ESTIMATION OF T H E IDEAL G A S ENTROPY OF ORGANIC COMPOUNDS D . N. R l H A N l Dejartment of Chemical Technology, Bombay Uniuersity, Bombay 79, India L. K. D O R A I S W A M Y National Chemical Laboratory, Poona 8, India
Earlier methods for estimating the heat capacity and heat of formation of organic compounds from structure are extended to the estimation of the entropy of organic compounds. Unlike the case of heat capacity and heat of formation, it is necessary to allow for contributions due to symmetry effects and optical isomerism in the case of entropy. Contributions have been worked out for a variety of groups, from which the two constants of a linear equation can be immediately written for estimating the absolute entropy as a continuous function of temperature. This method predicts the entropy with an average deviation of 1.2%.
is no reported method for the direct estimation of the T a b s o l u t e entropy (or entropy of formation) of organic compounds, particularly nonhydrocarbons, as a continuous function of temperature. Anderson, Beyer, and Watson (1946) (also Hougen, Watson, and Ragatz, 1959) have proposed an additive-group method to calculate the absolute entropy of a compound in the ideal gas state a t 298' K. For a hypothetical compound, C,H,N,O,X,S,, the standard entropy of formation a t 298' K . can then be calculated from Equation 1 : HERE
AS', = S,o,
- ms'c - n/2
So=,
- p/2
P
= contribution of composing groups
+ corrections where necessary
-
Sox- tS',
= AS0,298+I+II+4Rln-
T
where In u is zero in the case of heat capacity, enthalpy, and internal energy. In the case of entropy, Equation 5 has to be further modified to give
So = contributions of composing groups ccrrections where necessary
+
+RTlnu
298
where
-
and p i n t rot
dT
(4)
The values of the integrals, I and 11, have been tabulated for different temperatures. Besides the need for first estimating and then the values of the two integrals as step functions of temperature, this method does not give contributions for nonhydrocarbons. In the present paper an accurate group contributions method is developed for directly estimating the absolute entropy of an organic compound as a continuous function of temperature. From the tabulated contributions given, an equation can immediately be written for So as a function of temperature (which can be used for estimating AS' a t any temperature).
,
(5)
+RTlnu
(1)
Souders, Mathews, and Hurd (1949) have tabulated the group contributions for hydrocarbons to calculate AS', a t 298' K. Values of AS', a t other temperatures can then be obtained from
ASo,,
O n the basis of Pitzer's statistical mechanical treatment (1940), Franklin (1949) showed that any thermodynamic function of a paraffin hydrocarbon can be expressed as the sum of the contributions from characteristic groups and corrections plus a correction term for the symmetry of the molecule (where necessary). Thus the equation for any thermodynamic property, P, may be expressed as
Sox2
- r/2
4/2 So,,
Proposed Method
R T In 9
(6)
where u is the symmetry number defined as the number of identical spatial orientations that a molecule may assume by rigid rotation about any axis or by rotation within the molecule. Determination of u is not always easy, and construction of three-dimensional models was found to be necessary in determining it for several structures. q is the number of optical isomers-e.g., in the case of 3-methylhexane the number of probable orientations is doubled. There is thus an additional contribution of R T In 2 to the entropy value. The sign of the term for optical isomerism is opposite to that for symmetry correction, because it increases the number of possible orientations whereas symmetry decreases this number. An examination of the reported values of So a t different temperatures for a variety of compounds has shown that plots of So us. T for any compound can be divided into two temperature ranges, 300' to 550' K. and 550' to 1000° K. A similar behavior was observed for AH', by Verma and Doraiswamy (1965), but the two temperature ranges were different. The general form of the equations for any compound is given by S,o,
= A'
VOL. 7
+ B'T
NO. 3
AUGUST 1 9 6 8
(7) 375
Table I.
Group -CHI -CHr-
21.58 4.21
I I
-CH
-0,66536 0.01721
24.21 5.83
-0.66951 0.01434
-0,10926
-17.63
-0.10878
-40.45
-2.16592
-42.29
-2.16510
21.57
'
27.72
"
-1.35716 0.71370
Ring Formation and Branching in Cycloalkanes 300-550' K . 550- 1000' K .
Nature of Ring or Branching
-16.10
=CH2
H
Table 111.
Aliphatic Hydrocarbon Groups 300-550 K. 550-lDoon K. A B A B
23.09
- 1 ,36006
29.88
0.70868
A
B
31.02 28.88 28.47 19.24
3-Membered ring 4-Membered ring Pentane ring Hexane ring Single branching in pentane ring
A
-3.44661 -3.99176 -4.13747 -3.55946
5.37
4.92735
Double branching in pen-0.07 tane ring Single branching in 6.65 hexane ring Double branching in 3.63 hexane ring
B
30.27 26.32 20.39 12.54
-3.46349 -4.00975 -4.12312 -3.54124
5.88
4.92815
4.34906 -0.67
4.35353
4.34750
3.24
4.35867
3.79147
1.64
3.79049
H
/"
b=C
/
11 .oo
0.02080
9.79
Table IV.
0.02122
\ 7.40
0.02770
9.01
0,02241
Nature of Branching Double branching 1,2 position 1.3 Dosition lj4 position
7.46
0.02670
10.01
0.02119
Triple branching 1,2,4 position 1,2,3 position 1,3,5 position
H
Branching in Aromatics
300-550' K. A B
550-1000' K. A B
-4.35 -2.71 -4.35
-3.54810 -3.55006 -3.54810
-1.84 -0.26 -1.84
-3.55138 -3.55255 -3.55138
-5.56 -6.53 -7.04
-9.27496 -9.27562 -9,27770
-0.00
-9.28075 -9.27995 -9.28009
-2.29 -3.66
H
\
/
c=c
=CH
19.49 7.54
EC-
Table II.
A
Group
HC
/
z
300-550° K. B
3.42296
3.62
C
z
- 0.67500
22.05 7.02
1.37615
-3.10406
8.09 -8.20
=
A'
+ B'T =
Z(A
=
+
ZSogroUpB RT In u
11.98
0.01366
-COOH
43.17
0.05578
54.01
0.58931
18.50
1.91816
20.96
1.91464
8 \
From the reported data a t several temperatures, S'C1H6
- RT
In q
+ BT),,,,, + R T In u - R T In q
-CH3 group (temperature range, 300' to 550' K.) : Parent compound: C ~ H uB = 2, q = l R In u = 1.37, R In q = 0 l&EC FUNDAMENTALS
0.01690
I
/ 0
-3.02143
= 43.15
+ 0.03928
Contribution due to two-CH3
(8)
where A and B represent the group constants. T h e proposed method now consists in plotting So us. T for the parent compound and fitting straight-line relationships for the two temperature ranges. The contributions, A and B, of the different groups (taking into account the effects of symmetry and optical isomerism) can then be estimated according to the typical procedure given below.
376
10.95
\
Written in terms of the composing groups and corrections, this equation becomes
So,,,,
c=o
-OH -OH -OH
=co
3,42352
10.40
550-1000' K . A B 27.57 0.69360 30.71 1,50140 32.78 4.24252 27.57 0.69360 6.41 0.00713 32.47 0.69967 29.26 0.01373
-OH
-0.81030
Oxygen-Containing Groups
300-550' K. A B 26 37 0.69658 27.16 1.50718 29.74 4.24772 26,37 0.69658 6.15 0.00552 28.74 0.71408 25.52 0.02074
Group (primary) (secondary) (tertiary) (phenol)
-0-CHO
550-l00Oo K . A B
-0,80886
-7.12
fl
++
-0.66990 1 ,37563
Aromatic Hydrocarbon Groups
7.40
t
-C
Table V.
Could not be estimated
T (A' = 43.15, B' = 0.03728) groups
+ RT In u
R T In q = 43.15 Contribution due to two-CH3
groups = 43.15
Contribution due to one-CHI
+ 0.03928 T
group
1
+ (0.03928 - 1.37) T = 21.57
- 0.66536 T
=A-BT Using this procedure the values of A and B were calculated for different groups in the tlvo temperature ranges mentioned. These constants are temperature-independent, and can be used to estimate So of any compound as a function of temperature
Table VI.
Nitrogen-Containing Groups
300-550" K .
Group -C=N -N=C -NH2
23.19 24.72 25.06
X H
6.87
B -0.66589 -1.47636 0.70276
A
/ \
Table IX.
Use of Proposed Method
550-1000° K .
1,38240
A 27.25 26.97 27.40
B -0,67364 -1.48192 0.69804
5.89
1 .38248
CHI 2-Methylhexane
I
H-C-CH2-CH2-CHz-CHa
I
CHa u=6, ~
=
2
Temperature Range 550- 1000° K .
300-550OK.
Group
7-
-18.10
Table Vll.
s8
19.40
*4
1.92356
A 31.44 11.37 21.54
24.02
3 X --CHI
64.74
3 X -CHz-
12.63
1
550- 7000' K .
B 0.70132 0.01391 0,02888
A 28.58 11.15 16.55
-S-S--S-
0.70178
Sulfur-Containing Groups 300-550'K.
Groi@ -SH
2.06340
34.37
0.70664
32.02
-NO2
-14.81
2.06924
n 0.69531 0.01059 0.01786 1.91585
Table VIII.
B
A
1 X -CH
I
-16.10
u
...
R In 17
...
A, B
61.27
R In
So2-Methylhexane 61.27
-1,99608
3.54500 -1,37000 0.12129
+ 0.12129 T
A
23.79
23.99
-2.00853
17.49
0.04302
-17.63
-0,10878
... .. .
3.54500 -1 ,37000
72.49 72.49
0.10071
+ 0.10071 T
Halogen Groups 300-550" K .
Group
72.63
0.05163 -0,10926
B
A
550-1000' K .
B 0.69184
-0,68064
A
B
24.19
0.69066
24.41
0.68097
26.62
0.69143
H
I I
H-C-C1,
-C1
(aromatic)
25.32
0.69496
H H
I - - -c-c1, I
H
I - - -C-CI,
1
- - -c-CI
I
H
24.40
-0.67494
26.81
-0.67958
I
H
I I
H-C-Br,
-Br
(aromatic)
29.61
0.69277
29.09
0.69237
H
H
I - - -C-Br, I
H
I
- - -C-Br, I
I
- - -C-Br 1
27.14
-0.67440
30.18
-0.67985
I
H
H
I I
H-C-I,
-1
(aromatic)
31.23
0.69326
31.84
0.69170
32.94
-0.68037
H
28.20
-0,67155
VOL. 7
NO. 3 A U G U S T 1 9 6 8
377
d O N m 3
m. +. ? 0 0
++ I ++
0 0 0 0 0
m w w r - r -
?'1"00
++ I ++
3 0 0 0 0
f8
m m m w m m m - - m o w m m w o o r - N o m w N r 0 0 0 0 0
I
I
l + + l
; 3 ;
I + l
0 0
I
A A I
I
m r - - m r - o d N m r m c! a-. 0 0 0 0 N, 7
0
0 0 o 0 o - N o d -
I + l I + l + + + l
N m o m -
o. e .3 m . .. -. N O 0 0 1 3
+ I
I
I
I
m 3 r - * m
?Y"'7N. N
O
+ I
* 0
0
0
3
I
I
I
I
* O m d o
N?"?d:
++ +
m o o o o I I m m d m m ww.-r?m
++ I + N
O
0
0
0
I
m d m
te,
378
l&EC FUNDAMENTALS
k
from Equation 8, provided u and 7 for the compound are known. Hydrocarbons. T h e constants of the composing groups of paraffin hydrocarbons in the range of 300’ to 1000’ K. were estimated from the published entropy data (Rossini et al., 1947) for a variety of hydrocarbons. For olefin the following basic structural groups
H
H
H
rather than the simpler
H
=cH2,
,
=C
