CALCULATION OF HEAT OF REACTION FROM EQUILIBRIUM CONSTANTS AT TWO TEMPERATURES; SOME NEW HEATS OF IONIZATION OF ORGANIC ACIDS A. W. WALDE Research Department, Dr. Salsbury'a Laboratories, Charles City, Iowa Received Auguat 66, 1938 THEORETICAL
A recently published note (2) pointed out the fact that van't Hoff's isochor AH d T d (In K) = (1) RT2 which relates equilibrium constant, heat of reaction, and absolute temperature, can be combined with the equation for the linear variation of heat of reactlon with temperature, AH=a+bT
(2)
and integrated between limits to give1
It was also pointed out that if a temperature, To, is defined by the equation
the right-hand member of equation 3 is AHo, the value of AH at TO,and
It was shown that when is a linear function of temperature equation 5 can be used to calculate AH from two values of K and their corresponding temperatures, and that a knowledge of the values of a and b is not required.
* An error in aign was observed in the original equation. 43 1
432
A. W. WALDE
The present paper will undertake to show that AH may be approximated very closely by a similar procedure, even though it varies as a general equation of higher degree where the coefficients of the temperature t e r n are constants:
AH
= a
+ bT + C P+ dTP + eT4
(6)
Substitution of equation 6 in equation 1 and integration between the h i t s KI, Ka and T I , T I gives
+d
-
(Ti - TI) + e (T: T:) 2 3
(,I
and multiplication by ___ TiT2 and simplification of tenns gives T2 - Ti
If
and if T I and TS are near room temperature and are not taken over too )ill not differ appreciably from T:, nor wide a temperature range, ( T I T S w (T2
+
2
T ~ Tfrom , T: , nor (Ti
+
3
+ T:) T I T z
from G. A comparison of temperatures where T I = 0°C. and TZ= 35OC. shows that Tois 16.8"C., while (T1T2)"2= 17.OoC.,
[
+ 2
T1T2]'I8 = 17.1"C.
the temperature range being not more than 0.5"C.,a fairly close approximation. The error introduced in AH for the temperature interval will be small, particularly if the constants c, d, and e are small.
433
HEATS OF REACTION
On replacement of the above terms by To as a close approximation, equation 8 becomes
+ bTo + cTi + dT: + eTi
RT1T2 In 5 = a
Ki
T,-i
Combining with equation 6, equation 9 becomes identical with equation 5. In a similar manner it can be shown that equation 9 can be used for higher powers of TO. We have shown therefore that, when AH is a linear, quadratic, cubic, or quartic function of temperature, equation 5 can be used as a very close approximation for the calculation of A H 0 a t a temperature To (as defined by equation 4) from the values for K a t temperatures T1 and Tr. Such a calculation does not require any knowledge of the constant coeffi-
TABLE 1 Comparison o j two methods for heat of ionization ACID
-
1
Ti
--
*C. Formic (6). . . . . . . . . . . . . . 0 Acetic (4) . . . . . . . . . . . . . . . 0 0 Chloroacetic (19).. . . . . . . 0 0 Propionic (5). ........... 0 n-Butyric (8).. . . . . . . . . . 0
TI
-,;'
L-
'C.
ac.
6060 6 0 6 0
25 40 25 60 35
25 40 25 60 35
.C.I------
1 CddMCdhM
28.0' 1.6381 1.551 1.6571 1.542 1.657 1.754 19.1 152.8 122.9 I 12.1, 152.8 137.8 28.01 1.2741 1.160 16'8' 1'563'596. 1.439
Sulfuric (second hydrogen) (3).. . . . . . . . . . . . . . 0 j12w. 486.
-165 -217 368 -926 -669 -283 -395
-138 -215 316 -956 -681 -283 -338
&a
-27 -2 52 30 12 0 -57
-27421-2509 -233 -13571-1116 -241 10591 1102 43
cients, a, b, c, d , and e. The method is very useful in the determination of approximate values of AH at a given temperature when only one value of the heat of reaction is required and when only two values of K are known. Table 1 shows that the heat of ionization (13) of the carboxylic acids obtained by the a p p r o k a t e method differs from that obtained by equation 6 or by similar procedures by a maximum of 57 cal. Since the variation of AH depends primarily upon the temperature interval selected and upon the value of the constant coefficients in the terms Tz and T8, it would be expected that, if the coefficientswere large enough to contribute several thousand calories, the difference in values obtained by the two methods, corresponding to a dxerence in T of 0.5OC., would be large. Such is the case for the second hydrogen of sulfuric acid, for the higher order terms contribute appreciably to the value of -0.
. . WALDE
434
A W
TABLE 2 Heats of ionization of aome organic acids Temperature = 16.8"C., approximately NO . -
KIX 101
AaD
(0'C.J
......
1
Benzoic (16)
2 3 4
m-Nitrobenzoic (18) . . . . . . . . . . . . . . . p-Nitrobensoic (17) .... 3, 5-Dinitrobenzoic (17)
3.31 3.62 13.4
5 6 7 8 9 10
0-Hydroxybenzoic (16) . . . . . . . . . . . . . m-Hydroxybenzoic (16) .... p-Hydroxybenzoic (16) . . . . . . . . . . . . . 2, 4-Dihydroxybenaoic (17) . . . . . . . . . 2. 5-Dihydroxybenzoic (17) . . . . . . . . . Gallic (16) . . . . . . . . .
8.3 0.725 0.251 3.95 10.4 0.338
11 12 13 14
0-Chlorobenzoic m-Chlorobenzoic p-Chlorobenzoic m-Bromobenzoic
15 16 17
O-TolUic (16) . . . m-Toluic (16) . . . . . . . . . . . . . . . . . . . . . . p-Toluic (16) ......................
18 19 20 21 22 23
0.611
539
504
3.41 4.14 16.4
142 641 965
188
10.6 0.789 0.287 5.25 12.9 0.394
1169 1360 1029 733
11.9 1.54 0.68 1.55
.673 421 1014 731
1.59 0.515 0.383
1.25 0.554 0.437
-1150 349 630
Anisic (12) . . . . . . . . . . . . . . . . . . . Vanillic (12) ....................... m-Acetoxybenzoic (11) . . . . . . . . . . . . . Acetylsalicylic (12) . . . . . .
0.291 0.300 1.19 3.10
0.330 0.355 1.32 2.72
601 804 495 .625
Cinnamic (16) .....................
0.322 0.220 0.233
0.363 0.217 0.242
. 66
29
Naphthionic (12) . . . . . . . . . . . . . . . . . . 11.7 . . . . . . . . . . . . 0.285 9.25 . . . . . . . . . . . . . . . 4.30 0.220
27.6 0.254 8.93 4.24 0.246
30 31 32 33
Acetic (16) . . . . . . . . . . 0.175 Phenylacetic (16) . . . . . . . . . . . . . . . . . . 0.540 Cyanoacetic (17) . . . . . . . . . . . . . . . . . . . 38.7 Propionic (16) ..................... 0.133
0.183
24 25 26 27 28
.
(17) . . . . . . . . . . . . . . . 13.7 (11) . . . . 1.41 (11) . . . . . . . . . . . . . . . 0.55' (11) . . . . . . . . . . . . . . 1.33
0.684
A
-1060
181 4101 -550 . 168 .67 534
214
163
-311
0.136
.
333
573
0.506 34.8
The subscript zero does not refer t o a standard state
To = 163°C. t Rderence 9.
404 640
I
-608 107
136
is oalc
rted for
435
HEATS OF REACTION
TABLE 2-Concluded NO.
!
ACID
KIX101 (O'C.)
-- I -
34 35 36 37 38 39
40 41
42 43
a-Bromopropionic (17). . . . . . . . . . . . . . 8-Iodopropionic (17). . . . . . . . . . . . . . . . n-Butyric (16). . . . . . . . . . . . . . . . . . . . . . a-Bromobutyric (17). . . . . . . . . . . . . . . . Isobutyric (16, 17). . . . . . . . . . . . . . . . . . Hydroxyisobutyric (17) . . . . . . . . . . . . . Isovaleric (17) ...................... Caprylic (17). ...................... Crotonic (16) ...........t. . . . . . . . . . . . . Phenylpropiolic (8). . . . . . . . . . . . . . . . .
12.4 0.977 0.163 14.98
1
Kt X 104 (36'C.)
9.2 0.910 0.147 11.5
0.96
~
AHo' (16.8'C.)
-1426 -450 -494 -1263 518
0.125 0.199 63.5
0.211 53.8
280 -792
HEATS O F IONIZATION O F SOME ORGANIC ACIDS
The new method outlined above makes it possible to calculate, with a relatively small error, heats of ionization from dissociation constant data obtained at only two temperatures. The author obsellied that this method could be used to obtain some heats of ionization hitherto unknown, and that it could also be used to study the relationship of heat of ionization to ionization constant in various organic acids. Table 2 presents in column 3 calculated heats of ionization which are new to the literature in most cases, as compared, in column 4, with values calculated by other methods. The values of K are the classical constants, rather than the thermodynamic values corrected to infinite dilution. The difference between the classical constant and the thermodynamic constant of weak organic acids is usually very small. o-Nitrobeneoic acid has not been included in the table, because it is so strong that Ostwald's dilution law does not hold even approximately and dilution has a marked effect upon K . In order to eliminate personal errors, only those values of K were used which were determined a t different temperatures by the same worker. Table 2 shows that the values for AH obtained by the approximate method compare very favorably with those obtained by classical methods (9). Figure 1 shows log K plotted against AH,the numbers on the graph corresponding with those of the acids listed in table 2. By use of the equation
-RThK
= AH -
TAS
(10)
where R, T , K , and AH have the usual notation and A S represents the increase in entropy due to ionization, the variable most concerned in the change in structure of an organic acid, such as the introduction or substitution of groups or a change in resonance energy, may be studied.
430
A. W. WALDE
Figure 1 shows that there is no simple relation between the ionization constant, K, and the heat of ionization, AH,of organic acids. The two constants seem to be in no way dependent upon each other. For example, the plotted points of benzoic acid, m-nitrobenzoic acid, and p-nitrobenzoic acid form an equilateral triangle, while those of benzoic acid and the three monohydroxybenzoic acids form a parallelogram.
AH,
(CALORIES)
FIQ.1
Introduction of a hydroxyl group into the ortho position in benzoic acid and into mhydroxybenzoic acid causes about the same change in AH and causes parallel changes in log K of the two compounds. Likewise, introduction of a hydroxyl group into the meta position in benzoic acid and into o-hydroxybenzoic acid (giving 2 ,5-dihydroxybenzoic acid) causes parallel changes in AH and in log K , AH decreasing in both cases and log K increasing. Para-substitution of the hydroxyl group in benzoic acid
HEATB OF REACTION
437
and in o-hydroxybenzoic acid (giving 2 ,4dihydroxybenzoic acid) causes increases, though not parallel ones, in log K and decreases in AH. These changes are perhaps fortuitous, because gallic acid bears no such close relationship to either mhydroxybenzoic acid or phydroxybenzoic acid. The plot of the chlorobenzoic acids shows a linear relationship between AH and log K. The stronger the acid, the lower the heat of ionization. The saturated aliphatic acids have a narrow range of K (between 1 X 10-5 and 2 X but their heats of ionization range from -809 cal. to 214 caL2 Of the six listed in table 2, those of lower molecular weight have the higher heats of ionization except for caprylic acid, which lies between propionic and isobutyric acids. This fact might be interpreted to mean that the carbon chain of the caprylic acid molecule is folded. As might be expected, isobutyric acid with its more compact structure has a slightly higher heat of ionization than n-butyric acid. Increase in the molecular weight of propionic acid by substituting a phenyl group on the omega carbon atom (hydroxycinnamic acid) causes the same sort of lowering in heat of ionization as noted above in saturated aliphatic acids. However, this relationship does not hold where polar groups are substituted on the aliphatic acids, since the heat of ionization of 8-iodopropionic acid is higher than that of a-bromopropionic acid. A comparison of isobutyric acid and hydroxyisobutyric acid shows that hydroxyl groups tend to increase the heat of ionization. A similar effect has been noted in the aromatic series when hydroxyl groups are substituted in the ortho and para positions. It has been pointed out (1) that resonance energy plays an important part in the dissociation of ortho- and para-substituted benzoic acids. Table 2 shows that four Merent groups (including ortho-para orienting groups as well as so-called “electronegative” and “electropositive” groups) -methyl, hydroxyl, chloro, and nitro groups-raised the heat of ionization of benzoic acid when substituted in the para position. All except the hydroxyl group decrease the heat of ionization when substituted in the ortho position. It has been postulated (14) that numerous other factors influence the ionization of ortho-substituted derivatives. The theory (1) leads one to expect that resonance energy is not concerned in the ionization of derivatives with one substituent in the meta position (15). The data in table 2 show that each of the four groups mentioned above caused a decrease in the heat of ionization when sub-
+
* These relationships cannot be expected to be very close, since disaociation constants at O’C. were compared with aR values obtained at about 16.8%. If both had been considered at the same temperature, a better interpretation could have been made. However, the data are not yet available.
4338
A. W. WALDE
stituted in the meta position of benzoic acid.’ It may therefore be said that in the absence of resonance effect the methyl, hydroxyl, chloro, and nitro groups contribute a decrease to the heat of ionization when substituted in the benzoic acid molecule. The increase in the heat of ionization when these groups are substituted in the para position must be due to increased resonance energy. It may be said in general that, since specific heats of ionization are all of about the same order of magnitude, and since they vary negatively with an increase in temperature, the acids having the higher heats of ionization will reach maximum ionization at a higher temperature (7). 0-Y
1. A new approximation method for the calculation of the heats of ionization of organic acids has been presented. 2. Some new heats of ionization of organic acids have been calculated. 3. Resonance energy has been shown to increase the heats of ionization of certain substituted benzoic acids. 4. The relation between the heat of ionization and the ionization constant in certain organic acids has been presented. (1) (2) (3) (4) (5) (6) (7)
(8) (9) (10) (11) (12) ,(13) (14) (15) (16) (17) (18) (19)
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* m-Bromobenzoic acid and m-dinitrobenzoic acid have higher values for AH than does benzoic acid, perhaps owing to the effect of increased molecular weight. Obviously more exhaustive study is necessary before drawing rigid conclusions. FIQ. 1. Relation of ionization constants of some organic acids toheatsof ionization
