ESTIMATION OF HEATS OF FORMATION OF ORGANIC COMPOUNDS K. K. VERMA AND L. K. DORAISWAMY National Chemical Laboratory, Poona, India
A procedure based on group contributions has been developed for estimating the heat of formation of organic compounds as a function of temperature. The temperature dependence of any group can be expressed as a straight-line relationship, and two such equations are required to cover the entire temperature range of 300"to 1500' K. The values of the two constants appearing in these equations for the two regions of temperature have been tabulated for a variety of hydrocarbon and nonhydrocarbon groups, In the temperature rlange 300' to 1500" K. the proposed method predicts the heat of formation of hydrocarbons with an average error of 0.35 kcal. and of nonhydrocarbon compounds with an average error of 0.26 kcal. per gram-mole. standard heat of formation of a compound in its ideal gaseous state relative to the component elements, all in their standard state of unit activities at any temperature, is expressed by the equation HE
(AH~')T =
[(HT" -
&Bo)
+ (AHf')oIcompd
Ho')ele
(1)
Expressing the enthalpy function ( H T o - H,') in terms of C', and using 298' K. as base temperature, = (AHfo)298$-
C,"
(Compd) dT
Method T h e symmetry effect is absent for the heat content function. Therefore, from Equation 1, it should also be absent for
-
c (HT' -
variety of hydrocarbon and nonhydrocarbon structures (which would not require the value of AH,' a t any base temperature).
-
48t 40
-
Methods for estimating, (HTo H,"), and C ', of organic compounds as additive functions of the composing groups of any given molecule include those of Anderson, Beyer, and Watson (7), Franklin (9),and Souders, Mathews, and Hurd ( 2 7 ) . These (and a few others) have been critically reviewed by Reid and Sherwood (27) and Janz (74). None of these methods can be used for estimating the heat of formation as a continuous function of temperature, and those that enable estimation a t different temperatures are restricted to certain discrete temiperatures only. O n the other hand, methods are available ((22, 28) for estimating the other two important thermodynamic properties, AGf' and C,', a t any desired temperature in the range 300' to 1500' K. It is possible to obtain an expression for AH,' as a function of T from Equation 2, using the group methods for Cp' developed by Johnson and Huang (75) or Rihani and Doraiswamy (22) together with the C', values of the elements, provided that (AH,'),98 (or AH; a t any other base temperature) is known. T h e object of the present paper is to develop a relationship between heat of formation and temperature, based directly on the principle of group additivity, for a
"2CP.C-cc=c(
Figure 1. Temperature dependence of heat of formation of representative hydrocarbon groups VOL. 4
NO. 4
NOVEMBER 1 9 6 5
389
Table 1.
A
Group
Aliphatic Hydrocarbon Groups
300-850 ' K. B X lo2
850-7500° K.
A
B X lo2
Highesj Temp., K.
-8.948
-0.436
- 12.800
0.000
1500
-CH2
-4.240
-0.235
-
6.720
0.090
1500
I -CH I
-1.570
0.095
-
2.200
0.172
1500
-0,650
0.425
0.211
0,347
1500
7.070 27.276 27.242 33.920
-0.295 0.036 -0.046 -0.563
4.599 27.600 27.426 33.920
-0,0114
1500 1500 1500 1500
16.323
-0.437
12.369
0.128
1500
16.725
-0.150
15.837
0.038
1500
30.129
0,299
1500
19.360
0,080
1500
19.212
0.102
1500
-CHI
1
\
C=CH2
/ \
/C=CHz
\
/
/
\
c=c
29.225
c=c
'
20.800
0.415
-0.100
-0.010
-0,077 -0.563
\H 20.100
0.000
H
\c=c /" /
19.088
-0.378
17.100
0.000
1500
18.463
-0.211
16.850
OIO0O
1500
51,450
-0.050
50,200
0.100
1500
50.163
-0.233
48.000
0.000
1500
53.967
0.133
1500
\
(cis)
H
\
/
/
\
c=c
H
(trans)
\
C=C=CHz
/ \
C=C=CH2
/
H
\
/
54,964
/c=c=cH'
0.027
H 5
Temperature ranges: 300-7700° K. and 7100-7500aK.
Temperature ranges: 300-600" K. and 600-7500° K.
(AHf')T = A
T h e following empirical equation can then be written:
(AH,'), compound
=
(AH,")* of composing groups corrections if any
9 (3)
An examination of the estimated values for a variety of groups at different temperatures has shown that the plot of AH," us. T for any group can be divided into two portions in the temperature range 300' to 1500' K., the general form of the equations being 390
I&EC FUNDAMENTALS
+ BT
(4)
(AH,"), is plotted as a function of temperature in Figures 1 and 2 for representative hydrocarbon and nonhydrocarbon groups!, respectively. I t is evident that the two temperature ranges over which straight-line relations are obtained are not the same for all the groups. For the majority of groups, however, the approximate ranges are: 300' to 850', 850" to 1500'; and 300' to 750°, 750' to 1500' K.
~-
Table II.
Aromatic Hydrocarbon Groups
300-750" K.
Group
850-7500" K. A B X 702
B X 702
A
Highest
~ ~ ~ p , , K.
H C (
3.768
-c
