I
CURT W. BECK and LILY Y. BECK Department of Chemistry, Vassar College, Poughkeepsie, N. Y.
Hyperconjugation Calculating N o r m a l Boiling Points of Alkenes a n d Alkynes Normal boiling points of alkenes and alkynes can now be calculated from those of the parent alkanes in terms of a single structural parameter MOL,, VOLUMES of alkenes and alkynes may be derived from those of the corresponding saturated hydrocarbons as a linear function of the number of hydrogen atoms (excluding tertiary ones) in hyperconjugation with the multiple bond (2). This empirical approach has been justified by Kreevoy and Eyring ( 3 ) who found by molecular orbital calculations that the energy of simple hyperconjugated molecules is proportional to the number of hydrogen atoms in a 1,3 relationship with the 7r-orbital. To develop the relationships between physical properties which depend primarily on intermolecular forces: and structural features which determine such forces, methods are discussed for calculating the normal boiling points of these compounds. Within groups of position isomers of unsaturated hydrocarbons, a qualitative direct correlation exists between boiling point and the number of hyperconjugated hydrogen atoms ( 7 ) . Applying a method analogous to that for molar volumes (2) to the best available data (4: 5 ) !differences between the normal boiling points of alkenes and the corresponding alkanes, d T t , have been calculated in the CB to C8 range. T h e equation for the best straight line through these points (Figure 1) is
dTt
=
1.56 LYH- 8.15
(1 1
Tables I and I1 illustrate the derivation and application of Equation 1. hTegative deviations predominate in small molecules and positive deviations in larger ones. This dependence of d T b on molecular weight is also seen in the variation of the d T b values of the 1alkenes (Figure 2), which fit the equation dTb X
c,
= 33.19
(2)
I n principle, Equation 1 could be improved by combining it with Equation 2. However, Equation 2 holds for 1alkenes only, and it cannot be assumed that it will fit other homologous series. For the 2-methyl-1-alkenes from Cs to C ~ O for, example, the product d T t X C, is less nearly constant and has an
Table I. Calculated Boiling Point Changes Have a Mean Deviation Only Slightly Higher Than Experimental Ones No. of (Y Hydrogen
No. of
Atoms
Compounds
0 2
25
3 4 5 6 7 8 9 10 11 12
Total
18 18
14 27 11
6 9 2 2 2 1 -
Mean Boiling Point Change from Corresponding Alkane Experimental Calculated" Mean dev. Mean Mean dev. Mean -7.90 -4.83 -4.34 - 1.31 0.15 1.76 2.77 4.44 6.76 2.8 6.89 15.22
...
...
135
1.00 1.11 1.75 1.58 1.23 2.06 0.76 1.51 3.97 4.7
-8.15 -5.03 -3.47 - 1.91 -0.35 1.21 2.77 4.33 5.89 7.45 9.01 10.57
1.01 1.13 1.49 1.71 1.20 1.99 0.76 1.52 3.97 1.5 0.73
2.12
4.65 1.48
...
1.36
From Equation 1.
Table II.
Boiling Points Are Calculated Within 2" C. for of CB to Cg Alkenes
Compound 1-Butene trans-2-Butene trans-2-Pentene 3-M ethyl-1-butene 2-Methyl-2-butene 2-Methyl-1-pentene 3-Methyl-cis-2-pentene 4-Methyl-cis-2-pentene 2,3-Dimethyl-2-butene cis-3-Heptene 4-Methyl-tram-2-hexene 2,4-Dimethyl- 1-pentene 3,4-Dimethyl-l-pentene 3-Ethyl-2-pentene 1-Octene 2-Methyl-2-heptene 3,3-Dimethyl-1-hexene 2-Ethyl- 1-hexene 4-Ethvl- 1-hexene 2,3-Dimethyl-2-hexene 5,5-Dimethyl-trans-2-hexene 2,2-Dimethyl-cis-3-hexene
3-Ethyl-3-hexene 2,3,3-Trimethyl-l-pentene 2,4,4-Trimethyl-l-pentene
LYH 2 6 5 0
9 5 8 3 12
4 3 5 0
7 2 8 0
4 2 11 5 2 6 3 5 10
3-Ethyl-2-methyl-2-pentene 2-Ethyl-3,3-dimethyl-l-butene 2 2-Isopropyl-3-methyl-I-butene 0
Boiling Point Exptl. Calcd. -6.26 0.88 36.35 20.06 38.57 62.11 70.44 56.39 73.21 66.45 87.56 81.64 81. 96.01 121.28 122.6 104. 120. 113. 121.77 104.1 105.43 116. 108.31 101.44 117.0 110. 104.
-5.53 0.71 35.72 19.70 33.74 59.92 67.61 56.80 68.56 66.83 88.38 80.15 81.63 96.25 120.64 121.98 103.82 117.02 113.50 124.62 106.49 101.81 119.74 111.29 98.89 123.10 104.81 105.32
70%, and 3" C. for 90% Diff.
d Tb"
Exptl.
Calcd.
-5.76 1.38 0.28 -7.79 10.72 1.84 7.16 -3.88 15.22 -2.29 -4.29 1.14 -8.8 2.53 -4.39 5.0
-5.03 1.21 -0.35 - 8.15 5.89 -0.35 4.33 -3.47 10.57 - 1.91 -3.47 -0.35 -8.15 2.77 -5.03 4.33 -8.15 -1.91 -5.03 9.01 -0.35 -5.03 1.21 -3.47 -0.35 7.45 -5.03 -8.15
-8.
1. -5.5 6.16 -2.7 - 1.41 -2.5 -6.45 2.20 1.3 0.
-9.5
dTCslod. -dT~xptl.
+0.73 -0.17 -0.63 -0.36 -4.83 -2.19 -2.83 +0.41 -4.65 +0.38 +0.82 -1.49 +0.6 +0.24 -0.64 -0.7 10.
-3. +0.5 +2.85 1-2.3 -3.62 t3.7 +2.98 -2.55 +6.2 - 5. 11.3
Difference from corresponding saturated hydrocarbon.
VOL. 51, NO. 2
FEBRUARY 1959
223
t 20 t
-101 '
O I 2 3 4 5 G 7 8 9 1 0 1 1 l 2 d -H Figure 1. Mean boiling point changes of Cs to CS
,
,
I
2
3 -!H
Figure 3. Mean boiling point changes of C3 to Ci. alkynes from parent alkanes are proportional to hyperconjuga tion
alkenes from parent alkanes are proportional to hyperconjugation
= 4.38aH
(4a)
4.51aH
(4b)
4.68
(4~)
=
These equations have very nearly identical slopes (Figure 4). Using the average, 4.58, new intercepts are calculated to minimize the deviations, and an additional intercept is obtained for the single point (propyne) a t C S . T h e modified equations
/.
i
ca d T b
= 4.58aH f 5.10
c1 d T b
= 4.58cuH
c s d T b = 4.58aH
C g d T b = 4.58aH
C?dTb
average value of 19.13. When more data are available, inclusion of a C, term in Equation 1 should be possible; but on the basis of present data such treatment complicates the calculation without significantly improving accuracy. Therefore, Equation 1 may lead to substantial errors for compounds far above C S . For the alkynes of the C3 to C7 range
- 8.72
INDUSTRIAL AND ENGINEERING CHEMISTRY
Ca d T b
4.73aH - 0.86
4.58aH
Intercept = d T b ( a H = 0 ) = 14.53 - 3.43 C ,
Equation 3 fits the average boiling point changes fairly well (Figure 3), but the individual deviations are as high as 11O C. T h e reason lies in the large variation of the boiling point changes, at constant a H , with increasing molecular weight. This variation is greater than that for alkenes and can be expressed by establishing linear relationships for each group of isomers:
(3)
=
- 0.28 - 3.15 - 5.9; - 9.28
(5) (5a) (5b) (5C)
(jd)
show the decrease of the boiling point change with increasing molecular weight. T h e calculated intercepts (Figure 5) are closely reproduced by
O from parent Figure 2. Boiling point changes of Cs to C ~ 1-alkenes alkanes vary as a hyperbolic function of molecular weight
224
- 2.67 - 5.13 a H - 9.56
cj d T b CsdTb C7 d T b
d T a = 5.52 aH
5
4
(4)
(6)
Adding the slope term 4.58aH to Equation 6, the boiling point change can finally be expressed as d T b = 4.58aH
- 3.45 C,
- 14.53 ( 7 )
Equation 7 gives the boiling points of the Cs to C7 alkynes from the parent alkanes with a maximum deviation of 6.4' C. Over 80% of the calculated values are within 3' C. of the experimental ones (Table 111).
HYPERCONJUGATION
I
2
3
4
5 Cn
A-H
Figure 5. Intercepts of calculated straight lines for isomeric alkynes are closely proportional to molecular weight
Figure 4. Plotting alkynes in groups o f isomers yields a family of nearly parallel straight lines Acknowledgment T h e authors gratefully acknowledge the support of p a r t of this work by a Frederick Gardner Cottrell G r a n t from
Table Ill.
Consideration of Molecular Weight Improves Accuracy of Calculated Boiling Point Changes of Alkynes
No. of
com-
cuH C, pounds
0 0 0 2 2 2 2 3 3 3
4 4 5 5 5 6
5 6 7 4 5 6 7 3 6 7
6 7 5 6 7 4
Research Corp. They are further indebted to Stewart S. Kurtz and to Joseph A. Dixon for comments and suggestions.
Experimental Calcd. by Eq. 3 Calcd. by Eq. 7 hIean dTb“ Mean dev. Mean dTbn Mean dev. Mean dTb“ Mean dev.
1 2 4 7
-1.50 -8.8 - 10.6 -8.76
1 1 2 5 9
8.59 4.11 1.75 0.84 2.26
1 1 2 4
18.85 12.86 5.75 10.80
1 1 2
12.69 8.73 10.71
1 1 2 4
20.00 15.78 13.0 15.45
1 27
27.49
...
... 3.2 2.8 3.5
-2.72 -6.17 -9.62 -8.72
3.52
... ...
0.85 2.28 2.52
2.32
2.52
... ... 1.95 5.06
7.84
5.06
... ... 1.98
13.36
2.65
0.6 2.44
18.88
4.00
...
24.40
3.09 3.41
3.12
...
Difference from corresponding saturated hydrocarbon.
...
1.22 3.3 2.7 2.52
9.89 6.44 2.99 -0.46
1.30 2.33 1.25 2 -54 2.09
17.95 7.57 4.12
0.93 5.29 . -. 1.94 2.52
12.15 8.70
0.54 0.03 0.29
20.18 16.73 13.28
0.18
...
...
...
...
28.21
...
0.. 9.5-
0.59 0.58 0.72 1.83
literature Cited (1) Beck, C. W.: Experientia 10, 14 (1954;. (2) Beck, C. W., Beck, L. Y . , IND.EKG. CHEM.5 0 , 1301 (1958). (3) Kreevoy, M. M., Eyring, H., J . Am. Chem. SOG.79, 5121 (1957). (4) Li, K., Arnett, R . L., Epstein, M. B., Ries, R. B., Bitler, L. P., Lynch, J . M.. Rossini, F. D., J . Phys. Chcm. 60, 1400 (1956). ( 5 ) Rossini, F. I)., Pitzer, K. S., Arnett, R.. L., Braun, R. M., Pimentel, G. C., “ S e lected Values of Physical and Therniodynamic Properties of Hydrocarbons and Related Compounds” (API 44 Tables’, Carnegie Press, Pittsburgh, Pa., 1953. RECEIVED for review March 25, 1958 ACCEPTED September 25, 1958
Correction Fracture of Non-Newtonian Fluids at High Shear Stresses I n the article on “Fracture of NonNewtonian Fluids a t High Shea: Stresses” [IND.ENG. CHEM.50, 1577 (195S)l the second paragraph of the first column should end : “velocity profile alone increases the average fluid velocity and therefore causes a 137, radial contraction of the jet.’’
A. B. VOL. 51, NO. 2
MEnsEK
FEBRUARY 1959
225
