I
YOSHIRO OGATA and MASARU TSUCHIDA Department of Industrial Chemistry, Kyoto University, Yoshida, Kyoto, Japan
linear Boiling Point Relationships
A simple equation for predicting boiling points of a wider range of organics has been applied to 600 compounds; calculated results for 80% fall within 2" C. of experimental values
Emmic.m FORMULAS eipressing physical constants of organic compounds in some structural parameters are important. Several expressions for calculating boiling points have been devised, mainly from molecular weight (7, 2, 72), but no simple expression covering a wide range of organic compounds has appeared. Literature expressions often involve various powers of molecular weight (7, 72) or the sum of similar structural factors such as boiling point numbers (6). Some systematic deviations in these expressions are attributable to choice of molecular weight or a unique number of parameters for each atom. For example, according to previous authors, RCOCHs and RCOOCHa should have considerably different boiling points, but values observed in several laboratories are almost identical. For boiling points of compounds,
R-(CHJ,,--R', Egloff, Sherman, and Dull (3) have suggested the equation t = o log ( n
+ b) + k
(1)
where k is a constant characteristic of alkyl groups, R and R'; and where a and b are constants common to all series. Recently, Fujita (4, Kozuka (7, 8), and Hamamura (8) pointed out a qualitative parallelism among boiling points for several homologous series of, straight alkyl chains.
Results The boiling point equation, t=#Y+q
(2)
is satisfactory for practical purposes. Here, y is a constant for each alkyl group, R ; p and q are constants characteristic of each functional group, X (Table I).
The acetate series, CHICOOR, was chosen as the standard, and constants p and q were assumed as unity and zero, respectively. For some other related series, both these constants and y are estimable from constants in Table I. Of the boiling points calculated for 600 compounds, 80% is within 2' of experimental values, 11% within 3", 1% within 4 O , and only 2Oj, deviates more than 5' C. As observed by other investigators (70), the deviation usually occurs in the germinal members-i.e., methyl and seldom ethyl. Even in these members, however, the deviation is nonrandom-some homologous series with similar external structure usually have similar deviation. For closer approximation, two sets of constantsy are necessary for the germinal members-one for paraffins, alcohols, ethers, amines, and alkyl halides, and another for the carbonyl series. Aryl VOL. 49, NO. 3
MARCH 1957
41 5
Figure 1.
I
I
I
IO0
150
200
Y
Linear relationship between latent heat of evaporation ( H ) and y 3 RCOOH
0 ROH 0 CHiCOOR
0 RCOOCHa 3 HCOOR
groups also need two sets, probabl!- because the! usually resonate with the functional group. Hence, molecular bulkiness expected from aliphatics wi!l not appl>- to aromatics because of restricted free rotation, shortening or bond length, and enhanced polarity \vhich altrrs degree of association
Since literature boiling puilits c r f members higher than octyl deiivativrs are often uncorrected or unkrio~vr~, rhey are not treated in this article.
Discussion .According to 'Trouton's rule. entroiiy of evaporation for a l l compounds is
I oc
5c
* C
nearly constant. Of course, ~ 1 1 ~ * : 1t t ~ r liquid is associatcd. deviation frotn tlii.; rule is unavoidable. However, evc.11 in this instancr, available datd ( i l show that latent heat o f evapordiioii is correlated linearly Ivith the s a m r ~ I I ~ J stituent constantj J , for boiling 1 ) i i i i t t h (,Figure 1 ) . Enrrgy usrd for evaporation of ii I n ( i l 1 . rule at thr boiling point. c.qiiais t111. energy necessary for its rcleasr CI.rirn IYIhesive forces among those i n c ~ i r c u l ~ s croivded a t the sudacr of the liqiiitl plus that needed to overcomr estern;ll r . pressure. 1hr lattrr energy conilxiirtl to the former is ncgligiblr; thrrrfot.c.\ difference in energy nredrd k1r r\-;ipor.ition of t\vo kinds of molecules shuiild IJC related to diffrrencr i t 1 cohesivc forct..; whicii in iurn may l x inHur:ncrcl i ) \ t\vu factors- - van der \,\.sals forcc. I V lated to bulkiness. or inow prrcisely. to effectivr surfacc area of thr molrculr ( 9 ) . that depends on numbrr and kind (11 constituent atoms: and electrostatic i n trraction, particularly hydi'ogeti Iiondinq, Lvhich srems nrarly ciinstani for i t hotnologous series. Constant y in Equation 2, characteristic for each alkyl grouii R. is rclatrd t o effective surface arca. 'l'hus. its va1uc.s increase in the order, Me < Et < Pr. When the nurnbcr of carbon atoms is the. same, inoi'r branched groups havr smaller values- e.g., priinary < sty'ondary < tertiary. .4s for p valiirs 01' allyl groups when compared witti t h o s l . of n-propyl, (or 2-butenyl with n - b u t ! 1 groups), the effect of isolated doillill, bonds is sinall. T'alue p rrprcsents mainly sensitiviiy of nonelectrostatic forcr:- -i.e., sensitivitv of boiling points to change of alk\l group R. Hence, Lvith such exception5 as RSR, ROR, and (RCO)L), i t should have the samr value for cacti group S which has txvo alkyl groril)h for which p values should be ahour twice as large as the corresponding serir.: having one K group. I n reality, ho\vever, values of p show considerable variation, because the longer the alkyl chain, the more elec,trosratic interaction of group S is inhibited, and the morr polar X is, the greater the inhibition: hence, the smaller p will be. 'Thus, for the series having two polar groupse.g., CICH&OOR, ClzCHCOOR, KrCH?COOR, and NCCH?COOK valurs of 0,721, 0.745, and 0.565. resprctively, are small while the nonpolar l U I series has a large value of 1.615. If variation in p values is caused only by polarity of functiona! group X, thrse values for series RX should be constani when group X is also an alkyl group. This is confirmed by the following interpretation of Egloff's equation f i ~ rI
-
1.146 1.080 1.937
RSMe RSEt RSR
-
Me
6.8 58.8
Me, Rep
Me Me, Et
- 39.4
-
2.6 29.0 19.0 5.3 28.6
Standard series
Constant y R
Y
Me Et n-Pr Iso-Pr n-Bu
55.5 77.1 102 * 0 92.0 124.5 113.0 116.5 96.0 149.0 140.5
sec-Bu
ISO-BU t-Bu n-Am Iso-Am
R t-Am Reopent n-Hex Iso-Rex n-Hep n-Oct
Vinyl Allyl 2-Butenyl
(Ph
alkyl group R and kz is a similar constant characteristic of (CHJ,R’. When Equation 1 is applied to these compounds, R-(CH,),-R’, kl and [ a log (n 6) k z ] correspond to p y and q in Equation 2, respectively, wherein p remains constant. Hence, Egloff’s equation is a special case for the equations given here, where X is limited to alkyl groups, and where all p values remain constant regardless of branching of group X. Value q in Equation 2 indicates a magnitude of the electrostatic interaction of functional group X and depends only on polarity and bulkiness of group X. But this value involves various additional effects such as inhibition of the interaction by alkyl group R’ mentioned before. Therefore, this value represents a mixture of these effects. This electrostatic interaction constant, q, is particularly significant when hydrogen bonding exists. Linearities exist between the carbon numbers of R’ and p or q values for series RCOOR’, RCOR’, ROR’, and RSR‘ (Figure 2 ) ; but for R C O O H , linearity departs. The expected points of p and q are marked with crosses in Figure 2. These positions are consistent with that of H C O O R . This phenomenon is attributable to presence of hydrogen bonding in R C O O H and its absence in H C O O R ; the difference in boiling points between these two series is about 80’ C. Similar considerations are applicable to the alcohol series-the thioalcohol series ( 7 7 ) shows no abnormality, which indicates little contribution by hydrogen bonding. Likewise, the aldehyde series shows little contribution by such bonding.
Y 122.0 125.0 171.0 168.0 191.5 210.0 71.0 104.0 127.0 197.0)
literature Cited Boggio-Lera, E., Gazz. chim. ital. I, 29, 441 (1892). Burnop, V. C. E., J. Chem. SOC.826, 1614 (1938). Egloff, G . , Sherman, J., Dull, R. B., J . Phys. Chem. 44,730 (1940). Fujita, A., “Qualitative Organic Analysis,” p. 66, Kyoritsu Publishing Co., Tokyo, 1953. International Critical Tables, vol. V, McGraw-Hill, New York, 1929. Kinnev. C. R.. J. Am. Chem. SOC. 60, 3039 (1938); IND. ENG.CHEM. 32, 559 (1940); 33, 791 (1941); J. Org. Chem. 6, 220, 224 (1941); 7, 116 (1942). Kozuka, T., J. Chem. SOC.Japan 77, 203, 208 (1956). Kozuka, T., Hamamura, Y . , Ibid., 76, 1275 (1955). (9) Kurata,’M., Isida, S., J . Chem. Phys. 23,1126 (1955). (10) Pearson, D. E., J. Chem. Educ. 28, 60 (1951). (11) Plant, D., Tarbell, S., Whiteman, C., J.Am. Chem. SOC.77,1572 (1955). (12) Walker, J., J . Chem. SOC. 65, 193 (1894). RECEIVED for review April 4, 1956 ACCEPTED September 6, 1956 VOL. 49, NO. 3
MARCH 1957
41 7
