The agrrerneot hetween the first two values is as close a h collld iJe expected, while the second reverse rate i i low hecause of approach to equilibrium. In a similar way, the ethylene presfiure in Xixturc 2 i. 42.jr; ol the ac.etylenr pressure in Mixturc 5, 1 comparihoii will he made a t lO*/T = 8.23, or 7' 1L?130~fixture ~ ~ 2 data for L l , v c obtain Fornard rat(,: 1 T 5 X 0.060 X 5 = 0.52 atm. see.-' Reverse rat(%( 1 i: 0.0105 x o.o1+l1 x 5 = o.37 atm. __0.002 -
sInwm
This discrepancy bet\Teen formard and reverse reaction rates call be accoullted for by temperature pyrolysis measurements of in l j O ,or in acetylene hydrogenation measurements of f 30-50° ~ (since ~ ~the ,temperature dependence is smaller), The discrepancy would hare been much greater if the Mixture 1 rate coiistaiit had been uqed instead of that for Mixture 2 , which contained the correct equilibrium pressure of ethylene.
EQUATIONS FOR CALCULATING BOND DISSOCIATIOS ESERGIES' BY L. A. ERREDE
S o . 170 .from the Cenlral Research Laboratories of the Minnesota Mining and Manujactzcizng Co?izpanij, St Paiil, Ifinn. Ricewed Febtuarv 22, 1960
Simple equations for calculating bond dissociation energies were deduced empirically from the great number of experimentally determined bond disbociation energies now available in the literature. Thus, for the bond Rl-Rz where R1 is E(?-,, R?C=CR-, RCO and CN, and Rz is R,, H, X, CN, OH, OR, NR2, S O , S O , and SR,the bond D ) is given bv D = S l e l e 2 where el is a constant characteristic of the group RI. The e of a group R = A,C
b:
-
o - -
Y
-'
h'
6gxO.43
t
2.4 2.6 2.8 3.0 3.2 3.1 3.6 3.5 4.0 4.2 4.4 4.6 4.8 5.0 e
(C-It)
-t e (C-R,)
Fig. E~.-Rclntionship of
cp
+
E
80 -
$ 2
0.162 .Z€;
0.60
ZE!=
-
e
(C-It3).
g
60-
6
40-
-z
to Zei for Rn-C 20
It / i ' 0
20
40
60
50
100
120
140
Calcd. D(R-R),kcal./mole. Fig. i.-Comparison of calculated and observed bond dissociation energies for molecules of type RL-R? where: Itl is CX3-, CR,-, CR2=CRCR,-, RCEC-, CN, C ~ H V CK2- and R2 is -CX3, -CX, -OH, -KHe-KOz-I\'O, -SR, --C=CR, -CRG,Hs.
40 60 80 100 120 140 Calcd. LXR-X). kcal./mole. Fig. 6.-Comparison of calculated and observed bond dissociation energies for molecules of type R-S where: R is CXs-, ( X - , RCO--, C R * = CR-, CRz = CRCR2-, C6HhC6HbCR2-and X is -H, -F, -C1, -Br, -I. 0
20
x m bond dissociation energies. The number of constants c:tn be reduced further to m 3 since it was found empirically that a simple linear relationship exists between the E for groups of the R type and the E of its substituents, ie., of atoms or groups attached to the central carbon atom of the group R. This relation determines eg = a bZei and to wh:tt extent it is valid is seen in Fig. 5 . The best line through the loci of available points is given by n
+
+
cg
= 0.43
+ 0.162Zei
This relationship, however, does not apply to groups such as C6H5, RCO-, C S , -HC=CHr, -C=CH, and perhaps KO2 and NO. Hence, the E value for groups like CaH5CH2-, CH=CHCH2-, CH2=CHCH2-, and N=CCH2- must be determined from the experimental bond dissociation energy in conjunrtion with the relation D = Xe1e2. Once this 1s done. however, the E can be used to calculatr: €-value\ of composite groups as explaiiied prwiously. The €-values for numerous
0 0
1
'
1
1
8
1
1
1
'
1
'
1
'
1
80 100 120 110 Calcd. D(A-B), kcal./mole. Fig. S.-Comparison of calculated and observed bond dissociation energies for bond between two non-carbon atoms. 20
40
60
groups commonly found in organic molecules are listed in Table I. The validity of the proposed equation D = XE,E, can be tested by comparing all the bond dissociation energies determined experimentally with the corresponding calculated values. The results are shown in Fig. 6 and 7, the straight line of unity slope represents the ideal relation. I t is seen that the agreement is good. Actually about of the data agree within 1-2 kcal. which is highly satisfactory in view of the fact that the best experimental data are only reliable to about 1-2 kcal. It is interesting to note that the bond dissocia-
1034
PRODYOT ROY,RAYMOXD Id. ORR .\si)R.ILPII HLTLTGREN
J701.G4
bond dissociation cnergies of the tli>ulfidec (RSSR) are given by c, 'ollp
I1
E
-F -H
1 04 1 00 0 97 0 92 1 08 1 05 1 os I 03 101 0 05 1 44 1 42
-c1 -Br
-I -CS
-O€I -SH2 -0Et -0CEI -SH -SCH7 -0OH -SCH212Hj
T.IBLEI1 Atom !XI C F €I Paiiiing'selectroneastiritS(E) 2 . 5 4 . 0 2.1 C-X boml distanw 0,) 1 . 3 2 1 10 v% i,. 1 32 1 . 3 3 e 1 . 4 9 1 32
C1 Br I 3.0 2 8 2.4 1 . 7 9 1 94 2 14 0.98 0 . 8 0 0 . 7 3 1 04 0 . 8 i i 0 1;s
=
84€~€.
and ESR
= 0
73 f 0.21ER
The bond dissociation energy equations for hydrazines (R2K-SR2), and nitroso or nitro compounds (ONX or 02SX)appear to be D = 5 4 ~ 1 ~ 2 and D = 7 0 € , ~respectively. ~, There is considerable uncertainty in these two series, however, hecause of the very limited number of reliable data and consequently the corresponding X constants may require correction at a later date when more data become available. The validity of these equations can be seen froin the examples shown iii Fig. 8. The bond dissociation energies for the diatomic inolecules Hq, F?,C12, Brz, I? do not fall into a general series having a comnion X. On the contrary, each has a X characteristic of the element in question :tnd its isotopes. It is interesting to notice that the €-values for F, H, C1, Rr and I may be related to Pauling's electroiiegatis-ity E.S The quantity E is given almost exactly by y ' z / r where I* is the correspondiiig C-X bond length. (See Table 11.) This is c~ousi~tent with the observations of Glocklerg who reported that the hoiid dissociation energy of 11-S in the series, n-here X is F,C1. Br and I (but not H) is inversely proportioiial to the C-X bond clistance. The present correlation accounts for the earlier anomalous hehavior of 13. I t is also noted that the expre=ioii for calculating ep, for the group RlR2R C, i y very nearly equal to
THE THERPIIODYS,IRIICS O F BISMUTH-LEAD ALLOYS' BY PRODYOT ROY,RIYMOYD L. O m C'ontrihvtion .from the Department
0.f
AID
R ~ L P HYLTGREN H
Jlzneral Technolog?,, ~'niwrsatyof Calffornia, Berkeley, Cal
