June, 1956
767
ENTROPIES OF ASSOCIATION FOR AMIDESIN BENZENE SOLUTIONS
ENERGIES AND ENTROPIES OF ASSOCIATION FOR AMIDES IN BENZENE SOLUTIONS. PART I1 BY MANSELDAVIEPAND D. K. THOMAS The Edward Davies Chemical Laboratories, University College of Wales, Aberystwyth, England Received September 7,1066
A simple method based on the "thermoelectric osmometer" of Hill which uses single drops of solution and a pair of matched thermistors to compare vapor pressure lowerings is described. One-half per cent. or better accuracy can be attained readily for non-volatile solutes above 0.05 M. One N-propyl and four N-methyl amides were studied in benzene. After an initial dimerization, chain-association to high mean molecular weights occurs in dilute solutions except for trichloroacetamide and its N-methyl derivatives which produce cyclic dimers and trimers. The H-bridge energy in all these cases is 3.6 1 0.2 kcal./mole. The entropies of association also are discussed.
The experimental method used in this Part stems from the "thermoelectric osmometer" due to Hill' and developed by Baldes.2 McBain, Brady and Huff8 described the use of matched thermistors for this method and it is essentially their arrangement which we have adapted to our needs. Nulkarni and, more particularly, Muller and Stolten4 have given accounts of a similar procedure whilst the present work was in progress.
Experimental The vapor pressure difference between solvent and solution is measured in terms of the temperature difference between individual isolated drops placed in the saturated solvent vapor. Condensation of the latter occurs on to the solution drop until its temperature rises so that the solvent partial pressure equals that of the pure liquid. For a 0.010 44 ideal benzene solution this temperature difference is approximately 0.018' at 25'. Our drops were placed on a matched pair of Stante1 thermistors (type 2311/300), the resistance element being a minute bead having a very thin glass cover. At 20" each thermistor was of approximately 2000 ohm and maximum continuous power dissipation 10 milliwatt. Figure 1 shows the essential features of their mounting: in this the fixture of the leads in the glass tube was sufl6ciently rigid that no change in resistance occurred on raising and lowering the thermistors between the Dewar and the loading chamber. Care was taken to ensure maximum thermal insulation of the individual thermistors. The assembly was sunk in a thermostat controlled to 1 0 . 0 1 " and the silvered Dewar provided a well-dehed vapor bath. At least 24 hours were needed for adequate temperature constancy to be attained within it. Observations were made with a simple Wheatstone bridge, each resistance being approximately 2000 ohm, and a moving coil lamp-and-scale galvanometer having a sensitivity of 218 nun.per PA. The applied e.m.f. could be reversed by a key and was tapped off a 2 volt battery via a potentiometer to ensure that excessive power was not developed in the thermistors. With both thermistors bare, the bridge was balanced as nearly as the box resistances would allow: this gave the galvanometer zero. Drops of solvent were then placed on each thermistor and the steady galvanometer deflection on reversing the bridge e.m.f. noted: this provided the solvent reading, which was subtracted from subsequent readings when solvent and solution drops were equilibrated. The reversal of the e.m.f. which was always made, served inter alia, effectively t o double the deflections. Steady readings were usually attained about four minutes after the thermistors had been lowered into the equilibrium chamber. Between any pair of solutions the galvanometer zero was checked to ensure constancy in the thermistor conditions : further, the "solvent reading" and that for standard (calibrating) solutions could be checked at frequent intervals in measuring new solutions. (1) A. V. Hill, Proe. Roy. SOC.(London), A197,9 (1930). (2) E. J. Baldes, Biodynamiea, No. 46 (1939). (3) J. W. McBain, A. P. Brady and H. Huff, THISJOURNAL,66, 304 (1951). (4) Nulkarni, Nature (London), 171, 4344 (1953).
The accepted deflections were the mean of five or six observations. Biphenyl was chosen as the standard, ideal, solute in benzene (see Part I) and the results for a typical calibration at 25.01" may be given. The deflections, A, recorded for the solutions are those obtained after subtraction of the (constant) solvent reading. 108 X mole fraction biphenyl (Nd) 3.75 7.30 9.39 11.92 16.07 Galvanometer deflection (A m.1 34.0 66.5 85.5 108.0 147.0 A/(Nd X IO3) 9.07 9.11 9.10 9.07 9.15 Not only are the deflections proportional to the molefraction of the ideal solute, but the effective mole fraction ( N ) of any non-volatile solute in a solution giving a deflection A is clearly the biphenyl mole fraction ( N d ) giving the same deflection. Accordingly, the apparent mean degree of association of the solute is its stoichiometric mole fraction divided by Nd. All solutions were made up by weight and samples kept in closely stoppered bottles in the thermostat for some time before use. Two of the tests we made of the method may be briefly mentioned. We measured trichloroacetamide at low concentrations in benzene and compared the results with those of previous isopiestic determinations. The apparent molecular weights found for identical concentrations were 108 X N Thermistor mol. wt. Isopiestic mol. wt.
2.55
3.16
3.34
3.99
4.32
181.9
195.3
204.6
213.1
218.0
190.8
199.4
203.0
212.4
218.8
The apparent molecular weights by the isopiestic method are certainly correct to better than one unit: the thermistor values are acceptable down to N = 3.3 X lo3or 0.04 M. We tested our whole procedure by determining the association constant, KIZ,tor benzoic acid in benzene at 25.0": this is not a favorable case, as thg dimerization is almost complete over the accesRible concentration range. On a log Klz against 1/T plot our value a t 25.01' (%I* = 5.5 X loa in mole fraction units) agrees excellently with the line defined by the recent ebullioscopic data of Allen and Caldins a t 54.1, 65.5 and 80.3" and the isopiestic data of Wall and Banes6 at 32.5 and 43.3". Materials.-N-Methylformamide: prepared from formic acid and methylamine: b.p. 102-103' (20 mm.), n l 9 ~ 1.4313 (lit. n Z 51.4310). ~ N-Methy1acetamide.-The fraction boiling 108" (15 mm.) melted sharply at 28". N-Methylbenzamide: pre ared by the Schotten-Baumann reaction, and recrystallized !om alcohol; m.p. 82". N-Methyltrichloracetamide: prepared from methylamine and the ethyl ester: recrystallization from ether: m.p. 105'. N-Propylacetamide: propylamine in aqueous acetic acid was treated with acetic anhydride, and the product fractionated; b.p. 223" (lit. 222-225'). Owing to their hygroscopic nature, particular care was taken in storing and handling these amid9s. As for the (5) G. Allen and E. F. Caldin, Trans. Faraday Soc., 49, 895 (1953). (6) F. T. Wall and F. W. Banes, J . A m . Cham. Soc., 67, 898 (1945).
MANSEL DAVIES AND D. K. THOMAS
768
Vol. 60
TABLE I N-METHYLACETAMIDE IN BENZENE AT 24.57"
10s x
f
m
1.00 1.07 0.946
a
R (Klo = 69)
.. .
2.00 1.18s 0.881 152 173
4.00 1.49 0.748 154 161
i? (Kir 60) ... R (from C Y ) ... ... ... isopiestic method, the non-volatility of the solute is a necessary condition in these studies: the practical limit was reached in the case of N-methylformamide which proved too volatile to give reliable results at 45'. E
Results The most obvious feature of the results is the pronounced abnormality of these solutes: for N-methylformamide at 25" and N = 10 X 10-3 (0.13 M ) , the apparent molecular weight is already three times that of the monomer. The infrared and dielectric polarization data' leave no doubt that the major source of the abnormalities is the molecular association of the solute. N-methylacetamide provides a pattern typical of a number of these amides. Representation of the results in terms of Kreuaer's relations (e.g., f against iV plot) shows the process to consist of an initial dimerization followed, even at our lowest concentrations, by further stages having higher association constants, Le., qualitative and quantitative considerations suggest type (iii) association where Klz < = KM = . . . R . At the lowest concentrations the f-R curve for N-methylacetamide at 25" in benzene suggests the initial dimerization constant K12 is 70 10 in mole fraction units. Using this value, one can then calculate R from equation 11 (Part I). This treatment is summarized in Table I for which, as in the other tables, f values have been read off a large scale plot off against i". The original curves have a minimum of six experimental points for the ranges quoted, the actual deviations from the smooth curves being usually less than 0.01 in the f values. In Table 1 the R values are in mole fraction units, two of the sets corresponding to the different K l z values of 60 and 69. It is clear that the latter provides the better fit for the data and leads to R = 148 1. In the last row some values of R have been calculated from the E values using the relation deduced by Coggeshall and Saier.8 Not only is the latter a cumbersome relation to evaluate but the fi values are, in this case, only obtainable indirectly, by graphical integration from the Kreuzer equation
*
*
In (l/a)=
h3
(f
- l)/fR d x
The degree of agreement found suffices to establish the practical consistency of the relations used. The experimental data for these systems are summarized in Table I1 and the association equilihrium data are collected in Table 111. The equilibrium constants are in mole-fract,ion units, the enthalpies ( A H ) in kcal./mole, and the entropies ( A s ) in cal./mole perOK. (7) C. R. Leader and J. F. Gormley, J . Am. Chem. Soc., 78, 5731 (1951). ( 8 ) N. D. Coggeshall and E. L. Saier, ibid., 7 8 , 5414 (1951).
6.00 1.8% 0.638 148.5 149.8 145
7.00 2.05 0.693 147.8 147.5 144
8.00 2.285 0.551 148.3 146.8 146
9.00 2.52 0.515 148.1 145.5 145
10.00 2.76 0.482 147.6 144.4 145
Discussion The N-methyl derivatives of formamide, acetamide and benzamide and N-propylacetamide all show the same pattern, Le., they consistently provide apparent mean degrees of association (f) conforming to an initial dimerization constant followed by successive and approximately equal association constants: K12 < K23 = K34. . = R. The 3.0 at 0.12 M ) large f-values encountered (e.g., f suffice to establish that all associates up to a t least a tetramer stage appear in dilute solutions. Although t o within the experimental uncertainty, the data can be fitted by only two equilibrium constants that agreement, of course, only indicates the approximate equality of the association steps after the dimerization. For N-methylformamidg it appears that K 1 2 R, the condition K12 < K being more pronounced for the acetamide and benzamide derivatives. Like trichloroacetamide itself, the N-methyl derivative does not follow a chain-association: the degree of association is now very much smaller: at 25" and N = 4 X trichloroacetamide has f = 1.38, the N-methyl compound has f = 1.05. In fact, over the measured concentrations and especially a t 35 and 49" the Nmethyltrichloroacetamide is mainly involved in a monomer i? dimer process. However, at the three temperatures, the data indicate that some further association does occur with K1 < KZ3. Marked differences from the preceding cases are also found for the corresponding heats. Perhaps the most significant feature in these data is the approximate constancy in the heats of association : where dimerization is followed by chainassociation these are all 3.6 0.2 kcal. per mole of monomer added in the association. Clearly, this measures the energy of the "hydrogen bridge" in the polymolecular structures: in those cases where approximately the same value is found for AH12 it is suggested that only one hydrogen bridge is present in the dimers. This figure (3.6 kcal./ mole) is probably the best available estimate of this interaction energy in amide structures, but it is important to remember that the solvent can have a considerable influence upon it.9 By the same criterion (the value of AHlz) it appears that both trichloroacetamide and its Nmethyl derivative give rise to cyclic dimers in which, as for the carboxylic acid dimers, two hydrogen bridges are formed. These compounds are also unique in that there is no certainty that the association proceeds beyond the trimer, although there is some slight indication for N-methyl trichloroacetamide that this is so. The values of AHz3 ( = AHla - AHl2) show that one further
*
19) E. A. Moelwyn-Hughes, D. Patraik, M. Davies and P. 0. Jones, J . Chsm. SOC.,1249 (1951).
ENTROPIES OF ASSOCIATION FOR AMIDESIN BENZENE SOLUTIONS
June, 1956
769
TABLE I1 MEANDEQREESOF ASSOCIATION (f) AND DEDUCED FRACTIONS OF SOLUTE PARTICLES FORMED BY MONOMER ( a )IN BENZENE l0.X
N
Solute
N-Methylformamide
1.00
2.00
3.00
4.00
6.00
8.00
10.00
f:
At 24.92' 1.10 1.316 1.59 1.84 2.37 i . 9 0 ... 0.944 0.847 0.749 0.665 0.539 0.451 ...
f:
1.178 1.34 0.852 0.743
a:
a:
.. . .. .
12.00
14.00
16.00
18.00
20.00
...
... ...
... ...
... ...
...
.. . ...
... ...
...
...
A t 35.07' 1.697 2.05 2.40r 2.76 3 . 1 2 0.591 0.490 0.418 0.365 0.324
...
...
... ...
At 24.57'
f:
N-Methylacetamide
a:
f: a:
I
...
...
...
...
...
...
...
... ...
... ...
...
...
...
...
I
.
.
... ...
At 48.90" 1.26 1.39 1.55 1.71 1.88 2.05s 2.26 0.801 0.726 0.663 0.608 0.561 0.520 0.484
... ...
...
1.01 0.990
1.02 0.980
... ...
1.04 0.974
At 24.92' 1.10 1.24 1.44 1.76 2.17 2.59b 0.939 0.902 0.854 0.799 0.742 0.687
... ...
... ...
1.01 0,992
...
a:
... ...
At 35.07" 1.03 1.06 1.11 1.19 1.30 0.981 0.969 0.945 0.918 0.887
f:
...
...
...
a:
1.007 0.987
At 48.90' 1.018 1.02 1.04 1.07 1.12 0.980 0.973 0.962 0.948 0.928
f:
1.01 0.992
1.02 0.984
...
...
At 24-57' 1.05 1.11 1.20 1.326 1.50 1.63" 0.964 0.937 0.903 0.863 0.819 0.800"
1.006 1.01 0.995 0.989
.. . ...
At 35.07' 1.023 1.035 1.048 1.064 1.08 0.978 0.968 0.957 0.945 0.934
1.007 0.993
... ...
At 48.90' 1.013 1.02 1.026 1.032 0.987 0.980 0.974 0.969
1.046 1.095 0.957 0.916
... ...
At 21.80' 1.196 1.297 1.40 1.507 1.616 1.72 1.83 0.842 0.778 0.723 0.674 0.632 0.594 0.560
f: a:
f:
&:
f: &:
(N-Methyltrichloroacetamide)
. . *
1.13 0.894
a:
N-Methyltrichloroacetamide
1.18s 0 * 881
1.06 0.944
f: N-Methylbenramide
1.49 1.845 2.285 2.76 ... ... 0.748 0.638 0.551 0.482 . . . At 35.07' 1.06 1.13 1 226 1.34 1.636 1.94s 2.26 2.56s 0.951 0.899 0.847 0.795 0.698 0.615 0.546 0.492
1.07 0.946
f: &:
N-Propylf: acetamide a: 0 N = 13.00 X 10-8.
-
... ...
...
... . ..
...
1.576 1.91 2.27 0.851 0.810 0.765
...
1.28 1.39 1.50 0.887 0.850 0.821
. ..
..,
...
...
...
... ..,
... ...
... ...
1.12 1.15 0.910 0.897
, . .
...
1.045 1.05 1.065 1.083 0.957 0.951 0.944 0.938
, ,
, . .
...
...
,
TABLE I11 Solute
N-Methylacetamide N-Methylformamide N-Methy lbenzamide N-Propy lacetamide N-Methyltrichloroacetamide' Trichloroacetamide" a For R , A B , A3read
t,
OC.
Kl# 69f3 56.sf2 43.612 213f5 175f3 5.2410.1 4.2s f 0 . 1 3.30 f 0.05 50 8.48 f 0 . 2 5.56 f 0 . 1 3 . 4 o i 0.05
24.57 35.07 48.90 24.92 35.07 24.92 35.07 48.90 21.80 24.57 35.07 48.90 See Part I in these cases &a,
- 4H11 3.45 3.71 3.49 3.57 3.71
... 7.32 6.9s 7.1 f 0 . 4
AHa, A&.
x 148 f 2 1 1 8 . 6 f2 91.712 218 f 4 175 f 3 75.0 f 1 6l.if 1 47.0 f 0.5 52 f 2 28.2 f 1 . 0 23.4 f 1 . 0 17.8 f 0 . 5
...
-A i i
- 481;
- 43
3'91 3.64
3 . 7 f0 . 7
2 . 7 3~ 0 . 5
1 . 3f 0 . 5
2 . 4 f0 . 7
8.8k 0.6
3 . 9 f0 . 7
...
...
3.8, 3'67 3.75
... 3.26 3,92 3 . 7 f0 . 1
19.6 f 1
5 . 5 f0 . 5
15.8 & 0 . 4
8.6 f 0 . 4
MANSELDAVIESAND D. K. THOMAS
770
“hydrogen bond” is probably formed in the trimer, Le., that the latter is also a cyclic structure. The entropy changes on association also reflect these different categories. For an ideally simple process, (monomer) (n-mer) --t (n 1 mer), in which only translational and rotational energy changes occurred, one would expect A S -60 cal./”K. per mole of monomer. However, to be set against this are the positive contributions to A S resulting from the conversion of the degrees of freedom of the monomer into low (“intermolecular”) vibrational frequencies in the association complex. This condition is partly reflected in ASlZ = -28 e.u. for the gaseous dimerization of acetic acidloor in entropy of polymerization values, e.g., for methyl methacrylate monomer,” A S = -28 e.u. However, the values observed here, especially for -A$ are still very much smaller. This is almost certainly due to solvation changes which accompany association. If for each monomer molecule added to an existing complex, the net effect were to free one solvent molecule previously “frozen” in a solvation shell, the degrees of freedom changed for the monomer would be approximately balanced by those for the solvent. Some such compensation must certainly be involved as, were A S = -30 e.u. and AH = - 3.7 kcal./mole, K would be c X rather than of the order shown in Table 111. This solvent factor plays an essential role in the association of these compounds, for only monomer can be detected spectroscopically in their saturated vapors. l 2 The larger values of - A S for the trichloroacetamide molecules conform well with the different (cyclic) structures found in these cases. The greater degree of order, or precision of orientation, probably involved in the cyclic structures relative to chain association makes A S = S(dimer) - 2 S(monomer) smaller than would otherwise be the case. We may conclude with a reference to the frequently presented proposition that the chain-
+
+
Vol. 60
association often found for the amides is a consequence of the trans-configuration I of the monomers13-it being averred that the cis-form (11) would, for steric reasons, be essentially confined to cyclic dimerization. This argument is devoid of 0 R’ 0 H \ /\ / C-N R/ ‘R’
7-Y
R
*H
I’ IT substantial foundation. Thus, if the free-energy changes in a simple representation are AGa
cis-monomer +cyclic association AG
J. AGz
trans-monomer +linear (chain) association
+
(10) H. L. Ritter and J. H. Simons, J . A m . Chem. SOC.,67, 757 (1945). (11) P. A. Small, Trans. Faraday Soc., 49, 441 (1953). (12) J. C. Evans, J . Chem. Phys., 22, 1228 (1954); M. Davies, J. C. Evans and R. L. Jones, Trans. Faraday SOC.,51,761 (1955). and
then if (AGI AGz) has a larger negative value than AG3, we would have a monomer stable in the cis-form leading t o linear (trans) associated molecules. The converse relations may arise for methyltrichloroacetamide (R = CC13; R’ = CHI). As would be expected, accurate (Courtauld’s) models show that the trans-configuration (I) is much easier to attain than the cis (11). The latter, although free from strain, requires coordinated packing of the -Ccl3 and H3C- groups (so that on entropy considerations I is the favored form) which also results in the C=O and N-H groups of I1 being markedly exposed in fixed and adjacent positions on one side of the molecule. What is quite definite from our studies is that this molecule is almost restricted to cyclic dimer formation under conditions in which N-methylacetamide, for instance, shows xarked chain association. The absorption spectra for these different examples of association processes have not yet been reported. We wish to thank the D.S.I.R. for a Maintenance Award (to D.K.T.) and the Shell Petroleum Co. for financial assistance. (13) A. M. Buswell, J. N. Downing and W. H. Rodebush, J . A m . Chem. Soc., 62, 2759 (1940); M. Tsuboi, Bull. Chem. SOC.Japan, 22, 215 (1949); J. E. Worsham and M. E. Hobbs, J . A m . Chem. SOC.,76,
unpublished observations in these laboratories.
206 (1954).
v-
