THESOLUB~LITY OF VARIOUS GASESIN N-METHYLACETAMIDE
4651
The Solubility of Helium, Nitrogen, Argon, and Ethane in N-Methylacetamide, a High Dielectric Solvent without Anomalous Structural Effects112 by R. H. Wood and D. E. DeLaney Department of Chemistry, Univers$ty of Delaware, Newark, Delaware 10711 (Received July 8, 1068)
The solubilities of helium, nitrogen, argon, and ethane in N-methylacetamide (NMA) have been measured from 35 to 70" and values of the free energy, heat, and entropy of solution have been calculated. A BarclayButler plot of A H , vs. AS, indicates that NMA unlike water behaves as a normal polar solvent toward nonpolar gases. The application of regular-solution theory gives values of the solubility which are far too low. 'The hypothesis that nonpolar solutes dissolve in NMA without disrupting the linear hydrogen-bonded chains of solvent molecules can explain both the solubility of inert gases in NMA and the fact that NMA dissolves 1,argequantities of many nonpolar solutes.
Introduction The present measurements represent a small step in the investigation of the structure and thermodynamics of N-methylacetamide (NMA) solutions. It is known that the structure of the water molecules plays an important role in determining the properties of aqueous solutions and t,hat thermodynamic measurements are a useful way of investigating structural effects.*--" Thus it seems reasonable that a knowledge of the structure of NMA and how this is affected by solutes will be useful for an understanding of NRlA solutions. I n the cryst,alline state, the NMA molecules are hydrogen bonded together into long linear chains12 with the nitrogen and oxygen atoms trans to each other. Infrared, Raman, dipole moment, and dielectric constant measurements indicate the presence in the pure liquid of long chains of molecules in the trans position.18-lg I n addition, the dipole moment of a chain increases substantially with chain length. a, 14, The solubilitieag of nonpolar gases in NMA reported here can be explained by the hypothesis that small amounts of nonpolar solutes dissolve in NMA without appreciably disrupting the hydrogen-bonded chains of NRiIA molecules. Experimental Section The details of the gas solubility measuring apparatus are given elsewhere.20 Basically, the apparatus consisted of a gas buret and a solvent buret connected by a three-way capillary stopcock. A known amount of gas was quantitatively transferred to a known volume (about 100 ml) of degassed solvent, and the total pressure and volume of the system were observed when equilibrium was reached. Measurements a t several temperatures were made and then the system was returned to the lowest temperature to check the initial
reading. Constant-temperature water circulating through a water jacket controlled the temperatures of the solvent and gas burets. Degassing was checked by measuring the vapor pressure of the solvent and by compressing the vapor and looking for a residual gas bubble. The observed solubility did not change after 3 hr of equilibration, but for safety at least 12 hr (1) This work was supported by a grant from the National Science Foundation which is gratefully acknowledged. (2) Presented a t the 155th National Meeting of the American Chemical Society, San Francisco, Calif., April 1968. (3) D. D. Eley, Trans. Faraday Soc., 32, 1281, 1421 (1939). (4) H.9. Frank and M. W. Evans, J . Chem. Phys., 13, 507 (1945). (5) W.-Y. Wen and H. S. Frank, Discussions Faraday SOC.,24, 133 (1957). (6) D. N. Glew, J. Phys. Chem., 66, 605 (1962). (7) L. A. D'Orazio and R. H. Wood, ibid., 67, 1435 (1963). (8) G. NQmethy and H. A. Scheraga, J . Chem. Phys., 36, 3382, 3401 (1962); 41, 680 (1964); J . Phys. Chem., 66, 1773 (1962). (9) A. Ben-Naim and's. Baer, Trans. Faraday floc., 59, 2735 (1963); 60, 1736 (1964). (10) A. Ben-Naim, J . Chem. Phys., 42, 1512 (1965); 45, 1848 (1966); J . Phys. Chem., 69, 1922,3240,3245 (1965); 71, 448, 1137 (1967). (11) A. Ben-Naim and M. Egel-Thal, ibid., 69, 3250 (1965). (12) J. L. Kats and B. Post, Acta Crystallogr., 13, 624 (1960). (13) 8. Mizushima, T. Simanout, 8. Nagakura, K. Kuratani, M. Isuboi, H. Baba, and 0. Fujioka, J . Amer. Chem. SOC.,72, 3490 (1950). (14) G. Leader and J. F. Gormley, ibid., 7 3 , 5731 (1951). (15) M. Davies and D. K. Thomas, J . Phys. Chem., 60, 767 (1956). (16) R. Linn and W. Dannhauser, ibid., 67, 1805 (1963). (17) I. M. Klotz and J. S. Franzen, J . Amer. Chem. Soc., 84, 3461 (1962). (18) S. J. Bass, W. I. Nathan, R. M. Meighan, and R. H. Cole, J . Phys. Chem., 68, 509 (1964). (19) L. A. Planche, H. B. Thompson, and M. T. Rogers, ibid., 69, 1482 (1965). (20) D. E. DeLaney, M.S. Thesis, University of Delaware, Newark, Del., 1968.
Volume 7.9, Number 18 December 1088
R. H. WOODAND D. E. DELANEY
4652 was allowed for equilibration. In addition, approach to equilibrium from undersaturation and supersaturation gave identical results. The solvent was recrystallized three times in a drybox and typically had a water content of 0.04 mol yo after a run. The helium, nitrogen, and argon were all high purity grade (99.99%) and the ethane was C P grade (99.0%). Duplicate runs checked to within 0.5% for low solubilities (3 ml of gas/lOO ml, of solvent) and within 0.1% for high solubilities (100 ml of gas/100 ml of solvent). As an additional check, the solubility of argon in water was measured at 25". The result (a = 31.05) agrees nicely with the value of Ben-Naimg (a = 31.21).
Table 11: Constants in Eq 1
a
b C
Helium
Nitrogen
Argon
Ethane
-1152.5 OQ -6.0579
-245.7 OQ -7.514
-399.4 -1.12 -0.0278
352.7 -2.32 6.704
This was set equal to zero, since including this term did not appreciably help the least-squares fit.
Table I11 : Mole Fraction Solubility ( X lo4), Free Energy, Enthalpy, and Entropy of Solution of Helium, Nitrogen, Argon, and Ethane in N-Methylacetamide a t 35O ACptQ
Results and Discussion The experimental results were fit by the method of least squares to the equation In Xz = ( a / T )
+ b In T + c
(1)
where X 2 is the mole fraction of gas in the solvent when the partial pressure of gas is 1 atm. The smoothed values at 5" intervals are given in Table I and the constants of the equation are given in Table 11. The heat, free energy, entropy, and change in heat capacity on solution were calculated (Table 111) by the equations
AG = -RT In X Z
AH = -aR
+ bRT
A S = (AH
- AG)/T
AC, = bR The results in Table I show that the larger nonpolar gases are much more soluble in NMA than they are in water. This seems to be a general characteristic of NMA, because Dawson, Berger, Vaughn and EckstromZ1 have shown that unlike water, NMA will dissolve large amounts of nonpolar liquids. For instance, the following dissolve to an extent greater than 30 wt % in NMA: dioxane, cyclohexane, toluene, pyridine, and naphthalene. If KMA solutions are compared with typical nonpolar solvents, the solu-
Table I : Solubilities of Helium, Nitrogen, Argon, and Ethane in N-Methylacetamide (35-70') from Least-Squares Fit T,
7 -
OC
Helium
35.00 40.00 45.00 50.00 55.00 60.00 65.00 70.00
0.557 0.591 0.626 0.663 0.699 0.738 0.776 0.816
Mole fraction X lo4 (at 1 atm) Nitrogen Argon
2.461 2.492 2.523 2.554 2.583 2.613 2.641 2,669
The Journal of Physical Chemistry
4.444 4.456 4.466 4.476 4.483 4.490 4.494 4.498
Ethane
41.91 39.63 37.52 35.57 33.76 32.07 30.50 29.03
Gas
He
N2 Ar
CiHe
104xa
0.557 2.461 4.444 41.91
Aa, kcal/ mola
6.00 5.09 4.73 3.35
AH, kaal/ mol"
2.3
0.5 0.1 -2.1
AS, oal/deg mol
cal/ deg mol
-12.0 -14.9 -15.0 -17.8
0 -2 -5
0
The estimated 95% confidence limits are: AG, about 0.01 kcal/mol; A H , about 0.1 kcal/mol; and ACp, about 10 cal/deg mol.
bilities in Table I are a little lower than those observed for nonpolar solvents. Frank and Evans4 used a Barclay-Butler Plot22 of AS, vs. AH, to show that nonpolar solutes in water created much more structure in the solvent than would be expected on the basis of the heat of interaction. This ability of a nonpolar solute to structure the water molecules around it has a very important influence on the properties of aqueous solutions. a-11 A BarclayButler plot of the present results on NMA solutions is shown in Figure 1. This plot shows that nonpolar solutes in NMA do not have an unusual effect on the structure of the solutions. The line marked nonpolar in Figure 1 is Frank's23 modification of the BarclayButler correlation. It shows how the entropy of vaporization and heat of vaporization of nonpolar solutes in nonpolar solvents are related. The data for NMA are only slightly higher than what would be expected for a nonpolar solute in a nonpolar solvent. The slightly high entropy of vaporization shown by NMA solutions is a characteristic of many somewhat polar solvents. I n contrast, the line marked water shows the very high entropies of vaporization of aqueous solutions of nonpolar gases. This means that the nonpolar solutes do not appreciably affect the structure of (21) L. R. Dawaon, J. E. Berger, J. W. Vaughn, and H. Eckstrom, J. Phys. Chem., 67, 281 (1963). (22) I. M. Barclay and J. A. V. Butler, Trans. Faraday SOC.,34, 1446 (1938). (23) H.8.Frank, J . Chem. Phys., 13, 493 (1946).
THESOLUBILITY OF VARIOUSGASESi~ N-METHYLACETAMIDE I
I
-'Z
I
I
I
0
I
I
b
I
4
AH" Figure 1. Heat alf vaporization us. entropy of vaporization for gases in water, NMA, and nonpolar solvents.
NMA solutions and that the anomalous effects in water are not present in NMA solutions. Another effect of the water structure around nonpolar solutes is to produce a very large increase in the heat capacity of the solutions.3-6 Table IV shows that the change in heat capacity upon dissolving these gases in NMA is very small compared with the results for aqueous solutions. This reinforces the conclusion that these solutes do not affect the structure of the solvent .5-' -
Table IV : Change in Heat Capacity on Dissolving Gases in N-Methylacetamide
4653
of NMA solutions discussed above. The model assumes that when small amounts of a nonpolar solute are dissolved in NMA the chains of NMA molecules are not appreciably disrupted but that the solute fits in between the chains. Thus toward a nonpolar solute, NMA behaves like a linear (but not rigid) polymer. The solute molecules are in contact with the nonpolar sides of the KMA polymer so that NMA behaves like a relatively nonpolar liquid toward these solutes. This explains why NMA dissolves so much ethane and why hydrocarbons are so soluble in it. I n addition, the lack of any unusual entropy effects is also expected. Naturally, this assumption fails when polar solutes are introduced. The solubility of electrolytes in NMA is undoubtedly due to the solvation of the ions by the NMA. It is these two possible ways of interacting with solutes that explains why NMA is a good solvent for both electrolytes and nonpolar solutes. The above model can be made somewhat more quantitative by applying eq 2 to the NMA polymer. If an n-mer is assumed, the equation for the solubility becomes
+ 0.4343( V2/RT)(61 - + log (P2/V1O) + 0.4343[1 - (~2z/nV1O)] (3)
-log XZ0 = -log .Xi
62)2
where the superscript zero represents monomer values, and we have used VI = nVloand X2 N nX20. There is very little difference between eq 2 and 3. If anything, eq 3 predicts a lower solubility than eq 2 by a factor of 3 or so. However, there is a large difference in the solubility parameter 6 = ( ( A H , R T ) / V l ) l ~ * The . appropriate solubility parameter for the n-mer is calculated from AH, for the process nNR'IA(1)
NMA
0 0 -2
-5
If the heat of hydrogen bonding in the gas phase is known, then it can be shown that the appropriate solubility parameter is
H2O"
24 41 38 66
a Values from D. N. Glew and E. A. Moelwyn-Hughes, Discussims Faradag SOC.,15, 150 (1953).
The solubility of nonpolar gases in nonpolar liquids can be roughly predicted by applying the equations for a regular solution24 to the liquefied gas.26 The resulting equation is -log X2 = -log log
X2' (V2/V1)
(NMA),(g)
cal/deg-
-ACP,
+
0.4343(P2+z/RT)(61- 6 ~ ) ~
+ 0.4343[1 - (V2/VJ]
(2)
where X: is the "ideal solubility"26 and 6 is the solubility parameter.24 When this is done for NMA times solutions, the predicted solubilities are 1/lo-1/16 the experimental solubilities. 26 A very simple model will explain all of the properties
where AH(HB) is the heat of forming a hydrogen bond in the gas phase. Unfortunately the heat of hydrogen bonding in the gas phase is not known. If the calculation is reversed, the gas solubility data are explained by a solubility parameter of 9.3 =k 0.3 and a chain length (n) of 15. This requires a gas-phase heat of hydrogen bonding of -6.5 kcal/mol, which is the correct order of magnitude. The reported values of the heat of hydrogen bonding (24) J. H. Hildebrand and R. L. Scott, "The Solubility of Nonelectrolytes," 3rd ed, Reinhold Publishing Gorp., New York, N. Y., 1950,p 240. (25) J. Chr. Gjaldbaek and J. H. Hildebrand, J. Amer. Chem. Soc., 71, 3147 (1949). (26) The heat of vaporization of NMA, AH" = 13,290 kcal/mol, was obtained from L. R. Dawson, W. H. Zuber, and H. C . Eckstrom, J . Phys. Chem., 69, 1335 (1965). Volume 7.2,Number 19 December 1068
ROBERTN. GOLDBERG AND LOREN G. HEPLER
4654 are -3.6 kcal/mol in ben~ene,~'-4.2 kcal/mol in carbon tetrachloride,28 about -8 kcal/mol in solid NMA,29and -4.5 kcal/molin liquid NMAa30 The model is crude enough that good agreement is not expected and the only conclusion is that the correction for the heat of hydrogen bonding is of approximately the right magnitude to explain the results. For quantitative predictions, the experimental solubility parameter 6 = 9.3 should be used. At high concentrations of nonpolar solute, the hydrogen-bonded chains will break apart and this will have to be taken into account. Appropriate theories are a ~ a i l a b l e but ~ ~ -there ~ ~ are no data to test them.
Acknowledgment. The authors thank Professor Carl
A. von Frankenberg and Mr. Jonathan P. Hopkins for helpful discussions.
(27) M.Davis and D. K. Thomas, J . Phys. Chem., 60, 767 (1956). (28) I. M. Klotz and J. S. Franzen, J . Amer. Chem. Soc., 84, 3461 (1962). (29) M. Davis in "Hydrogen Bonding," D. Hadzi, Ed., Pergamon Press Inc., New York, N. Y.,1959,p 393. (30) R. Lin and W. Dannhauser, J. Phys. Chem., 67, 1805 (1963). (31) A. V. Tobolsky and P. J. Blatz, J . Chem. Phys., 13, 379 (1945). (32) P. J. Flory, ibid., 14, 49 (1945). (33) 0. Redlick and A. T.Kister, ibid., 15, 849 (1947).
Thermodynamics of Ionization of Deuterium Oxide by Robert N. Goldberg' and Loren G. Hepler2 Department of Chemistry, Carnegie-Mellon University, Pittsburgh, Pennsylvania
(Received July 9, 1968)
Heats of neutralization of HC1 (in HzO) with NaOH (in H20) and of DC1 (in DzO) with NaOD (in DzO)have been measured calorimetrically. Heats of dilution of NaOD (in DzO) have also been measured. Results of these measurements have been combined with other heat of dilution data to yield standard heats of ionization of HzO and DzO at 298°K. The results are AH" = 13,350cal/mol for H20 and AHo = 14,488 cal/mol for D20. This AH" for HzO is in excellent agreement with results of several other calorimetric investigations but is smaller than a value derived from the variation of the ionization constant of HzO with temperature. Our calorimetric AH" for DzO is larger than the value derived from variation of the ionization constant of DzO with temperature. Standard states and concentration scales for aqueous solutions are discussed, followed by calculation of free energies and entropies of ionization of H20 and D2O.
Introduction Just as knowledge of thermodynamics of ionization of HzO is important for many aspects of chemistry involving acids and bases in ordinary water, knowledge of thermodynamics of ionization of D2O is important for this solvent. Since many earlier workers have also shown that comparison of thermodynamics of reactions taking place in HzO with thermodynamics of analogous reactions taking place in DzO can lead to useful information about solutes and the structures of aqueous solutions, it is clear that reliable and directly comparable data for ionization of HzOand DzO should be available. For HzOwe have equilibrium constants for ionization at several temperatures that permit calculation of AGO, AH", and AS" of ionization. Values of AH" derived from calorimetric measurements are also available. For DzOthere are equilibrium constants a t several temperatures but no calorimetric investigation of the enthalpy of ionization. Since there are important disThe Journal of Physical Chemistry
crepancies between the equilibrium and calorimetric data for HzO, we have undertaken the calorimetric investigation of the enthalpy of ionization of DzO that is described in this paper. Results of our measurements are presented along with detailed comparison with enthalpies calculated from equilibrium data of earlier investigators. We also discuss in detail the important question of standard states for solutions in HzO and DzO.
Experimental Section The calorimeter used in this investigation and an earlier investigation of water-triethylamine mixtures3 consisted of a dewar vessel (capacity -300 ml) from Sears and Roebuck. This inexpensive vessel, which (1) This paper is based on part of the Ph.D. Thesis of R. N. Goldberg, Carnegie-Mellon University, 1968. (2) Some of the calculations and writing of this paper have been done at the University of Louisville. (3) G.L. Bertrand, J. W. Larson, and L. G. Hepler, submitted for publication.
