THE JOURNAL OF
PHYSICAL CHEMISTRY (Registered in U. 1.Patent Office)
(0Copyright. 1957, by the Amerioan Chemical Society)
I
i
SEPTEMBER 30, 1957
VOLUME61
NUMBER 9
~
BOND LENGTH AND BOND ENERGY I N HYDROCARBONS BYHANSFEILCHENFELD Research Council of Israel, P.O.B.6198, Jerusalem, Israel Raceitred October 99,1068
It is shown that in hydrocarbons the bond energy is inversely proportional to the cube of the bond length; the following equations summarize the observed data: ECH= 128.21Lo~-~;Ecc = 312.33Lcc-a. The increase in energy associated with the shortening of a CIX bond adjacent t? an unsaturated CC bond is of the same magnitude aa that associated with the shortening of a CC bond due to hyperconjugation.
Recently Pauling’ and Jenkins2 have published calculations to show how bond energies vary with the bond lengths in related molecules. According to Pauling “in a series of similar bonds the bond energy is proportional to the reciprocal of the equilibrium interatomic distance,” while Jenkins favors the reciprocal of the square of the distance. I n both works the related molecules are of different elements of the same group - of the periodic system, e.g., 02, Sa,Sea,Tea. It _ _ is - interesting to check whether a similar relationship would n’ot hold for different bonds between the same elements as they are found among the hydrocarbons. Glockler3 has expressed the energies of the CH and the different CC bonds, ECHand Ecc, as a power series of theinteratomic distances LCH and LCC. Since data for five substances only were known with sufficient accuracy at that time, he could determine algebraically five parameters of his equations ~
1
+
1450.762 - 1644.151Lcc 491.936LccZ Ecc ECH= 252.956 - 1 4 1 . 7 2 1 L ~ ~
These equations were based on a heat of sublimation of graphite of 169.75 kcal./g.-atom. As additional experimental data become available they can be made to fit this type of equations only by increasing the number of parameters. In this work it was attempted to find a simpler function connecting E with L. The use of the inverse type of relationship advocated by Pauling and Jenkins was accepted. A rough Check Shows that for hydrocarbons the best power is not the first (Pauling) nor the second (Jenkins) but rather the (1) L. Pauling, THISJOURNAL, 58, 662 (1954). (2) H. 0. Jenkins. T ~ a n sFaraday . SOC.,61, 1042 (1955). (3) G. Glockler, J . Chem. Phys., 21, 1242 (1953).
third: E = ?CL-~.Two parameters only, one for the CH and the other for the CC bond must be determined. The heat of formation A H o of a hydrocarbon C,H, has been published4 with reference to carbon in its standard state of graphite and to hydrogen in its standard state of a molecule. To find the heat of formation A H o o of the hydrocarbon from free atoms of carbon and hydrogen, the heat of atomization of graphite and hydrogen must be subtracted from A H ” . The negative heat of formation a t 0°K. from the atoms equals on the other hand the sum of the bond energies nd
+ mB = AH’
=
-AH’’
= lEcc
+ mEcH
(i)
where A and B are the heats of atomization of graphite and hydrogen and I and nt are the number of CC and CH bonds/molecule, respectively. In diamond there are two CC bonds for each carbon atom and in graphite 3/2 in plane and one out of plane CC bond for each carbon atom. I n Table I the values of A. B and AHo from ref. 4 and 5 are inserted. In Table I1 the experimentally determined bond lengths are listed (those for the lowest vibrational state were taken, wherever available). W t h the help of the proposed equations ECH= ~ L c H -and ~ Ecc = k a L c ~ -the ~ bond lengths were substituted for the appropriate bond energies of Table I and the parameters kl and k , determined by the method of least squares. It was found that the relations hold (4) F. D. Rossini, K. s. Pitzer, R. L. Arnett, R. M. Braun and G . C. Pimentel, “Selected Values of Physical and Thermodynamia Properties of Hydrocarbons and Related Compounds,” Carnegie Press, Pittsburgh, Pa.. 1953. ( 5 ) F. D. Rossini, D. D. Wagman, W. H. Evans, S. Levine and I. Js5e, “selected Values of Chemical Thermodynamic Properties,” U. S. Government Printing Office, Washington. D. C., 1952.
1133
HANSFEILCHENFELD
1134 ECH= 128.21Lca-8 Ecc = 312.33Lc~-~
(ii)
(iii)
With these relations the bond lengths were calculated which would fit the heats of formation exactly (Table 111). It will be seen that in every case the calculated value falls within the range of the experimental value. TABLE I NEGATIVEHEATS OF FORMATION FROM THE ATOMSAT OOK. (-AH””) IN KCAL./MOLE Methane 392.837 = ~ E C H Ethane 667.017 = 6Eca Eco Ethylene 532.738 = ~ E C H Ecc Acetylene 389.691 = ~ E C H Ecc Benzene 1308.060 = ~ E C H 6Ecc ’ 2Eco Diamond 169.237 = Graphite 170.390 = 1.5Eoc Ecc’
+ + + -+
+
TABLE I1 OBSERVEDBONDLENQTHS IN A. Ref. LCH Lc a Methane 1.093 ... b Ethane 1.102 1.543 C Ethylene 1.071 1.353 d Acetylene 1.058 1.208 e Benzene 1.084 1.397 ... 1.5445 Diamond f ... 1.42 Graphite in plane B out of plane 3.41 a D . M. Dennison, Revs; Mod. Phys., 12, 175 (1940). * G. E . Hansen and M. D . Dennison, J. Chem. Phys., 20, 313 (1952). W.S. Galloway and E. F. Barker, ibid., 10, B . D . Saksena, ibid., 20, 95 (1952). 8 A . 88 (1949). Langseth and B. P. Stoicheff, Can. J . Phys., 34,350 (1956). f K. Lansdale, Trans. Roy. Soc. (London), A240, 219 (1947). 0 J. D . Bernal, Proc. Roy. SOC.(London), A106, 749 (1924).
...
TABLEI11 COMPARISON OF OBSERVED A N D CALCULATED LENGTHS IN LCR Lcc Methane Ethane Ethylene Acetylene Benzene Diamond Graphite in plane out of plane
d.
Obsd.
Calcd.
Obsd.
1.093 1.102 1.071 1.058 1.084
1.093 1.098 1.078 1.062 1.079
,..
...
1.543 1.353 1.208 1.397 1.5445 1.42 3.41
1.538 1.362 1.212 1.391 1.545 1.426 3.41
... ... ...
... ... ...
Calod.
Since the value of the heat of atomization of graphite has been a bone of contention for the last decades6 the calculation was carried out also without inserting the numerical value of A in expression (i). The best fit was then found for the three free parameters to be A ’ = 177.93 kcal./g.-atom kl‘ = 130.70 kcal./g.-atom/A.a kz’ = 312.33 kcal./g.-atom/A.3
The value of A‘ calculated without any assumption other than E = kL-a falls naturally into the range of the newest published values (6)
D. M. Kern, J . Ghem. Ed., 33, 272 (1956).
Vol. 61
Chupka and Inghram’ Rossini4 Hoch, et a1.8 ChupkaQ This work Chupka and Inghramlo Honig”
170 i 7 170.39 171.4 i 2.2 176 i 6 177.93 178;5-i 10 179 i 10
This good agreement strengthens confidence in the reliability of the proposed relation. Furthermore it is additional evidence that the highest spectroscopic value of 170.39 kcal./g.-atom is the correct one. I n Table IV the values for the bond energies calculated from equations (ii) and (iii) are assembled. Of special interest is the effect of unsaturation. It is obvious that the energy of a double bond is greater than that of a single bond; but it will be seen from Table IV that the energy of the associated C-H single bond also rises with unsaturation of the CC bond (as witnessed experimentally by a shortening of the CH bond). In the last column of Table IV the “apparent CC bond energy” has been listed, this is the value of the CC bond energy, calculated on the erroneous assumption that the CH bond energy is constant and equal t o its value in ethane
.t
TABLE IV CALCULATED BONDENERGIES IN BCAL./G.-BOND Methane Ethane Ethylene Acetylene Benzene Diamond Graphite in plane out of plane
ECH 98.19 96.86 102.35 107.05 102.05
Eco
85.85 123.62 175.04 116.04 84.93 107.67 7.88
“Apparent
Ecc”
85.85 145.56 195.42 121.23
(96.86 kcal./g.-bond). The CC bond energy usually cited in text-books is the apparent energy. It is seen that in unsaturated compounds part of the “apparent CC bond energy” is used to strengthen the C-H bond rather than the unsaturated CC bond. This effect can be extended to a neighboring carbon atom instead of a hydrogen atom; if, for instance, in acetylene one of the hydrogen atoms is exchanged for a methyl group, it is reasonable to suppose that the extra 10.2 kcal./g.bond which the C-H bond in acetylene possessed over and above the usual C-H bond energy will be transferred to the new C-C bond. By application of eq. (iii) this extra energy will shorten the CC bond from about 1.54 to 1.48 A. The experimental value cited12is 1.46 i 0.02 A. It is therefore suggested that this effect is nothing else than what has been described as “hyperconjugation.” The double bonds in allene are another instance of this phenomenon, The extra 11.0 kcal./g.-bond shortens the neighboring double bond. Since in ethylene its energy is 123.6 kcal./g.-bond, it should in allene rise to 134.6 kcal./g.-bond which corre(7) W. A. Chupka and H. G. Inghram, THISJOVRNAL, 19, 100 (1955). (8) M. Hoch, P. E. Blackburn, D. P. Dingledy and H. L. Johnson, ibid., 69, 97 (1955). (9) W. A. Chupka, J . Chern. Phys., 21, 1313 (1953). (10) W. A. Chupka and H. G. Inghram, ibid., 21, 371 (1953). (11) R. E. Honig, ibid., 22, 126 (1951). (12) L. Pauling, H. D. Springall and K. J. Palmer, J . Am. Chem. Soc., 61, 927 (1939).
c
*
Sept., 1957
ADSORPTION OF TRITIATHD SODIUM DODRCYL SULFATE
sponds according to eq. (iii) to 1.32 k . This compares well with the values quoted in literature 1.34 f 0.02k.,lS 1.30k.14and1.309.15 It will be noted that eq. (iii) holds for the CC bond irrespective of whether ’the bond is single, double, triple or intermediate. It is even possible to extrapolate below the single bond. I n graphite it is not usual t o write a bond for the energy hold(13) L. Pauling and L. 0. Brockway, J . A m . Chem. Soc., 59, 1223 (1937). (14) J. Overend and H. W. Thompson, J . Opt. Sac. Amer., 43, 1065
(1953).
(15) B. P. Stoicheff, Can. J . Phya., 33, 811 (1955).
1135
ing parallel layers together. Since the distance between them is 3.41 k. the “inter-layer bond” which might be stipulated would amount to 7.88 kcal./g.-bond. If this energy is subtracted from the heat of atomization of graphite and the difference multiplied by 2/3, the resultant bond energy gives the observed value for the in plane CC bond length in graphite within the experimental error (see Table 111). Acknowledgment.-The author wishes to express his thanks to Mr. S. Zacks for his help in the statistical evaluation of the data.
THE ADSORPTION OF TRITIATED SODIUM DODECYL SULFATE AT THE SOLUTION SURFACE MEASURED WITH A WINDOWLESS, HIGH HUMIDITY GAS, FLOW PROPORTIONAL COUNTER BY GOSTANILSSON Division of Physical Chemistry, Royal Institute of Technology, Stockholm, Sweden Received November 85,1366
Tritiated sodium dodecyl sulfate, TSDS, was prepared from tritiated dodecanol and purified. Tritiated dodecanol TD, was prepared by condensation of decyl aldehyde with malonic acid, reduction of the 2-dodecenoic acid obtained by LiAlH4 to 2-dodecen-1-01 and catalytic tritiation of the alcoholic double bond. The boiling point, melting point, refractive index and density of 2-dodecen-1-01 have been determined. A windowless flow roportional counter has been constructed and used for surface adsorption measurements at 25’. The sensitive volume o?the counter extends to the surface of the solution and the flow gas (propane) had a relative humidity of 68% in order to minimize evaporation from the solution surface. The adsorption isotherms of TSDS in water and in a buffer solution (pH 6.5) containing a constant excess of neutral salt mole/1000 g. solution. A constant surface concentra(0.1 m ) have been determined in the concentration range 0-1 X tion, corresponding to a monolayer with a surface area of 33 .*/molecule, was obtained when the bulk concentration in the buffer Bolution had reached a value of 2 X mole/1000 g. There is some evidence that micelles are formed below the CMC. The surface excess of TSDS in an aqueous solution has been determined a t a constant bulk concentration’of TSDS (1 X 10-3 mole/1000 g.) and different bulk concentrations of sodium tetradecyl sulfate and dodecanol. It was found that sodium tetradecyl sulfate is more effective than dodecanol in displacing TSDS from the solution surface. A qualitative measurement of the adsorption of T D at the surface of an aqueous solution of sodium dodecyl sulfate containing 1 mole % T D as “impurity” has also been performed. It is shown that the alcohol gradually disappears from the surface above the CMC and that the alcohol comprises at least 50% of the mixed film at a sodium dodecyl sulfate concentration of 1 x 10-8 mole/1000 g. The tritium method developed here for surface adsorption measurements permits an increase in accuracy and an extension .of such measurements to lower values of r/C.
B
Introduction The tracer technique for measuring the surface adsorption of surface active agents was introduced by Dixon, et uZ.,l and Aniansson and Lamm.2 In the last few years a large number of such measurements have been By labelling both (1) J. K. Dixon, A. J. Weith, A. A. Argyle and D. 3. Salley, Notwe, 163, 845 (1949). (2) G . Aniansson and 0. Lamm, ibid., 165, 357 (1950). (3) C. M. Judson, A. A. Argyle, D. J. Salley and J. K. Dixon, J . Chem. Phys., 18, 1302 (1950). (4) E. Hutchinson, J . Colloid Sci., 4, 600 (1950). (5) D . J. Salley, A. J. Weith, A. A. Argyle and J. K. Dixon, Proc. Boy. Sac. (London), 8203, 42 (1950). (6) G . Aniansson, THISJOURNAL, 58, 1286 (1951). (7) G. M. Judson, A. A. Argyle, J. K. Dixon and D . J. Salley, J . Chem. Phys., 19, 378 (1951). (8) R. Loos, Mededel. Koninkl. Vlaam. Acad. Wetenschap. Belg. K l . Welenschap., 13,3 (1951). (9) G . Nilsson and 0. Lamm, Acta Chem. Scand., 6, 1175 (1952). (10) C. M. Judson, A. A. Lerew, J. K. Dixon and D. J. Salley, J . Chem. Phys., 20, 519 (1952). (11) C. M. Judson, A. A. Lerew, J. K. Dixon and D. J. Salley, THISJOURNAL, 57,916 (1953). (12) R. Ruyssen, Bull. soc. chim. BeEgee, 62, 97 (1953). (13) R. Ruyssen and J. Moebe, Mededel. Koninhl. Vlaam. Acad. Wetenschap,B d g . Kl. Wetenachap., 15, No. 4, (1953). (14) G . Aniansson and N. H. Steiger, J . Chem. Phys., 21, 1299 (1953).
the surface active ion and the gegenion with suitable &emitters, their adsorption a t the solution-air interface have been studied. The principles involved in the method are illustrated as follows. A solution of the labeled agent is prepared and a detector, usually a G-M tube, is placed close to the free surface of the solution. All measurements with the detector are carried out using the same geometry. Then two separate cases are distinguished. I. A solvent is used in which the agent is not surface active, Le., the Concentration of solute is constant right up to the interface and the activity detected is given by Ai = TCrsG
e-rrz
dz = TCCsG (1 - e-c&)c.p.m. u
(1)
where T is the surface area of the solution, C (mole/g.) the concentration of the solute, l(g./ (15) N. H.Steiger and G. Aniansson, THIEJOURNAL, 58, 228 (1954). (16) C. P. Roe and P. D. Brass. J . Am. Chem. Sac., 76,4703 (1954). (17) J. K. Dixon, C. M. Judson and D. J. Salley, A m . Assoc. Advance. Sci. Monomol. Layers, 63 (1954). (18) R. Ruyssen, Compl. rend., 3 (1954); Industrie chim. belpe, PO, Spec. NO.,783 (1955).
