2465
HYDRATION OF N-METHYLACETAMIDE IN CARBON TETRACHLORIDE
Hydration of N-Methylacetamide in Carbon Tetrachloride by R. D. Grigsby, Research and Decelopment Department, Continental Oil Company, Ponca City, Oklahoma
S. D. Christian, and H. E. Affsprungl Department of Chemistry, The Uniceraity of Oklahoma, Norman, Oklahoma
(Received December 18, 1967)
The problem of investigating the hydration of functional groups common to proteins has been approached by studying the equilibrium between K-methylacetamide (NMA) and water in carbon tetrachloride solution. Hydration data were obtained by two independent methods: in one, the concentration of water in solution was measured as a function of NMA concentration at constant water activity; in the other, the Concentration of NMA was held constant and the concentration of water was measured at increasing water activity. The relationship between NMA concentration, total water concentration, and water monomer concentration in solution was found to be the same as the Langmuir adsorption isotherm. The use of the Langmuir equation to explain the data is consistent with the assumption that NMA self-associates to form chains in dilute solution, with each chain containing multiple sites for the attachment of water molecules.
Introduction The significance of hydrogen bonding in protein structure has been well established in recent years, although the role played by water is at present only partially u n d e r s t o ~ d . ~ -Information ~ has been obtained by studying proteins in their natural or partially denatured state5 and by other methods; however, the large number and heterogeneity of possible hydration sites makes the interpretation of results difficult. For this reason, a number of investigators have attempted to study the hydrogen bonding and hydration of smaller, less complicated molecules which are chemically related to proteins. X-Nethylacetamide has been the object of much investigation because it is the smallest molecule containing a single peptide g r o ~ p . ~ + 'I~n the work to be described here, the hydration of NJIA was investigated in CCI, solution to avoid the inherent difficulties encountered in studying hydration reactions in aqueous media. To our knowledge the hydration of NAIA in nonpolar solvents has not been studied before, although the hydration of N,K-dimethylacetamide has the hydration been reported r e ~ e n t l y . ~I n? ~addition, ~ of 2-pyrrolidone and N-methyl-2-pyrrolidone has been investigated. 13,14 Experimental Section Materials. N-Methylacetamide (purchased from K & K Laboratories, Jamaica, N. Y.) was purified by vacuum distillation and fractional crystallization, The final product had a melting point of 30.5", A Kjeldahl analysis showed a purity of 99%. The purified SAIA was stored at 30.4" in a flask equipped with a P ~ O Bdrying tube. Before use, any liquid phase present was withdrawn and was discarded. Fisher Certified reagent carbon tetrachloride was purified by refluxing with mercury followed by distillation through a 30-plate Oldershaw column. The
boiling point of the collected fraction was 77" corrected to 1 atm. Before the solvent was used, it was extracted with water to remove residual, water-soluble impurities. Apparatus. The hydration of NYIA in CC14 was studied by two independent methods, which gave nearly equivalent results. I n the first, solutions of the amide in CC14 were suspended over constant-humidity solutions (dilute HzS04) in closed containers thermostated at 25 i. 0.1". After equilibrium was attained, samples of the NRIA-CC1, solutions were withdrawn and were analyzed for total water content. A detailed description of the equilibrators and the technique has been given earlier.15 The concentration of water in the samples was determined with a coulometric water (1) Deceased August 5, 1967. (2) C. Tanford, "Physical Chemistry of Macromolecules," John Wiley and Sons, Inc., New York, N. Y., 1961, p 130. (3) I. M. Klotz and J. S. Franzen, J . Amer. Chem. SOC.,84, 3461 (1962). (4) F. Takahashi and N. C. Li, ibid., 88, 1117 (1966). (5) H. A . Scheraga in "Polyamino Acids, Polypeptides, and Proteins," M. A. Stahmann, Ed., The University of Wisconsin Press, Madison, Wis., 1962, p 241. (6) S. Mizushima, T . Simanouti, S. Nagakura, K. Kuratani, M. Tsuboi, H. Baba, and 0 . Fujioka, J . Amer. Chem. Soc., 72, 3490 (1950). (7) M. Davies and D. K. Thomas, J . Phys. Chem., 60, 767 (1956). (8) L. A . LaPlanche, H. B. Thompson, and M . T . Rogers, {bid, 69, 1482 (1965). (9) F. Takahashi and N. C. Li, ibid., 68, 2136 (1964). (10) F. Takahashi and N. C. Li, ibid., 68, 2140 (1964). (11) F. Takahashi and N. C. Li, ibid., 69, 1622 (1965). (12) F. Takahashi and N. C . Li, ibid., 69, 2950 (1965). (13) D. D . Mueller, Ph.D. Dissertation, The University of Oklahoma, Norman, Okla., 1966. (14) J. D. Worley, Ph.D. Dissertation, The University of Oklahoma, Norman, Okla., 1964. (15) 8 . D. Christian, H. E. Affsprung, J. R. Johnson, and J. D. Worley, J. Chem. Edzic., 40, 419 (1963). Volume 78, Number 7
Julu 2968
R. D. GRIGSBY,S. D. CHRISTIAN, AND H. E. AFFSPRUNG
2466 analyzer similar to that described by Meyer and Boyd.16 Hydration data were obtained for NRIA solutions in CCl, ranging in concentration up to 0.0538 M and at water activities of 0.31, 0.47, 0.56, and 0.69. The second method used to obtain hydration data involved the measurement of the total pressure of 0.1”. N&IA-H20-CCL solutions thermostated at 25 Water was added in milligram quantities to the initially dry NMA-CCl4 solutions, whereupon the total pressure was measured at equilibrium. The apparatus and technique have been described el~ewhere.’~The concentration of S l I A ranged up to 0.0612 M ‘and the highest water activity studied was -0 6,
*
An-1
(Kn) where only two constants, K z and K,, are required to express the various equilibria.
Results Figure 1 shows the data obtained from the constanthumidity equilibrators. The total water concentration, [HaOlt, of the NMA-CCL solutions is plotted against the total amide concentration, [NMA],, a t constant water activity. Because of phase separation, the data taken at a water activity of 0.69 could not be obtained much past an NRIA concentration of 0.02 M . In the analysis of the data it was assumed that the water monomer concentration is directly proportional to the water a ~ t i v i t y ’ ~ ~ ~ ~
[HzO], = 0.0098P/P0 M
(25.0’)
The Henry’s-law constant (0.0098 M ) was determined from the slope of a plot (not shown) of water concentration us. water activity for cc14 solutions containing no NMA. The data taken from the total-pressure apparatus are shown in Figure 2. Total water concentration is plotted us. water activity a t constant NMA concentration. The vertical dotted lines represent water activities a t which phase separations occur for the given concentrations. The lower line in the graph gives the concentration of water in solutions containing no NMA. From these data the Henry’s-law constant was determined to be 0.0087 M ; consequently, the water monomer concentration for this technique is given by [HZO],
=
0.0087P/P0 M
(25.0’)
The constant obtained here is about 11% lower than the value obtained from the equilibrator data. However, the smaller figure is believed to be more accurate and agrees with the value (0.0087 M ) obtained by Johnson, et aZ.,19 and by Clifford.20
Discussion In the analysis of the data it is necessary to take into account the self-association of N-methylacetamide. Several independent studies have been conducted, 3 ~ 7 * 8 , 2 1 and it has been shown that the amide self-associates to form linear chains containing any number of monomeric units, depending on the total concentration of amide in solution. This process can be depicted as The Journal of Physical Chemistry
+ A ZAn
-
0 0.0040
8 0.0040
r/
, l -
,
0
0.0030
t
0.0020 ’,
0.0010 0.0000
0.000
0.010 0.020 0.030 0.040 [NMAlt, M .
0.060
0.060
0.070
Figure 1. Total water concentration us. total NMA concentration at constant water activity, PIP0 (25 & 0.1’): 0 , 0.31; 0.47; A, 0.56; 0 0.69. Lines are calculated with K1l = 10.7 l./mol and B = 0.0098 M .
,.
Because of chain formation, it is reasonable to assume that each chain contains multiple sites of the attachment of water molecules. Based on this assumption, an equation was derived to explain the relationship between total amide concentration, total water concentration, and water monomer concentration in solution. The resulting equation was found to be a form of the Langmuir adsorption isotherm. Although the derivation of the Langmuir equation is readily available in a number of t e ~ t b o o k sthe , ~ steps ~ ~ ~leading ~ (16) A. 5. Meyer and C. M. Boyd, Anal. Chem., 31, 215 (1959). (17) A. A. Taha, R. D. Grigsby, J. R . Johnson, 8. D. Christian, and H. E. Affsprung, J . Chem. Educ., 43, 432 (1966). (18) J. R. Johnson, 8. D. Christian, and H. E. Affsprung, J . Chem. SOC.,l(1965). (19) J. R. Johnson, S. D. Christian, and H. E. Affsprung, ibid., 77 (1966). (20) C. W. Clifford, Ind. Eng. Chem., 13, 631 (1921). (21) R. D. Grigsby, Ph.D. Dissertation, The University of Oklahoma, Norman, Okla., 1966. (22) T. L. Hill, “An Introduction to Statistical Thermodynamics,” Addison-Wesley, Inc., Reading, Mass., 1960, p 128. (23) B. Jirgensons and M. E. Straumanis, “A Short Textbook of Colloid Chemistry,” John Wiley and Sons, Inc., New York, N. Y . , 1954, p 75.
HYDRATION OF N-METHYLACETAMIDE IN CARBON TETRACHLORIDE 0.0080
On the assumption that each monomeric unit, A, contains only one hydration site, the species C-XnW, becomes A,W, and eq 2 can be written
I
0.0080
0.0070
2467
The possibility of having more than one hydration site per monomer will be discussed later. Using eq 3, an equation for the total concentration of water in solution can be derived. In terms of the water monomer concentration and all possible hydrated species present (assuming one hydration site per monomer), the total water concentration can be expressed as
+ [AW] + [&W] + [&W] + . . . + 2[AzWz] + 2[AsWz] + 2[A*Wz] + . . + 3[AaW3] + 3[A4Wa] + 3[A5Wa] + . . . + . . .
[Wlt = [W]
Similarly, the total amide concentration is 0,000
Figure 2.
0.100
0.200 0.300 0.400 0.500 0.600 0.700 P/PO(HoO).
Total water concentration us. water activity
at constant NMA concentration, M (25 f 0.1'); 0 , 0.0000; ,. 0.0311; A, 0.0442; 8 , 0.0612. Lines are calculated with KII = 12.8 l./mol and B = 0.0087 M .
to the present form will be outlined below because the application of the equation to dilute-solution chemistry is somewhat removed from the usual gas-solid interaction studies. If it is assumed that each chain contains n independent hydration sites, each of which can attach no more than one water molecule, then it can be shown that the equilibrium constant for the reaction
c-x,wu-l+ w
c-x,w,
is given by Knu
n-v+l v
Kii
where C-X, is a chain containing rb hydration sites of type X and W is a molecule of water. The symbol Kn, is thus the equilibrium constant for the reaction of one water with a chain having v - 1 attached water molecules. KI1 is the equilibrium constant for the reaction of one water with a chain having only one possible hydration site. The number of attached water molecules in the product of the reaction cannot be greater than the number of possible hydration sites; Le., v cannot be greater than n. By using eq 1, an equation for the concentration of the species C-X,W, can be derived in terms of the water monomer concentration and the concentration of C-X,. The result is
[AI,
=
+ 2[Az] + 3[&1 + . . . + [Awl + 2[AzWl + 3[A3W] + . . +
[AI
2[AzWz]
+ 3[&Wz] + 4[A4Wz] + . . . + . . .
By replacing the concentrations [A,W,] with the righthand expression in eq 3, the two series can be combined to give the final equation
which is a form of the Langmuir adsorption isotherm. Note that the self-association constants for the amide were not required in the d e r i ~ a t i o n . ~ ~ Although eq 4 was derived on the assumption that each monomeric unit of the chain contains only one hydration site, the same result, except with the second term multiplied by 2, will be obtained if it is assumed that each monomer has two sites for hydration. Thus it becomes evident that it is not possible to determine the number of sites per monomer by simply fitting eq 4 to the experimental data. It is interesting to note that eq 4 is also obtained if it is assumed that all of the amide is in the monomer form and that each monomer can attach one water. I n fact it might be argued that at the concentrations considered (24) An alternate derivation of eq 4 is simpler to follow and may shed light on the conclusion that values of the self-association constants of the amide are not required in the analysis of hydration data. It has been assumed that each amide molecule contributes exactly one hydration site (equivalent to and independent of all the other sites) regardless of the size of the polymeric unit in which i t is found. Therefore, the number of sites is directly proportional t o [A]t, the total or formal amide concentration. The equilibrium constant for hydration of the sites may be written K11 = [S-W]/ ([S][W]),where [S-W] is the concentration of hydrated sites and [SI is the concentration of unhydrated sites. Of the total number of sites, a fraction [S-W]/([S-W] [SI) = K11[Wl/(1 K11[W]) will be hydrated. The total concentration of bound water is thus equal to Kii [W] [A]t/ 1 K11 [WI ) , which is a Langmuir-type relation involving the activity or monomer concentration of water. Since the concentration of bound water is equal to [W]t [W], the expression leads directly to eq 4.
+
+
+
-
Volume '7B, Number 7'
July 1968
R. D. GRIGSBY,S. D. CHRISTIAN, AND H. E. AFFSPRUNG
2468 here, the amide exists almost entirely in the monomer state. We have, however, obtained data in our laboratory21 to indicate that NilIA is highly associated in dilute CC14 solutions. At 20" by a vapor pressure lowering technique, we have found Kz = 9.0 & 2.8 l./mol and K, = 61.6 f 5.7 I./mol. I n addition, appreciable association was noted a t 60 and 75" from data obtained by a liquid-vapor equilibrium technique (see Table I). The value of K, at 20' is in fair agreement with that of Klotz and Franzen (4.7 and 5.8 l./mol) obtained at 250a3 No value was given for K,. Other values of Kz and K , obtained for various solvents by different investigators are summarized in Table I. Table I : Self-Association of N-Methylacetamide in Various Solvents Temp,
Solution
cc14
Benzene
a
OC
20 25 60 75 25 35 49
CDCla
Room
Dioxane Water
25 25
Kz, l./rnol
9 . 0 =t 2 . 8 4.7, 5.8 2.7 & 0.7 1 . 5 =t 0 . 4 6 . 7 =t 0 . 3 a 5 . 5 =t 0 . 2 a 4.2 0.2" 1.25" 0.52, 0 . 5 8
+
0.005
K7h l./mol
6 1 . 6 =t 5 . 7 1 4 . 3 =t 1 . 5 1 3 . 8 k 1.1 1 4 . 3 i0 . 2 "
11.5 =t 0.2" 8 . 9 i 0.2" 1.35"
... ...
Ref
20 2 20
20 6 6 6 7 2 2
Values were converted from mole fraction units.
Equation 4 can be tested directly with the data from the constant-humidity equilibrators, as shown in Figure 1. Using a least-squares computer program,25 the best value of K11 was determined to be 10.7 f 0.5 l./mol. The water monomer concentrations required in the calculations were obtained with a Henry's-law constant of 0.0098 M , as explained above.
The Journal of Physical Chemistry
After putting the equation into the form
it can be tested with the data from the total-pressure apparatus (Figure 2). The least-squares value of K11 was found to be 12.8 f 0.3 l./mol. A value of 0.0087 M for the Henry's law constant was used to obtain the water monomer concentrations (see Results). The values of Kll (10.7 0.5 us. 12.8 0.3 l./mol) obtained by the two independent methods are in reasonably good agreement. It might be supposed that part of the difference could be attributed to the difference in the Henry's law constants (0.0098 us. 0.0087 M ) . However, an error analysis shows that this difference has little effect on the value of Kll if it can be assumed that the water concentrations from the two methods differ by a constant factor at all activities. Thus the difference in K11 must be attributed to unknown systematic errors. Because the self-association constants for JSMA do not appear in eq 4, it seems that the equation should apply to hydrated polymers in which the monomers are linked together by covalent instead of by hydrogen bonds. Thus it would be interesting to test the theory with data obtained for the hydration of small polyamides. If these molecules were found to hydrate in the same manner as N-methylacetamide, then with data from solutions of increasing dielectric constant it might be possible to formulate a model for hydrated proteins in aqueous media.
*
*
Aclcnowledgment. The authors wish to thank James R. Johnson and Delbert D. Jlueller for assistance in programming the least-squares analysis. This work was supported by the Kational Institutes of Health. (25) S. D. Christian, J . Chem. Educ., 42, 604 (1965)
