . cos2 a. In P,, each P-P bond is strained through an angle a = 15' from the normal : since E(,,-,) = 44, we have E,, = 44/cos2 15" or, the " normal P-P bond- energy, E,, = 47.2 k.cal.

The transformation formula E ( B - , ~ ) = Ee cos2 ct must be regarded as an ap- proximation : it is not certain that bond-stiength is quantitatively related to the degree of overlap of the wave-functions, which assumption is made in deriving the formula.

5 Pauling, Zoc. cit.l, p.. 85.

*The structure of As, is exactly analogous to that of P, with the angles The bond-energy 34.2 therefore refers to As-As bonds,

The *' normal " bond-energy of As-As bonds

Kinzer, Almy, Physzc Rev., 1937, 52, 814.

As-As-As = 60'. strained through an angle of 15". a t go" angle is derived as 36.7 k.cal.

Olsson, 2. Physik, 1936, 100, 656 ; Dissertation, Stockholm, 1938.

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648 REVISION OF SOME BOND-ENERGY VALUES

L = 136, and L = 170 k.cal. Pauling chose the lowest of the above values as correct, and thus assumed the C-C bond-energy = -62 k.cal. mole -l.

interpretation of the spectrum of CO. This author concludes that the most probable value for the dissociatiop energy of CO is D(C0) = 210.8 k.cal., which combined with the known heat of formation of CO yields the value 125 for L. On the other hand, Hagstrum and Tate 9 in a review of the evidence supplied by electron impact experiments on CO, conclude that the data is compatible only with the value D(C0) = 221-3 k.cal., corresponding to L = 136. Evidence for the highest value (L = 170) is provided by direct measurement of the sublimation heat by Marshall and Norton,lo from measurement of the dissociation energy of cyanogen by White,ll from theoretical calculations by Kynch and Penney,lz whilst indirectly, Baughan 18 has argued that the high value of L provides a suit- able explanation of the observed energy of rupture of the first C-H bond in methane, measured at N 102 k.cal. by Kistiakowsky, Stevenson, and others.14 Most of these arguments favouring L = 170 have been criticised by Herzberg : 15 in addition, Mulliken and Rieke lS deny that the theor- etical calculations by Kynch and Penney provide evidence favouring L = 170.

This short (and incomplete) summary of the available evidence is sufficient to indicate the present uncertainty : we shall, therefore, not specify any particular choice for the C-C bond energy, but write i t as = QL, where L is given the values 125, 136, and 170 k.cal.

(f) The 0-0 Bond-energy.-The value 34-9 k.cal. derived by Pauling for the 0-0 bond-energy was obtained from the experimental value for the beat of formation of H,O,, coupled with the assumption that the -OH bond-energy in H,O, is identical with the -OH bond-energy in H,O. In amending Pauling’s value, i t is in this latter assumption that we differ.

Dwyer and Oldenberg 17 have found that the bond energy in the free radical -OH is N roo kxal., whereas the accurate thermal measurements of Rossini 1s lead to a mean bond-strength of OH in H20 of 110.4 k.cal. This reduction in bond-strength in the free radical is reflected in the increase in bond-length compared with H 2 0 (0.971 A. in -OH, com- pared with 0.955 A. in H,O).

A tentative explanation of the weaker binding existing in the free radical, can be given in terms of the resonance structures participating in -OH

The principal evidence for the value L = 125 derives from Herzberg’s

- h S H

- + OLH 0 H H/O\H

(i) (ii) (iii) (iv) (v)

and H,O molecules. In the radical, the two major contributing structures (i) and (ii) are matched in the water molecule by the corresponding

structures (iii), (iv), (v), but the completely ionic structure H H

-- -I- O +

SHerzberg, Chem. Rev., 1937, 20, 145.

loMarshall and Norton, J . A . C . S . , 1933, 53, 431. llWhite, J , Chem. Physics, 1940, 8, 459. la Kynch and Penney, Proc. Roy. Soc., A , 1941, 179, 214. l3 Baughan, Nature, 1941, 147, 542. 14 Anderson, Kistiakowsky, van Artsdalen, J . Chem. Physics, 1942, 10, 306.

Kistiakowsky and van Artsdalen, ibid. , 1944,

16Mulliken, Rieke, Rev. Mod. Physics, 1942, 14, 259. l7 Dwyer, Oldenberg, J . Chem. Physics, 1944, 12, 351. l 8 Rossini, Bur. Stand. J . Res., 1931, 6, I.

Hagstrum and Tate, Physic. Rev., 1941, 59, 354.

Stevenson, ibid., 1942, 10, 291. 12, 469. lSHerzberg, ibid. , 1942, 10, 306.

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H. A. SKINNER 649

(which Pauling 1* has estimated to contribute some 8 % to the total resonance in H,O) bas no counterpart in the radical. It is possible that the resonance involving this structure is sufficient to explain the increased binding energy in H,O over that in -OH.

If this explanation is correct, we may argue from it that the binding- energy of --OH in H,O, is likely to be less than the energy in H,O. The major resonance structures in the molecule H,O, may be represented by (vi)-(ix)

+ + H - H - - H

+ 0-0 H/O-O H

H/o-O/ + G - d H H

(vi) (vii) (viii) (W and we may note that the purely ionic counterpart to the structure (x)

is not possible. On the other hand, the resonance involving (ix) may be expected to increase the OH energy in H,O, over that in the radical. These considerations lead to the general conclusion that the -OH bond energy in hydrogen peroxide should lie within the limits 110.4-100 k.cal., prob- ably slightly nearer the lower than the upper limiit. We

3- & _ _ 0 (x)

have chosen the value OH N 102 k.cal., as the most likely. Bichowsky and Rossini quote :

which yields for the heat of formation from gaseous atoms Qa(H,OB, = 255'7 k.ca1. Using our chosen value 102 for the OH bond-energy, we obtain - 52 k.cal. mole -1 for the 0-0 bond-energy.*

(g) The N-N Bond-energy.-The N-N bond-energy value of 20 kxal. obtained by Pauling from the heat of formation of hydrazine, and the assumption that the NH bond-energy in hydrazine is the same as that in ammonia, is probably a low value I this is partially due to the assumption made concerning the NH bond-energy, and also because of the change recently proposed by Gaydon 20 in the value for the heat of dissociation of nitrogen.

The relevant thermochemical data are :

(1) Ndg) --+ f") - 225 (Ref. : 20) {(z) 4N , ( g) + QH,(g) --f NH,(g) + 11 (Ref. : B. and R.)

from which k.cal.

from which Qa(N2H,) = 411-0 k.cal. The N-N bond-energy is thus given by 411-4 (NH) where (NH) is

the mean NH bond-strength in hydrazine. An estimation of the NH bond-strength in N,H, can be made from a

consideration of the resonance structures participating in the molecule, in similar manner to the estimation of OH in HzO,. The hydrazine molecule differs from NH, in that resonance structures of the type

= 279.6, and the NH bond-energy in NH, is 93.2

(3) N&) + 2HZk) --f NzHdg) - 22'3 (Ref. : 21)

lD Pauling, Zoc. cit. l, p. 71. * This value may be compared with a calculated value for the 0-0 bond-

energy of N 55 k.cal., derived from a semi-empirical quantum-mechanical method by Sokolov.22 In a footnote in his paper, Sokolov refers to an estimation of the 0-0 energy in the ion 0-0, for which Kazarnovsky 23 obtained a bond-energy value of N 53 k.cal.

- -

2 O Gaydon, Nature, 1944, 153, 407. 22 Sokolov, A cta Physzcochzm. U.R.S.S., 1944, 19, 208. 23 Kazarnovsky, J . Phys. Chem. RUSS., 1940, 14, 320.

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650 REVISION OF SOME BOND-ENERGY VALUES

_ _ _ H + N H+ are not possible : this should render NH a weaker bond in NBH4

H+ than in NH,. The difference is probably very slight, since it is unlikely that the triply ionised structure contributes in a major way to the reson- ance in the NH, molecule. We have chosen to take NH -92 k.cal. as the best value, which leads to a value of -43 k,cal. for the N-H bond energy. The chosen value may be compared with the value -48 k.cal. calculated by Sokolov 21 by a semi-empirical quantum-mechanical method.

(Ts ) The Si-M Bond-energy.-The value quoted by Pauling for the Si-Si bond-energy (42.5) derives from the heat of sublimation of silicon quoted at 85 k.cal. by Bichowsky and Rossini. There is, however, some uncertainty in this value ; as Rossini writes : 2 " Ruff and Konshak measured what they believed to be the vapour pressure of silicon ". Apart

TABLE I.-BOND-ENERGIES AND BOND-LENGTHS IN A-A BONDS.

H-H

0.74

Li-Li 27'2 2.672

Na-Na 18.5 3'079

K-K 12.8 3'923

Rb-Rb

104-1

12'2

(4'23)

cs--cS 11.3 (4'47)

C-C t L * 1'544

Si-Si

2-32

Ge-Ge (34) 2.41

(51.3)

~~

N-N (43) 1'47

P-P 47'2 2'20

As-As 36.7 2'44

0-0 (52) 1.46

S-S

2.07

Se-Se 40'8 2.32

53'9

F-F

1'435

CI-CI

1.989

Br-Br 46.1 2-284

1-1

2.667

63-5

58.1

36'4

* L = 125, 136 or 170.

from this rather dubious measurement, there does not appear to be any direct thermochemical data available from which to make a reliable estimate of Si-Si energy. Probably the best estimate a t present, derives from the kinetic measurements of Emeleus and Reid 24 on the thermal decomposition of disilane. These authors find that the first step in the decomposition is the rupture of the Si-Si bond, with which process an activation energy of 51.3 k.cal. is associated. We may identify this with the Si-Si bond-energy in disilane, and accept the value of - 51 k.cal. provisionally, until reliable thermal data is available.

(i) The Ge-Ge Bond-energy.-The sublimation heat of Ge is not known, and the value given by Rossini and Bichowsky (85 k.cal.) is an estimate only. As in the case of the Si-Si bond, no thermal data is yet available to enable an assessment to be made of the Ge-Ge bond-energy. The kinetic measurements by Emeleus and Jellinek 26 on the decomposi- tion of digermane, which the authors state proceed by an initial rupture of the Ge-G-e bond, may be interpreted to imply that the Ge-Ge bond energy is approximately 34 k.cal. /mole -1.

Hieber, Woerner, 2. EZektro., 1934, 40, 252.

21 Hughes, Corruccini, Gilbert, J.A.C.S . , 1939, 61, 2642.

24 Emeleus and Reid, J.C.S., 1939, 1021. 26 Emeleus and Jellinek, Trans. Faraduy Soc., 1944, 40, 93.

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H. A. SKINNER 651

In Table I, the bond-energies of single normal bonds of type A-A derived above, are collected together, and listed with the bond-lengths with which these energies are associated.

3. Bond-energies of Bonds Type A-B. The bond-energies of bonds of the general type A-B may be derived

directly in case of single-bonded diatomic molecules (e.g. HCI) from the heats of dissociation : in case of polyatomic molecules, AB2, ABs, AB4, etc., the bond-energy E is given by Qa/n, where Qa = heat of formation of the gaseous molecule AB, from the gaseous atoms A and B. This equation assumes that all the bonds A-B in AB, are equivalent. It should be pointed out that the bond-energies calculated as above give the mean bond-energy of a bond within a molecule a t the equilbrium internuclear distance : the E values so obtained are not necessarily the same as the energies that may be required to break an A-B bond in a mole- cule AB, : in general the energy required to break off a single atom from a polyatomic molecule will differ from the value E calculated as described.*

In Tables I1 and 111, bond-energies of a number of bonds to hydrogen and the halogens are tabulated, together with the relevant thermal data. In the columns headed Em calculated values of the bond-energies are given, derived from the arithmetic mean postulate of Pauling,26 i .e.

where the values A-A and B-B are taken from Table I. headed AE quote the values of E - E,.

Em = WA-A + EB--B) The columns

* TABLE II.-BOND-ENERGIES OF M-H BONDS.

Molecule. Bond.

C-H N-H 0-H S -H P-H AS-H F-H Cl-H Br-H

Si-H Se-H

I-H

(56.5 + &L)

83 75'9 57'2 148.8 102.9 876 71.2 79'9 65.4

93'2 110'2

(52 4- &L) 73'5 78.0 79'0 75'6 70'4 83.8 81.1

75'1 70.2 77'7 72'4

A E .

4'5 19.7 32'4 4.0 0'3

- 13.2 65.0 21.8 12.5 1'0 2'2

- 7.0

Q,, values from Bichowsky and Rossini heats of formation, except those marked (H), taken from

(a) Quoted by Hulbert and Hirshfelter." ( b ) Based on the assumption that the heat of sublimation of silicon = 102.6 k.cal. (i.8. twice the bond-

energy). The E(SLH) value may be compared with the value 80'5 k.cal., obtained experimentally by Emeleus, Maddock, and Reid.m

If the E and AE values given in Tables I1 and I11 are compared with the corresponding figures quoted by Pauling, it will be noted that although the E values differ in a number of the examples, the A E values are closely similar. The bond-energy values recommended here do not, therefore, call for alteration in the electronegativety scale set up by Pauling on the basis of his original bond-energy values.

* See papers by Butler and Polanyi,27 and by Evans, Baughan and Polanyi.28 2e Pauling, Zoc. cit . l , p. 48. 27 Butler and Polanyi, Zoc. cit., 1943, 39, 19. 28 Evans, Baughan, Polanyi, Zoc. czt., 1941, 37, 377. 29 Hulbert, Hirshfelter, J. Chem. Physzcs, 1941, 9, 61. 30 Emeleus, Maddock, Reid, J.C.S . , 1941, 357.

Herzberg?

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652 REVISION O F SOME BOND-ENERGY VALUES

Molecule.

CIF ClBr ClI BrI OF2 oc12 NFS

CF, CCl,

SiF,

XlS

PIS

NC1,

CBr,

SiC1, GeCl,

PBr,

AsBr, AsI,

ASUS

SF,

SeCI,

* TABLE III.-BoND ENERGIES OF M-HALOGEN BONDS.

Bond.

C1-F Cl-Br c1-I Br-I 0-F -1 N-F N 4 1 c--F C - c l C-Br Si-F S i 4 1 Ge-Cl P-CI P-Br P-I

A d 1 As-Br AS-I S-F Se-F Se-Cl

9.. E .

86.5 53'0 50'5 42.8 58.5 49'5 78.1 46-2

(72'5 4- f L ) (35'5 + fL) (24.0 + fL)

147'4 90'3 99'9 75'5 61.7 42'4 70'0 57'7 42'7 84-8 80.3 56.6

EAX .

60.8 52.1

47'2 41.2 57'7 55 53'2 50'5

(31.7 + f L ) (29.0 + fL) (23.0 + fL)

57'4 54'7 46.0 52.6 46-6 41-8 47'4 41.4 36.6 58.7 52.1 49'5

A E .

25'7 0'9 3'3 1.6 0'8

- 5'5 24'9

- 4'3 40'8 6.j

90.0 35.6 53'9 22.9 15.1 0'6

22-6

6.1 26.1 28.2 7'1

1'0

16.3

* The Qo values are derived from heats of formation by Bichowsky and Rossini, except those marked (H) from Herzberg, and those marked (R), taken from 0. K. Rice.'l

4. Bond-energies of Multiple-bonded Linkages and the Variation of Bond-energy with Bond-length.

(a) C-C Bonds,-The energies of multiple-bonded C-C linkages can be estimated from thermochemical data on the unsaturated hvdrocarbons,

if r e a s o n a b l e v a l u e s f o r t h e C-H bond-ener- gies in these mole- cules can be as- s u m e d . T h e simple assumption that the C-H bond-energy can be put equal to Eo,, in CH,seems to us only justifi- able in case where C-H h a s t h e same bond-length as it has in CH4. Exac t spec t r o- scopic measure- ment has shown that in ethylene the C-H bond- length is 1.071 A, and in acetylene, 1.057 A - i . e . in both these mole-

cules C-H is shorter than in CHI. We shall postulate that short bonds a y e strong bonds, and apply this in an arbitrary manner to estimate the

31 0. K. Rice, Electronic Structure and Chemical Binding, 1940, p. 192.

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H. A. SKINNER 653

variation of bond-energy with length in C-H bonds. The assumption made is that there is a linear relationship between the energy and length of C-H links. The two points by which the curve is fixed are taken as

(I) C-H in methane ; (2) the “ ideal ” covalent C-H bond.

The length of (I) is accurately known, ye = 1.093 A., and the energy is given by Q.14, where Qa = (226.1 + L). The length of (2) we assume

FIG. 2.

to be given by the sum of the covalent radii of C and H (r, = Qrcc + Qym) = 1-142 A., and the energy we assume to be given by the additive mean postulate of Pauling, i.e. E(CH) = &(104-1 + @). The C-H energy- length curves derived from these assumptions are given for each of the three possible values of L in Fig. I. From Fig. I, we can obtain the C-H energies in ethylene, acetylene, and allene, in which compounds the C-H

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654 REVISION O F SOME BOND-ENERGY VALUES

Diamond Graphite Ethylene Acetylene Allene

lengths are known. These assumed energies, plus the accurate thermalt data now available, enable the C-C energies to be obtained : the data are collected in Table IV, and the derived energy length curves for C-C bonds shown in Fig. 2. These may be compared with a similar curve drawn by Fox and Martin,sa from which they differ slightly, in view of our assumption of the variability of the C-H bond-energies.

1.54450 1.421ob 1.3530 1.204d 1.3300

TABLE IV.-BOND-ENERCIES IN C-C LINKS.*

68 90'7 97.6

134.5 103.0

85 113.3

101.1 131-2 101.9 186.1 99-5 137'0

- -

- -

- 12.56 -54.23 - 46-05

I i-

ECC .

62.5 82.5 86.0

117.5 92.0

- -

92'5 93'7 91.0

1-I-

Private communication from Dr. D. P. Riley. (c) Galloway and Barker.= (d ) Herzberg, Patat and Spinks.= (e) Eyster:= note that Eyster estimated C-H in allene, by use of Badger's rule, and that the

allene distances are therefore less certain than the others quoted. All Qt values are taken from R0ssini.8~

It will be observed from Fig. z that whereas the points calculated for L = 170 lie on a smooth curve, the points corresponding to the bond- energy in graphite lie slightly off the curves drawn for L = 125 and L = 136. This may be interpreted to imply that L = 170 is the correct value to assign to this quantity : but another explanation can be given, which would render the apparanetly good fit of the graphite point in the curve L = 170 fortuitous. The energy of C-C in graphite was assumed equal to +L, since i t is necessary to break the bonds attaching a given carbon atom to its three neighbours, when the given atom is volatilised from the graphite lattice. This assumption neglects the energy required to overcome the van der Waals attractive forces between the layers in the graphite lattice. Should the interlayer attractive forces correspond to an energy of 3-4 k.cal. per gram-atom (which would not seem un- reasonable), the calculated C--C energy in graphite should be reduced by this amount, and the points for L = 125 and L = 136 would now lie on the smooth curves, whereas the point for L = 170 would lie beneath the curve.

The C-H and C-C energy-length curves can be used as starting- points from which to derive similar curves for a number of different bonds. Before making this extension, however, we shall consider the C-C and G-H energies in the saturated hydrocarbons. Table V summarises the thermal data.

The assumption has been made (in Table V) that the C-C bond- distances remain the same in the higher hydrocarbons as in ethane : in so far as this is correct, there is a gradual decrease in the mean C-H bond-energy from CH, to ethane, and the higher homologues.

Some special interest attaches to the compound cyclopropane : the electron diffraction investigation of C,H, gives 1.53 f c-03 A. for the

32 Fox, Martin, J.C.S., 1938, 2106. 38 Riley, Nature, 1944, 153, 587. a4 Galloway, Barker, J . Chem. Physics, 1942, 10, 88. 36 Herzberg, Patat, Spinks, 2. Physili, 1934, 92, 87. 36Eyster, J . Chem. Physics, 1938, 6, 580. 37 Rossini, The Chemical Background to Engine Research, 1943, Chap. 2 .

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H. A. SKINNER 65 5

L = 125. L = 136.

rcc. -- Nolecule. Qr. Qa.

E C C . ECH. E C C - %a* -------

87.8 - 90'5

24-75 (441.2 + 3L) (1.55)b 62 86.5 67.4 89.3 %-C,Ha0 29.72 (550'2 + &) (1-55)b 62 86-4 67-4 89.2

34.72 (659.3 + 5L) (135)b 62 86.3 67'4 89.1 cyclo-propane - 12.81 (299'5 4- 3L) 1.53a (63.7) (80.6) (69.8) (83.0)

- - ~ 0 . 1 9 (332.5 + PL) 1.j5a 62 86.7 67'4 89.5

CH, (2% CSH,

C-C distance, which seems to imply that whereas the C-C bond-energy is greater than in ethane, the C-H energy is markedly less. Since the C-C-C bonds are relatively under a greater strain than the H-C-H bonds, we should expect the contrary state of affairs. Even if the upper limit allowed by the diffraction study of 1 . 5 6 ~ . is taken as the correct C-C distance, the C-H bond-energy still appears to be low. We are inclined to the view that in the case of cyclopropane, the C-C bond-energy is less than we should deduce from its observed length, and from Fig. 2.

L = 170.

E C C - ECH.

- 99'0 83.8 98.1 83.8 97'9 83-8 97'8 83.8 97'8

(87.8) (91.0)

L = 125.

The original statement made concerning the dependence of bond-energy and bond-length requires amendment, as follows : the bond-energy of a bond within a molecule is a function of the bond-length, and the bond-angle : when the bonds are disposed at the '' normal " bond angles, the energy is determined by the length, but should the bonds be strained through an appreci- able angle, the bond-energy may be reduced without effecting a corresponding increase in bond-length.

In cyclopropane, the C-C-C bond angle is 60°, corresponding to a strain in each C-C bond of 2 5 O . Applying the transformation formula given in the footnote (p. 647), we may estimate (approximately) t h e " true " C-C bond-energy in C,H6 by writing &00 = EIOBgo cosz 25'.

yield values (Table VA) for E(CH) which we

L = 170. L = 136.

TABLE VA.

The amended C-C energ& consider more likely than those quoted in Table V. The reduction in bond- energy resul t ing from angular strain assists in explanation of the ap- parently negative resonance energies (AE) in OCl,, and perhaps in NCl. (see Table

I I

TII). -The bond-length in OC1, is roughly normal, and the O - C l bond- energy should be equal to, or slightly greater than EAM. But the bond- angle in OC1, has been measured at 115O corresponding to an angular strain in each 0-Cl bond of I z Q O , the effect of which will be to reduce the bond-energy by some 3 k.cal.

The ozone molecule is a further example in which the observed bond- energy (relative to its length) appears to be small : it is possible that in this case also the low energy results from angular strain.

(b) S O Bonds.-The energies of the C-0 bonds in a variety of mole- cules have been estimated, using Figs. I and 2 to derive the energies of the associated C-H and C-C bonds. The calculated energies and other data are given in Table VI.

38 Pauling, Brockway, J . A . C . S . , 1937, 59, 1223.

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656 REVISION O F SOME BOND-ENERGY VALUES

* TABLE VI.-BOND-ENERGIES AND LENGTHS OF C - 0 BONDS.

Molecule. ?CN*

HCN 1.150 1-16"

--CN 1.172c CP2

C W Z 1.47''

co

HzCO CH,CHO

&OXd

co2

(CH,)*O ethylene oxide

E m ? ) d c .

'CE. 'CC. Qa . L = 125. L = 136. L = 170.

- ~ - --- 1-06 - (133.8 + L) 167.9 176.3 201'7 - 1.37 (154.0 -+ zL) 160.1 165-5 183.8 - - (13'4 -k L) 138.4 149'4 183'4 ? - (380'0 + L) 58.9 61.5 70'7

1.128 1-16 1-21 1-22 1-20

1-42 1-45

26.84 94.45 28.7 44 75 4 6 4 I7

1 L = 125. I L = 136. 1 L = 170.

1-1-1- 210'8 168.8 145'0 145.2

' 152.8 70.5 62.5

221.8 174'2 150'6 149'3 156.9 73'4 64-7

255'8 191.2 165.8 162.9 170'8 81.9 71'5

* Qf values from Bichowsky and Rossini, bond-distances from Maxwell.89

Since the C-H distances are not accurately known in any of the compounds listed, certain assumptions have been made regarding the C-H energies. The assumptions follow from a recent paper by Linnett,40 in which he has calculated the force-constants of the C-H bonds in several of the com$ounds here considered. Briefly, our assumptions are :

Formaldehyde.-The C-H distance is assumed = 1.114 A. in accord- ance with the estimate of this distance made by Linnett from the calculated force-constant and Clark's rule.*

Glyoxa1.-We have assumed C-H in this compound to be equivalent to the C-H bond in CH,O.

Acetaldehyde.-Linnett finds that the force-constant for the aldehydic C-H is roughly the same as in CH,O, and the methyl C-H force-constant practically identical with that of C-H in CH,. Accordingly, we assume the aldehydic C-H to be equivalent to C-H in formaldehyde, and write the energy of the methyl C-H bonds equivalent to the C-H energy in methane.

Dimethyl Ether.-The C-H force-constant is calculated to be almost identical with that of C-H in methane, and we assume the energies of C-H to be the same as those in CHI.

* TABLE VII.-BOND-ENERGIES AND LENGTHS OF C-N BONDS.

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H. A. SKINNER 65 7

Ethylene Oxide.-We assume C-H in ethylene oxide to be equivalent to C-H in cyclopropane. In the calculations of the C-0 energy, cor- rections have been made for the reduction in energy due to the angular strain.

Although we have calculated the C-0 bond-energies for all three values of L in Table VI, only the curve corresponding to L = 136 is reproduced here, for reasons of economy of space. The curves for L = 124 and L = 170 are very similar in general form to the curve shown. It should not be concluded that we have any particular preference for the value L = 136, which is chosen solely because i t approximates to a mean between the two extremes.

The energy-length curve for C-0 bonds is shown in Fig. 3.

220-

200-

f 8 0 -

160 -

140-

/ 2 0 -

f 00. -

80 - 60 ..

FIG. 3. (c) C-N Bonds.-The energy-length curve for C - N bonds is given

(L = 136) in Fig. 3, and the thermal and other data summarised in Table VII.

In the estimation of the C-N energy in methylamine, we have as- sumed the N-H energy to be slightly less than in NH, (E = go), and taken the C-H energy equal to the energy of C-H in ethane. These assumptions follow from the estimated force-constants in this molecule, as given by Linnett.40

(d ) N-0 Bonds.-The curve relating energy to length for N-0 bonds is given in Fig. 3, and drawn from the data summarised below :-

(a) NO. Q a = 149.9 ~ s o = 1.150 Eoo, = 149.9 (b) NO,. Qa = 222-6 YN, = 1-21 E o O , = 111.3 (c) HNO,. Q. = 376.0

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658 REVISION O F SOME BOND-ENERGY VALUES

Molecule. ‘CCL ‘CC. ‘CO.

--____.

CC14 1‘755 - - 1-73 1.38 -

1-38 - COCI, 1-68 - 1121

c2c14 CH,=CHCl 1-69

The structure of HNO, has been shown to be (xi).4*

op O / (xi) of the NO bond, Y,, = 1-41, is calculated at 52 k.cal.

The two bonds, r,, = 1-21 have energy = 222.6 (as in NOa) and

1-41 o/“ the -OH bond we assume to have an energy close to that of -OH in Hg02, which has been estimated previously a t N 102 k.cal. By difference, the energy

(d) CHsNO2. Q, a (405’2 + L ) = 1’47 YXO = 1-22.

E(C-CI) C A C .

Qa . L = 125. L = 136. L = 170. ---

(142.1 f L) 66.8 69.5 78.0 (110.2 + zL) 69.5 72’3 81.6 (176.2 + zL) 73-9 77.3 88.6 (170.6 + L) 75.3 78.0 87’4

-NO

- /oo

- 90

- 80

- 70

-80

c-Cl, c-s, and s-0 Bonds.

\ FIG 4.

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H. A. SKINNER 659

Molecule. Y c s . 'CO.

cs2 1.56 - cos 1.56 1.16

(CHd2S 1.82 -

The C-H bond-length in vinyl chloride has been assumed = 1.07 A., to comply with the calculated force-constant, which is slightly larger than that of C-H in ethylene.

(f) C-S and S-0 Bonds.-The curves for C-S and S-0 bonds given in Fig. 4 are based upon very scanty data, and can only be taken as a rough indication of the energy-length variation in these bonds. The data used are given in Tables IX and X.

E ( c - ~ ) calc.

Qa .

50.1 61.5

(91.2 + L ) (150'6 + L) (376.9 + 4

5. Discussion. The curves shown in Figs. I to 4 bear a close similarity to one another

in their general form. The deviation of the individual points from the smooth curves we have drawn is in no case large, and although the scarcity of molecules for which both reliable thermal and structural data is a t present available, prevents a detailed examination of the postulate of a close relationship between bond-energy and length, the available data would suggest that these quantities are interdependent. This has been suspected, in a qualitative manner, for some time-as can be illustrated by quotation from a recent paper by Phillips, Hunter and Sutton 44-

" (there is) a general principle which is gaining recognition : viz. : that there is a connection between the length and strength of a bond, in as much as abnormally strong bonds tend to be abnormally short, and weak ones long ". The quantitative relation between the energy and bond- length can be expressed, approximately, by the equation EP = A , where E is the bond-energy, A is a bond-constant, and n a further bond- constant which appears to lie between the values 2.5 and 5.0 (that is, for the bonds here considered). This equation applies except for the shortest bonds (e.g. the molecules CO and NO do not fit in at all well). An equation of the type E v = const. might be expected by combining the empirical rule of C. H. D. Clark 45 ( K v , ~ = const.), with the equation Kre2/E = const., proposed by S~therland.4~ The value of n, €or C-C bonds, depends upon the chosen value for L, and is best represented by the values 2-5, 2-7 and 3-1 for the L values 125, 136 and 170. For C-0 bonds, the best value

**Phillips, Hunter, Sutton, J . Chem. Soc., 1945, 158. 46 Clark, Phil. Mag., 1935, 19, 476. 46 Sutherland, J. Chem. Physics, 1940, 8, 161.

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660 REVISION OF SOME BOND-ENERGY VALUES

of n does not vary according to choice of L, and is 4.4 : for N-0 bonds we find n = 4.9, and for C-N bonds n = 4.4.

The initial assumption made that in the case of C-H bonds the variation of the bond-energy with bond-length is a linear function is probably incorrect : none the less, we do not imagine that the replacement of the C-H curves in Fig. I by curves following the equation E+ = wrist., would make an appreciable difference to the form of the curves derived from Fig. I.

The bonds that have so far been considered have in all cases been either ‘‘ normal ’’ or A few compounds in which the bonds are considerably longer than normal are known, and are of special interest, in so far as we should expect the long bonds to be weak.

This expectation is borne out by examination of the bond-energies of the N - C l and N-Br bonds in NOCl and NOBr, and of the SCl bond in thionyl chloride.

Electron diffraction measurements by Ketelaar and Palmer 4 7 on the molecules NOCl and NOBr have shown that in these compounds the N-halogen bonds are lengthened by some 0.2 A. : the heats of formation of both compounds are quoted by Bichowsky and Rossini, from which the N-halogen bond-energies may be derived :

short ” bonds.

NOCl : Qa = 187.8

NOBr : Qa = 180.8

v,, = 1-14, corresponding to Eoo, = 160 k.cal. YNal = 1-95, and E(N(J1) = 27.8 k.cal.

v,, = 1-15, corresponding to Eo,, = 150 k.cal. VNBr = 2’14, E ( N B r ) = 30-8 k.cal.

Both the N-CI and N-Br bonds appear to be weak compared with the normal bonds, for which r,,l = 1-73, Eool) = 50 k.cal., and yNBr = 1-88, E(NBi) = 45 kxal.. Even by comparison with the N-CI bond in NCI, (E = 46.2), which itself is a ‘‘ weak ” bond, the bond in NOCl is very much weakened.

The series of compounds Cl,SO, Br,SO, Me,NO and Me,SO are formally similar, in that resonance structures involving a co-ordinate linkage to the 0 atom probably contribute markedly to the total resonance in each of these molecules (xii-xv) :

c1 Me +

(xv)

gp-5 M 2 - 6 y-G c1

(xiii)

In each of these compounds, electron diffraction measurements 3 9

have shown the co-ordinate linkages to be short, and the bonds other than the co-ordinate link to be long : accordingly, we might anticipate that the bond-energies of the S-CI, S-Br, N - C and S-C bonds in these com- pounds are weaker than normal.

The thermal data required to test this expectation is available only in the case of thionyl chloride. From the heat of formation, we obtain Qa = 216-4 k.cal. : the observed S-0 bond-length corresponds to Eo,, = 113 k.cal., from which EoCl, = 51-7 k.cal. This is slightly less than the energy of a ‘‘ normal ” S - C l bond (E = 56 k.cal.), agreeing with expecta tion since the extension of S-Cl in SOCI, is also slight (observed S-Cl = 2.07 A., normal S-Cl = 2.03 A.). The bond is also weak by comparison with S-Cl in S,Cl,, for which ~~~1 = 1.99 A., and Etscl) = 61 k.cal.

A further group of compounds in which “long” bonds have been measured are the propargyl halides. Electron diffraction studies by Pauling, Gordy, and Saylor 48 show the C-halogen bonds to be extended

47 Ketelaar, Palmer, J.A.C.S., 1937, 59, 2629. 48 Pauling, Gordy, Saylor, J.A.C.S., 1942, 64, 1753.

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H. A. SKINNER 66 I

above normal by 0.07, 0.04, and 0.03 A. respectively, for the C-C1, C-Br and C-I bonds. f i e authors assume resonance in the propargyl halides among the structures (xvi-xviii) :

+ + H-EC-CH, H-C--(I--CH, H-EC-CH,

X X - -

(xvii) (Xviii) \x

(xvi) and it seems probable that the extension in the C-X bonds is to be attributed mainly to the contribution of the ionic “ no-bond ” structure (xviii) .

Similar resonance structures to those suggested in the propargyl halides have been postulated by Pauling, Springall, and Palmer 4 9 in the compound methyl acetylene, viz. (xix-xxi) :

+ - - + H,C+-G-H H C H e b C - H H CHpC=C--H

By analogy with the propargyl halides, we might predict that the C--H bonds in the methyl group of methyl acetylene are longer than normal, and also “ weak ” bonds. The thermal data is compatible with this expectation : from the heat of formation of methyl acetylene (Q, = - 44*3), we obtain Qa = (163.9 + 3L) : using the C-C curve in Fig. 2, and the known C-C distances, Eo,, methyl is estimated at 86.5, 88.1, and 94.1 kcal., for L = 125, 136 and 170. These are all lower than the corres- ponding C-H energies in methane.

The examples are sufficient to show that the general postulate of a close relationship between bond-energy and bond-length is followed both in the weakest and the strongest bonds : this may be taken as good evidence for the general applicability of the postulate. A general criticism may be raised that is worth attention: namely, that no account has been taken of the effect of variation in the bonding orbitals used by a given bond in different molecules. In particular, criticism of the C-H curve given in Fig. I may arise for this reason.

According to Coulson,Bo the wave-function for a C-H bond may be written in the form :

(=) (=I

*a = a 4 8 + 4-4, where +,, $g are the normalised 2s and 2p atomic wave-functions of the carbon atom, and a is a coefficient of “ mixing ”, with the values a = I, &, ./I and 4% for pure s, tetrahedral, trigonal, and diagonal bonds. Pauling has defined the strength of these bonds as = a +. 4 3 ( 1 - aa), so that the relative strengths of tetrahedral, trigonal and diagonal C-H bonds are expected to be in the ratio 2 : ~ * g g ~ : 1.932. This conclusion which implies that the C-H bonds decrease in energy passing from CH, to C2H2, is directly opposite to the assumption we have made.

This argument is, however, contradicted in a recent paper by Mulliken, Rieke, and Brown.6l These authors express the opinion that ‘‘ hyper- conjugation ” occurs between an apparently saturated group such as -CH,, and the bond adjacent to it. The -CH, group is regarded as comparable with the +N and - e C H groups, and may be written in the manner - E H , . Mulliken labels the single and multiple bonds of a conjugated system as “ acceptor ” and “ donor ” bonds, the effect of the conjugation being that the acceptor bonds gain in energy, and the donor bonds lose, the net effect for the system is an energy increase cor- responding to the resonance energy of hyperconjugation. Comparing

* O Pauling, Springall, Palmer, ibid., 1939, 61, 927. 5 o Coulson, Tvans. Faraduy SOC., 1942, 38, 433.

Mulliken, Rieke, Brown, J.A.C.S . , 1941, 63, 41.

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662 REVISION O F SOME BOND-ENERGY VALUES

ethane and acetylene from Mulliken's viewpoint, we may write the structures as H-EC-H and H3GC--EEH3. In acetylene the C-H bonds are " acceptor " bonds, whereas in ethane they are " donor " bonds, which difference in character implies that C-H is stronger in acetylene than in ethane.

Experimental investigation of the C-H energies in ethylene, and acetylene is needed to settle this point : in this respect, we may refer to two recent publications by Cherton 62 and Fonteyne 63 in which both authors claim to establish that the C-H energy is, in fact, larger in acety- lene than in methane.

In conclusion, an attempt by Warhurst 64 to estimate theoretically the effect of resonance energy on bond-length is of interest, as it represents an approach to the problem considered here, by less empirical methods. Warhurst considers two types of resonance-single-bond multiple-bond resonance, and covalent-ionic resonance. For both these types, he concludes that the resonance energy is associated with bond-contraction. In case of the single-multiple bond resonance, Warhurst 's conclusions are compatible, in general terms, with the empirical assumption of an energy-length relationship. The covalent-ionic type of resonance is more difficult to treat from a theoretical standpoint, and Warhurst's equations are not readily formulated in the manner of a simple energy-length relation. It may be that the chief exceptions to the simple rule are most likely to be found in bonds of the ionic-covalent type : and the method of approach to this problem, used by Warhurst, may reveal more exactly when ex- ceptions should occur, if the method can be extended beyond its present level.

Summary: The bond-energies of the P-P, As-As, S-S, Se-Se and C-C bonds

have been reconsidered in the light of recent spectroscopic and thermal data. * Tentative alterations in the values of the 0-0, N-N, Si-Si and Ge-Ge bond-energies are also proposed. The bond-energies of a number of bonds to hydrogen and the halogens are tabulated.

The assumption of a relationship between the energy and length of a bond is examined for C - C , C-0, C-N, N-0 and C-C1 bonds, using the thermal and structural data a t present available. The energy-length curves derived, are found to obey, approximately, an equation Er" = A, where E is the bond-energy, Y the bond-length, and n and A are specific bond-constants ; n lies between the extreme values 2-5-5-0.

It is found that certain bonds which are longer than would normally be expected are correspondingly weaker than normal bonds.

The writer wishes to express his thanks to Professor M. Polanyi for helpful discussion and advice during the preparation of this paper.

Chemistry Department, The University of Manchester,

Manchester 13 .

62Cherton, Bull. SOC. Chim. Belg., 1943, 52, 26 (reported in Chem. Abst.,

Fonteyne, Naturwiss, 1943,31,441 (reported in Chem. Abst., 1944, 38, 2863). 64 Warhurst, Trans. Faraday SOC., 1944, 40, 26.

1944, 38, 5138).

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