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Apparent molar volumes and apparent molar heat capacities of aqueous solutions ofN,N- dimethylformamide andN,N- dimethylacetamide at temperatures from 278.15 to 393.15 K and at the pressure 0.35 MPa
J. Chem. Thermodynamics 2001, 33, 917–927 doi:10.1006/jcht.2001.0817 Available online at http://www.idealibrary.com on
Apparent molar volumes and apparent molar heat capacities of aqueous solutions of N,N-dimethylformamide and N,N-dimethylacetamide at temperatures from 278.15 to 393.15 K and at the pressure 0.35 MPa M. L. Origlia, B. A. Patterson, and E. M. Woolleya Department of Chemistry and Biochemistry, Brigham Young University, Provo, UT 84602-5700, U.S.A.
Apparent molar heat capacities C p,φ and apparent molar volumes Vφ were determined for aqueous solutions of N ,N -dimethylformamide and N ,N -dimethylacetamide at temperatures from 278.15 to 393.15 K and at the pressure 0.35 MPa. The molalities investigated ranged from 0.015 mol·kg−1 to 1.0 mol · kg−1 . We used a vibrating-tube densimeter (DMA 512P, Anton PAAR, Austria) to determine the densities and volumetric properties. Heat capacities were obtained using a twin fixed-cell, power-compensation, differentialoutput, temperature-scanning calorimeter (NanoDSC 6100, Calorimetry Sciences Corporation, Spanish Fork, UT, U.S.A.). The results were fit by regression to equations that describe the surfaces (Vφ , T, m) and (C p,φ , T, m). Infinite dilution partial molar volumes V2o and heat capacities C op,2 were obtained over the range of temperatures by extrapolation c 2001 Academic Press of these surfaces to m = 0. KEYWORDS: apparent molar volume; apparent molar heat capacity; N ,N -dimethylformamide; N ,N -dimethylacetamide
1. Introduction In this paper, we have focused our attention on aqueous solutions of two nonionic solutes, N ,N -dimethylformamide (DMF) and N ,N -dimethylacetamide (DMA). Both DMF and DMA are used as solvents for many organic reactions and industrial applications. Because of their high polarity and electrical permitivity, they have been used extensively in binary systems with water to examine the enthalpies of solution of different solutes, especially alkali and tetraalkylammonium halides. (1,2) The physical and chemical properties of DMF allow it to be used widely as a solvent in many industrial, electrolytic, and petroleum processes. It is used in the manufacture of resins, polymers, acrylic fibers, and synthetic leathers. Salt solutions of DMF are used in a To whom correspondence should be addressed (E-mail: earl [email protected]).
0021–9614/01/080917 + 11 $35.00/0
c 2001 Academic Press
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M. L. Origlia, B. A. Patterson, and E. M. Woolley
electrolytic capacitors and electroplating baths. DMF, either pure or in solution, is used to extract aromatics from petroleum mixtures, and it also finds uses as a paint stripper and cleaner for machinery, moldings, and gas pipelines. DMA is a high boiling, polar solvent that readily dissolves gases and numerous organic and inorganic substances. It is a colorless liquid and is miscible with water and many common organic solvents. DMA has applications as a polar solvent for the manufacture of films and fibers; as a booster solvent in coating and adhesive formulations; as a reaction medium for the manufacture of pharmaceuticals, agricultural products, wetting agents, and plasticizers; and as a purification and crystallization solvent for aromatic dicarboxylic acids and extraction agent for gases and oils. (3) Our purpose in this work is to investigate the apparent molar volumes Vφ and apparent molar heat capacities C p,φ for DMF and DMA in water from 0.015 mol·kg−1 to 1.0 mol·kg−1 , at temperatures T from 278.15 K to 393.15 K, and at the pressure 0.35 MPa. We have fit by regression the (Vφ , T, m) and (C p,φ , T, m) surfaces, and we have obtained values of V2o and C op,2 by extrapolation to the m = 0 plane. Values of Vφ were calculated from densities obtained using a vibrating-tube densimeter (DMA 512P, Anton PAAR, Austria) at 278.15 < T /K < 368.15. A twin fixed-cell, powercompensation, differential-output, temperature-scanning calorimeter (NanoDSC 6100, Calorimetric Sciences Corp., Spanish Fork, UT, U.S.A.) was used to measure the heat capacities of the solutions at 278.15 < T /K < 393.15 from which values of C p,φ were obtained. (4–6) All experiments were performed at the pressure 0.35 MPa.
2. Experimental The DMF (Spectrum Quality Products, Inc., Gardena, CA, U.S.A., lot NG0090, 0.999 mass fraction, molar mass = 73.09 g · mol−1 ) and the DMA (Sigma-Aldrich, St Louis, MO, U.S.A., lot BU 12545MS, 0.999 mass fraction, molar mass = 87.12 g · mol−1 ) were used as received. The purity of the DMA and DMF were found by NMR spectroscopy (INOVA 500, Varian Inc., Palo Alto, CA, U.S.A.) to be 0.9994 mole fraction (mole fraction of total H due to DMA and DMF). Thus, we have used the 0.999 mass fraction from the manufacturers in our calculations of solution compositions. All solutions were made by mass, and buoyancy corrections were applied. We assumed that the only impurity in the solutes was water. Water used to prepare all solutions was distilled, deionized, autoclaved, and then degassed. The densimeter was thermostatted with a temperature controller–circulator (PolyScience 9510, Niles, IL, U.S.A.) which was programmed to be isothermal at each of several temperatures as described previously. (6) The period of vibration τ and temperature of the densimeter cell were recorded for at least 800 s while the period was stable. The pressure inside the densimeter cell was monitored and controlled with a pressure transducer (PX120-100GV, Omega Engineering, Stamford, CT, U.S.A.). With this system, the temperature of the densimeter was controlled within an average standard deviation of 0.0022 K, with a maximum deviation of ±0.004 K at all temperatures studied, and the pressure was controlled within ±0.001 MPa. For all solutions investigated and at all
Thermodynamics of N ,N -dimethylformamide and N ,N -dimethylacetamide
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temperatures, the period of vibration τ of about 4 ms had an average standard deviation of 0.7 ns and a maximum standard deviation of 2 ns. Densities were calculated by equation (1): ρs = ρw + {kρ · (τs2 − τw2 )}.
(1)
In equation (1), ρs is the density of the solution; ρw is the density of water; τs and τw are the periods of vibration of the vibrating tube when it contains the solution of interest and when it contains water, respectively; and kρ is the temperature- and pressure-dependent calibration constant. The values of kρ were determined from measurements at the same temperatures and pressure with water (7) and 1.0 mol · kg−1 NaCl(aq). (8) Measurements with water were repeated every few days to determine and compensate for possible drift in the cell characteristics and to verify the reproducibility of measurements. The values of τ were determined for rounded temperatures as described previously. (6) Densities of the solutions obtained with this system were reproducible to within ±7 µg·cm−3 for both compounds at all T and m. The calorimeter was calibrated and used as described previously. (4–6) Measurements were recorded at a scan rate r of 16.6667 mK · s−1 for both heating and cooling at 273.15 < T /K < 398.15 and at the pressure p = 0.350 ± 0.015 MPa. Data were collected for at least 4 scans up and 4 scans down for each solution. The massic heat capacity is given by equation (2): c p,s = {kc · (1Ps − 1Pw )/(r · ρs )} + (c p,w · ρw /ρs ).
(2)
In equation (2), c p,s and c p,w are the massic heat capacities of the solution of interest and of water, respectively; 1Ps is the difference in power applied to the heaters on the two calorimetric cells to maintain them at the same temperature when the reference cell contains water and the sample cell contains the solution of interest; and 1Pw is that same (very small) difference in power when both cells contain water. In equation (2), kc is the temperature- and pressure-dependent calibration constant of the calorimeter which was obtained from measurements with water (7) and 1.0 mol · kg−1 NaCl. (8) Experiments with water were performed every few days in order to account for small changes in the baseline signal of the calorimeter. Apparent molar volumes and heat capacities of DMF(aq) and DMA(aq) were obtained by equations (3) and (4): Vφ = (M2 /ρs ) − {1000 · (ρs − ρw )/(ρs · ρw · m)}, C p,φ = (M2 · c p,s ) + {1000 · (c p,s − c p,w )/m}.
(3) (4)
In equations (3) and (4), M2 is the molar mass of the solute and m is the molality of the solute in the solution.
3. Results and discussion Apparent molar volumes Vφ for DMF(aq) and DMA(aq) are given in tables 1 and 2. Figures 1 and 2 show these (Vφ , m, T ) results for the two solutes, where the regressed
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TABLE 1. Apparent molar volumes Vφ for DMF(aq) at p = 0.35 MPa. The ± uncertainties are standard deviations from 20 or more consecutive readings of the vibration period during at least 800 s m mol · kg−1
Vφ /(cm3 · mol−1 ) T = 278.15 K
T = 288.15 K
T = 298.15 K
T = 308.15 K
T = 318.15 K
0.0148
76.34 ± 0.18
76.48 ± 0.17
76.83 ± 0.16
76.28 ± 0.17
76.67 ± 0.28
0.0301
74.54 ± 0.09
74.31 ± 0.08
74.42 ± 0.07
74.97 ± 0.09
74.89 ± 0.09
0.0603
73.51 ± 0.05
74.39 ± 0.05
74.93 ± 0.04
75.63 ± 0.05
75.87 ± 0.08
0.1002
72.68 ± 0.03
73.59 ± 0.02
74.33 ± 0.03
75.17 ± 0.02
75.95 ± 0.07
0.2008
72.88 ± 0.01
73.65 ± 0.01
74.31 ± 0.01
75.23 ± 0.01
75.99 ± 0.01
0.4012
72.69 ± 0.007
73.56 ± 0.005
74.31 ± 0.007
75.10 ± 0.006
75.87 ± 0.007
0.7019
72.49 ± 0.003
73.39 ± 0.004
74.19 ± 0.004
75.00 ± 0.005
75.79 ± 0.004
1.0045
72.33 ± 0.002
73.26 ± 0.003
74.09 ± 0.003
74.91 ± 0.002
75.75 ± 0.005
T = 328.15 K
T = 338.15 K
T = 348.15 K
T = 358.15 K
T = 368.15 K
0.0148
77.11 ± 0.17
78.67 ± 0.18
78.42 ± 0.21
80.44 ± 0.22
80.03 ± 0.19
0.0301
76.28 ± 0.08
77.33 ± 0.07
78.13 ± 0.10
78.77 ± 0.10
79.60 ± 0.10
0.0603
77.19 ± 0.05
77.81 ± 0.04
78.24 ± 0.05
79.24 ± 0.05
80.09 ± 0.04
0.1002
76.64 ± 0.03
77.62 ± 0.03
78.20 ± 0.03
79.16 ± 0.03
80.09 ± 0.04
0.2008
76.74 ± 0.01
77.48 ± 0.01
78.38 ± 0.01
79.31 ± 0.01
80.35 ± 0.02
0.4012
76.64 ± 0.008
77.47 ± 0.007
78.36 ± 0.007
79.26 ± 0.007
80.26 ± 0.01
0.7019
76.58 ± 0.003
77.44 ± 0.004
78.30 ± 0.004
79.25 ± 0.004
80.25 ± 0.004
1.0045
76.52 ± 0.003
77.38 ± 0.002
78.27 ± 0.003
79.25 ± 0.003
80.25 ± 0.003
Average experimental values of ρs can be obtained with equation (3) and with ρw given in reference 12.
surfaces are for the empirical function given in equation (5): Vφ = v0 + (v1 · T 2 ) + (v2 · m).
(5)
The regression was performed with weighting factors equal to the reciprocal of the estimated uncertainties in Vφ from tables 1 and 2. The regression parameters vi for equation (5) are given in table 3. The largest deviations from the regression surfaces occur at the lowest m where the uncertainty in Vφ is greatest, corresponding to the smallest differences between ρ s and ρ w . Our Vφ results show a significant dependence on T for both amides, with (∂ Vφ /∂ T ) p ∼ 0.09 cm3 · mol−1 · K−1 . A small negative dependence of Vφ on m is evident. The magnitude of the dependence of Vφ on m and T is only slightly larger for DMA(aq) than it is for DMF(aq). This could be the result of the larger surface area of exposed hydrophobic moiety being exposed to the aqueous environment in for DMA. The DMF(aq) and DMA(aq) regression surfaces show the same trends, with a nearly constant difference between them at all T and m. The difference [Vφ {DMA(aq)}–{Vφ {DMF(aq)}] = (15.25 ± 1.0) cm3 · mol−1 is consistent with that expected for the -CH2 - functional group at T = 298.15 K and p = 0.1 MPa. (9)
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TABLE 2. Apparent molar volumes Vφ for DMA(aq) at p = 0.35 MPa. The ± uncertainties are standard deviations from 20 or more consecutive readings of the vibration period during at least 800 s m mol · kg−1
Vφ /(cm3 · mol−1 ) T = 278.15 K
T = 288.15 K
T = 298.15 K
T = 308.15 K
T = 318.15 K
0.0151
87.19 ± 0.19
88.95 ± 0.14
88.02 ± 0.19
89.63 ± 0.13
92.57 ± 0.39
0.0307
89.42 ± 0.09
89.15 ± 0.07
89.58 ± 0.10
90.31 ± 0.09
92.03 ± 0.12
0.0604
89.02 ± 0.04
89.43 ± 0.05
89.97 ± 0.03
90.49 ± 0.04
90.94 ± 0.04
0.0987
88.93 ± 0.03
89.30 ± 0.02
89.84 ± 0.03
90.34 ± 0.02
90.82 ± 0.03
0.2009
87.94 ± 0.02
88.69 ± 0.01
89.46 ± 0.01
90.18 ± 0.01
91.23 ± 0.02
0.4008
87.65 ± 0.006
88.51 ± 0.006
89.32 ± 0.005
90.11 ± 0.007
90.99 ± 0.007
0.6999
87.19 ± 0.003
88.07 ± 0.003
88.96 ± 0.003
89.82 ± 0.005
90.70 ± 0.004
1.0010
86.91 ± 0.002
87.84 ± 0.002
88.76 ± 0.003
89.65 ± 0.003
90.55 ± 0.003
T = 328.15 K
T = 338.15 K
T = 348.15 K
T = 358.15 K
T = 368.15 K
0.0151
91.27 ± 0.15
91.99 ± 0.18
92.71 ± 0.20
94.49 ± 0.20
94.49 ± 0.29
0.0307
91.80 ± 0.10
91.71 ± 0.08
93.06 ± 0.09
94.14 ± 0.09
95.39 ± 0.12
0.0604
92.40 ± 0.04
92.69 ± 0.04
93.59 ± 0.06
94.60 ± 0.06
95.41 ± 0.05
0.0987
91.53 ± 0.03
92.38 ± 0.03
93.21 ± 0.02
94.20 ± 0.03
95.11 ± 0.03
0.2009
92.05 ± 0.01
92.75 ± 0.01
93.66 ± 0.01
94.70 ± 0.01
95.70 ± 0.01
0.4008
91.86 ± 0.006
92.81 ± 0.006
93.71 ± 0.007
94.74 ± 0.006
95.91 ± 0.009
0.6999
91.64 ± 0.005
92.58 ± 0.003
93.60 ± 0.004
94.68 ± 0.004
95.87 ± 0.003
1.0010
91.51 ± 0.002
92.49 ± 0.002
93.54 ± 0.003
94.63 ± 0.003
95.81 ± 0.003
Average experimental values of ρs can be obtained with equation (3) and with ρw given in reference 12.
Values of C p,φ for DMF(aq) and DMA(aq) are given in tables 4 and 5. Figures 3 and 4 show the results for each solute and the regression surfaces obtained by equation (6): C p,φ = c0 + (c1 · T ) + (c2 · T 2 ) + {c3 + c4 /(T − 270)} · m.
(6)
The regressions used weighting factors equal to the reciprocal of the estimated uncertainties in C p,φ from tables 4 and 5. The regression parameters for equation (6) are given in table 6. As was noted with the regressions for Vφ using equation (5), the largest deviations from the regression surfaces using equation (6) occur at the lowest m where the uncertainty in C p,φ is greatest, corresponding to the smallest differences between c p,s and c p,w . The C p,φ and C op,2 values for both the amides are large and positive, and they increase with increasing temperature. The increase in C p,φ and C op,2 with temperature is approximately linear, with (∂C p,φ /∂ T ) p ∼ 0.5 J · K−2 · mol−1 . Our regression surfaces for both Vφ and C p,φ show parallel behavior. The large and positive values of C p,φ and C op,2 for aqueous DMF and DMA are undoubtedly related to the formation of an ordered water structure (“icebergs”) around these molecules. As
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M. L. Origlia, B. A. Patterson, and E. M. Woolley
82
–1 3 Vφ /(cm . mol )
80 78 76 74 380 360
72 1.0 0.6 m/(m ol . k 0.4 g –1 )
320
T/ K
340
0.8 300 0.2
280 0.0
FIGURE 1. Apparent molar volumes Vφ for DMF(aq) at p = 0.35 MPa plotted against temperature and molality. , Experimental values from table 1; , reference 9, T = 298.15 K, p = 0.1 MPa. The surface was generated from regression parameters in table 3 with equation (5).
◦
TABLE 3. Regression parameters of equation (5) for the apparent molar volumes Vφ of aqueous DMF and DMA. The ± values for each parameter are chosen to reproduce the generated Vφ values to within ±0.01 cm3 · mol−1 at m 6 1.0 mol · kg−1 and at 278.15 6 T /K 6 393.15 Parameter
DMF(aq)
DMA(aq)
ν0 /(cm3 · mol−1 )
62.894 ± 0.006
76.722 ± 0.006
104 · ν1 /(cm3 · mol−1 · K−2 )
1.2974 ± 0.0004
1.4326 ± 0.0004
ν2 /(cm3 · mol−2 · kg)
−0.386 ± 0.006
−0.665 ± 0.006
1a /(cm3 · mol−1 )
0.74
0.61
a Standard deviations from the regression.
was the case with the Vφ , the DMF(aq) and DMA(aq) regression surfaces for C p,φ show the same general trends, with a nearly constant difference between them at all T and m. The magnitude of the dependence of C p,φ on m is only slightly larger for DMA(aq)
Thermodynamics of N ,N -dimethylformamide and N ,N -dimethylacetamide
923
TABLE 4. Apparent molar heat capacities C p,φ for DMF(aq) at p = 0.35 MPa. The ± uncertainties are standard deviations for the average values obtained from a total of at least 8 total scans at both increasing and decreasing T m mol · kg−1
C p,φ /(J · K−1 · mol−1 ) T = 278.15 K T = 283.15 K T = 288.15 K T = 293.15 K T = 298.15 K T = 303.15 K
0.0148 0.0301 0.0603 0.1002 0.2008 0.4012 0.7019 1.0045
207.4 ± 10.0 208.4 ± 6.8 209.3 ± 2.9 208.3 ± 1.2 211.1 ± 1.0 204.4 ± 0.8 201.2 ± 0.7 198.3 ± 0.5
213.4 ± 9.4 214.1 ± 6.5 214.8 ± 2.8 214.0 ± 1.1 216.8 ± 0.9 210.7 ± 0.7 208.0 ± 0.6 205.4 ± 0.5
218.0 ± 9.2 218.7 ± 6.5 219.4 ± 2.7 218.7 ± 1.1 221.5 ± 0.8 215.8 ± 0.7 213.5 ± 0.6 211.2 ± 0.4
222.4 ± 9.9 222.8 ± 6.6 223.3 ± 2.7 222.8 ± 1.0 225.6 ± 0.9 220.3 ± 0.7 218.2 ± 0.6 216.2 ± 0.4
225.7 ± 10.1 226.1 ± 6.6 226.8 ± 2.6 226.4 ± 0.9 229.2 ± 0.8 224.2 ± 0.7 222.3 ± 0.6 220.5 ± 0.5
229.6 ± 9.5 229.8 ± 6.5 230.2 ± 2.6 229.8 ± 0.9 232.6 ± 0.8 227.8 ± 0.7 226.1 ± 0.6 224.4 ± 0.5
T = 308.15 K T = 313.15 K T = 318.15 K T = 323.15 K T = 328.15 K T = 333.15 K 0.0148 0.0301 0.0603 0.1002 0.2008 0.4012 0.7019 1.0045
232.8 ± 9.6 233.1 ± 5.9 233.2 ± 2.7 233.0 ± 0.9 235.7 ± 0.8 231.1 ± 0.7 229.5 ± 0.6 227.9 ± 0.5
235.8 ± 10.2 236.1 ± 6.8 236.2 ± 2.8 236.1 ± 0.9 238.7 ± 0.8 234.2 ± 0.7 232.7 ± 0.6 231.2 ± 0.6
238.9 ± 10.4 238.9 ± 6.9 239.0 ± 3.0 238.9 ± 1.0 241.4 ± 0.8 237.1 ± 0.7 235.7 ± 0.7 234.2 ± 0.6
241.7 ± 10.4 241.6 ± 6.9 241.7 ± 3.0 241.7 ± 1.0 244.1 ± 0.8 239.9 ± 0.7 238.5 ± 0.7 237.0 ± 0.6
245.1 ± 10.4 244.5 ± 6.8 244.5 ± 3.2 244.4 ± 1.0 246.7 ± 0.8 242.5 ± 0.7 241.2 ± 0.7 239.7 ± 0.7
248.2 ± 10.7 247.3 ± 6.8 247.3 ± 3.3 247.0 ± 1.1 249.3 ± 0.8 245.2 ± 0.7 243.8 ± 0.8 242.4 ± 0.8
T = 338.15 K T = 343.15 K T = 348.15 K T = 353.15 K T = 358.15 K T = 363.15 K 0.0148 0.0301 0.0603 0.1002 0.2008 0.4012 0.7019 1.0045
250.9 ± 10.8 249.9 ± 6.7 249.9 ± 3.4 249.6 ± 1.2 251.8 ± 0.8 247.7 ± 0.8 246.3 ± 0.8 244.9 ± 0.8
253.8 ± 11.1 252.2 ± 6.5 252.4 ± 3.5 252.0 ± 1.3 254.1 ± 0.8 250.0 ± 0.8 248.6 ± 0.8 247.2 ± 0.9
256.3 ± 11.4 254.5 ± 6.4 254.7 ± 3.7 254.3 ± 1.5 256.4 ± 0.7 252.3 ± 0.7 250.9 ± 0.9 249.4 ± 0.9
259.3 ± 12.0 257.2 ± 6.2 257.3 ± 3.7 256.6 ± 1.8 258.6 ± 0.7 254.6 ± 0.7 253.1 ± 0.9 251.6 ± 1.0
262.0 ± 12.7 259.8 ± 6.4 259.5 ± 3.9 258.9 ± 2.1 260.7 ± 0.8 256.7 ± 0.7 255.2 ± 0.9 253.7 ± 1.0
263.8 ± 13.9 262.0 ± 6.8 261.6 ± 4.2 261.0 ± 2.6 262.8 ± 0.9 258.7 ± 0.7 257.2 ± 0.9 255.7 ± 1.0
T = 368.15 K T = 373.15 K T = 378.15 K T = 383.15 K T = 388.15 K T = 393.15 K 0.0148 0.0301 0.0603 0.1002 0.2008 0.4012 0.7019 1.0045
266.4 ± 15.3 264.2 ± 7.8 263.6 ± 4.6 263.0 ± 3.3 264.7 ± 1.1 260.7 ± 0.7 259.1 ± 0.9 257.5 ± 1.0
268.1 ± 17.8 266.4 ± 9.8 265.6 ± 5.5 265.0 ± 4.2 266.5 ± 1.5 262.5 ± 0.7 261.0 ± 0.9 259.3 ± 1.0
270.7 ± 21.4 268.7 ± 13.2 267.4 ± 6.8 266.7 ± 5.5 268.2 ± 2.2 264.2 ± 1.0 262.6 ± 0.8 260.9 ± 1.0
273.1 ± 25.6 271.2 ± 17.6 269.4 ± 8.6 268.4 ± 7.2 269.8 ± 3.2 265.8 ± 1.4 264.3 ± 0.7 262.6 ± 0.9
274.4 ± 30.9 273.8 ± 23.4 271.1 ± 11.1 270.0 ± 9.3 271.3 ± 4.4 267.3 ± 2.1 265.9 ± 0.5 264.1 ± 0.7
277.3 ± 38.7 277.3 ± 31.3 272.8 ± 14.4 271.6 ± 11.8 273.0 ± 5.4 268.8 ± 3.3 267.5 ± 0.8 265.7 ± 0.5
Average experimental values of c p,s can be obtained with equation (4) and with c p,w given in reference 12.
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M. L. Origlia, B. A. Patterson, and E. M. Woolley
TABLE 5. Apparent molar heat capacities C p,φ for DMA(aq) at p = 0.35 MPa. The ± uncertainties are standard deviations for the average values obtained from a total of at least 8 total scans at both increasing and decreasing T m mol · kg−1
C p,φ /(J · K−1 · mol−1 ) T = 278.15 K T = 283.15 K T = 288.15 K T = 293.15 K T = 298.15 K T = 303.15 K
0.0151 0.0307 0.0604 0.0987 0.2009 0.4008 0.6999 1.0010
277.7 ± 12.6 279.8 ± 5.9 281.0 ± 1.4 280.8 ± 2.0 278.8 ± 0.6 275.3 ± 0.2 268.4 ± 0.1 263.0 ± 0.1
281.4 ± 12.3 284.0 ± 5.7 284.9 ± 1.5 285.0 ± 2.1 283.4 ± 0.7 280.6 ± 0.1 274.7 ± 0.1 269.9 ± 0.06
284.9 ± 11.9 287.4 ± 5.5 288.5 ± 1.6 288.6 ± 2.1 287.3 ± 0.8 285.0 ± 0.2 279.8 ± 0.1 275.6 ± 0.07
288.1 ± 11.9 290.3 ± 5.4 291.8 ± 1.5 291.9 ± 2.0 290.9 ± 0.8 288.9 ± 0.2 284.2 ± 0.1 280.6 ± 0.05
290.9 ± 11.9 293.3 ± 5.3 294.8 ± 1.5 295.1 ± 2.0 294.2 ± 0.7 292.5 ± 0.2 288.2 ± 0.1 284.9 ± 0.06
293.7 ± 11.4 295.8 ± 4.9 297.7 ± 1.5 298.1 ± 1.9 297.4 ± 0.7 295.8 ± 0.2 291.9 ± 0.2 288.9 ± 0.1
T = 308.15 K T = 313.15 K T = 318.15 K T = 323.15 K T = 328.15 K T = 333.15 K 0.0151 0.0307 0.0604 0.0987 0.2009 0.4008 0.6999 1.0010
296.8 ± 10.6 298.7 ± 4.6 300.6 ± 1.5 301.1 ± 1.8 300.4 ± 0.6 299.1 ± 0.2 295.4 ± 0.1 292.5 ± 0.1
299.2 ± 11.5 301.5 ± 5.1 303.6 ± 1.6 304.0 ± 1.8 303.5 ± 0.6 302.2 ± 0.2 298.7 ± 0.2 295.9 ± 0.2
301.8 ± 11.6 303.8 ± 5.2 306.4 ± 1.6 306.8 ± 1.8 306.3 ± 0.6 305.0 ± 0.2 301.6 ± 0.3 299.0 ± 0.2
304.2 ± 12.2 306.7 ± 5.1 309.1 ± 1.6 309.5 ± 1.8 309.1 ± 0.6 307.9 ± 0.3 304.5 ± 0.3 302.0 ± 0.3
306.9 ± 12.5 309.3 ± 5.1 311.8 ± 1.6 312.3 ± 1.8 311.8 ± 0.6 310.6 ± 0.4 307.3 ± 0.4 304.8 ± 0.4
309.7 ± 13.0 312.3 ± 5.2 314.5 ± 1.7 315.0 ± 1.7 314.5 ± 0.6 313.2 ± 0.5 310.0 ± 0.5 307.5 ± 0.4
T = 338.15 K T = 343.15 K T = 348.15 K T = 353.15 K T = 358.15 K T = 363.15 K 0.0151 0.0307 0.0604 0.0987 0.2009 0.4008 0.6999 1.0010
312.4 ± 13.4 315.1 ± 5.3 317.1 ± 1.9 317.6 ± 1.7 317.1 ± 0.6 315.8 ± 0.6 312.6 ± 0.6 310.1 ± 0.5
315.0 ± 14.1 317.4 ± 5.5 319.6 ± 2.0 320.1 ± 1.7 319.5 ± 0.6 318.2 ± 0.6 315.0 ± 0.6 312.5 ± 0.5
317.4 ± 14.8 320.2 ± 5.7 322.0 ± 2.2 322.4 ± 1.8 321.8 ± 0.6 320.5 ± 0.6 317.3 ± 0.7 314.7 ± 0.6
319.7 ± 15.3 322.5 ± 6.0 324.2 ± 2.3 324.8 ± 1.9 324.1 ± 0.6 322.7 ± 0.7 319.5 ± 0.7 316.9 ± 0.7
321.7 ± 15.7 324.8 ± 6.3 326.3 ± 2.6 327.0 ± 1.9 326.3 ± 0.7 324.9 ± 0.8 321.6 ± 0.8 319.0 ± 0.7
323.9 ± 16.1 327.1 ± 6.4 328.4 ± 2.8 329.0 ± 2.1 328.3 ± 0.8 326.8 ± 0.8 323.5 ± 0.9 320.9 ± 0.8
T = 368.15 K T = 373.15 K T = 378.15 K T = 383.15 K T = 388.15 K T = 393.15 K 0.0151 0.0307 0.0604 0.0987 0.2009 0.4008 0.6999 1.0010
326.0 ± 16.7 328.9 ± 6.5 330.4 ± 2.9 330.9 ± 2.1 330.2 ± 0.9 328.7 ± 0.9 325.3 ± 0.9 322.7 ± 0.9
328.2 ± 17.7 331.0 ± 6.9 332.2 ± 3.0 332.7 ± 2.2 332.0 ± 0.9 330.4 ± 1.0 327.1 ± 1.0 324.4 ± 1.0
329.2 ± 18.6 332.3 ± 7.2 333.6 ± 3.2 334.4 ± 2.2 333.6 ± 1.0 332.0 ± 1.0 328.6 ± 1.0 325.8 ± 1.0
329.8 ± 20.1 333.8 ± 7.4 335.0 ± 3.5 336.1 ± 2.2 335.2 ± 1.1 333.6 ± 1.1 330.1 ± 1.1 327.3 ± 1.1
331.4 ± 20.1 335.3 ± 7.7 336.4 ± 3.8 337.6 ± 2.2 336.6 ± 1.1 335.0 ± 1.1 331.5 ± 1.1 328.7 ± 1.2
332.2 ± 19.9 336.1 ± 8.2 338.0 ± 4.5 339.3 ± 2.3 338.2 ± 1.0 336.5 ± 0.8 333.0 ± 0.8 330.1 ± 1.0
Average experimental values of c p,s can be obtained with equation (4) and with c p,w given in reference 12.
Thermodynamics of N ,N -dimethylformamide and N ,N -dimethylacetamide
925
99
Vφ /(cm3 . mol – 1)
96
93
90
87 380
1.0
360
0.8
340
0.6 m/( mo l .k
320
0.4
g
–1
)
300
0.2 0.0
T/
K
280
FIGURE 2. Apparent molar volumes Vφ for DMA(aq) at p = 0.35 MPa plotted against temperature and molality. , Experimental values from table 2; , reference 9, T = 298.15 K, p = 0.1 MPa; H, reference 10, T = 298.15 K, p = 0.1 MPa; N, reference 11, T = 298.15 K, p = 0.1 MPa. The surface was generated from regression parameters in table 3 with equation (5).
◦
than it is for DMF(aq), but there is no statistically significant difference between the dependence of C p,φ on T for DMA(aq) and DMF(aq). The difference [C p,φ {DMA(aq)}– C p,φ {DMF(aq)}] = (67.4 ± 2.6 ) J · K−1 · mol−1 is consistent with that expected for the -CH2 - functional group at T = 298.15 K and p = 0.1 MPa. (9) The V2o and C op,2 values obtained in this investigation are in good agreement with values reported in the literature. Values of V2o reported by Cabani et al. (9) at T = 298.15 K and p = 0.10 MPa differ from ours by 0.07 cm3 · mol−1 and −1.05 cm3 · mol−1 for DMF(aq) and DMA(aq), respectively. Values of V2o , reported by Assarsson and Eirich (10) and by De Visser et al. (11) for DMA(aq) at T = 298.15 K and p = 0.10 MPa differ from those of this study by 0.56 cm3 · mol−1 and by −0.19 cm3 · mol−1 , respectively. The value of C op,2 given by Cabani et al. (9) for DMF(aq) at T = 298.15 K and p = 0.10 MPa differs by 2.6 J · K−1 · mol−1 from our results. All these differences are within the total uncertainties we expect, given the standard deviations in tables 1 to 6.
926
M. L. Origlia, B. A. Patterson, and E. M. Woolley
270
1 mol – )
240
Cp,φ/(J . K
250
–1
260
230 220 210 380 200
360
1.0 0.6 m/(m 0.4 ol . k g –1 )
320
T/
0.8
K
340
300 0.2
280 0.0
FIGURE 3. Apparent molar heat capacity C p,φ for DMF(aq) at p = 0.35 MPa plotted against temperature and molality. , Experimental values from table 4; , reference 9, T = 298.15 K, p = 0.1 MPa. The surface was generated from regression parameters in table 6 with equation (6).
◦
TABLE 6. Regression parameters of equation (6) for the apparent molar heat capacities C p,φ of aqueous DMF and DMA. The ± values for each parameter are chosen to reproduce the generated C p,φ to within ±0.1 J · K−1 · mol−1 at m 6 1.0 mol · kg−1 and at 278.15 6 T /K 6 393.15. Parameter c0 /(J · K−1 · mol−1 ) c1 /(J · K−2 · mol−1 ) 104 · c2 /(J · K−3 · mol−1 ) c3 /(J · K−1 · mol−2 · kg) c4 /(J · kg · mol−2 ) 1a /(J · K−1 · mol−1 )
DMF(aq) −196.30 ± 0.04 2.1544 ± 0.0001 −24.556 ± 0.002 −5.20 ± 0.04 −80.8 ± 0.3 1.6
a Standard deviations from the regression.
DMA(aq) −82.50 ± 0.04 1.8913 ± 0.0001 −20.828 ± 0.002 −7.57 ± 0.04 −103.2 ± 0.3 2.1
Thermodynamics of N ,N -dimethylformamide and N ,N -dimethylacetamide
927
Cp,φ/(J . K
–1
1 mol – )
330
315
300
285 380 360
270 320
0.8 0.6 m/(m ol . k
300
0.4
g – 1)
T/K
340 1.0
0.2
280 0.0
FIGURE 4. Apparent molar heat capacity C p,φ for DMA(aq) at p = 0.35 MPa plotted against temperature and molality m. , Experimental values from table 5. The surface was generated from regression parameters in table 6 with equation (6).
◦
REFERENCES 1. De Visser, C.; Somsen, G. J. Chem. Thermodynamics 1972, 4, 313–319. 2. De Visser, C.; Somsen, G. J. Solution Chem. 1974, 3, 847–854. 3. Eberling, E. L. Kirk-Othmer Encyclopedia of Chemical Technology: 3rd edition, Vol. 11. Grayson, M.: editor. John Wiley and Sons: New York. 1980, 263–267. 4. Woolley, E. M. J. Chem. Thermodynamics 1997, 29, 1377–1385. 5. Ballerat-Busserolles, K.; Origlia, M. L.; Woolley, E. M. Thermochimica Acta 2000, 347, 3–7. 6. Ballerat-Busserolles, K.; Ford, T. D.; Call, T. G.; Woolley, E. M. J. Chem. Thermodynamics 1999, 31, 741–762. 7. Hill, P. G. J. Phys. Chem. Ref. Data 1990, 19, 1233–1274. 8. Archer, D. G. J. Phys. Chem. Ref. Data 1992, 21, 793–829. 9. Cabani, S.; Gianni, P.; Mollica, V.; Lepori, L. J. Solution Chem. 1981, 10, 563–595. 10. Assarsson, P.; Eirich, F. R. J. Phys. Chem. 1968, 72, 2710–2719. 11. De Visser, C.; Heuvelsland, W. J. M.; Dunn, L. A.; Somsen, G. J. Chem. Soc. Faraday Trans. I 1978, 74, 1159–1169. 12. Ford, T. D.; Call, T. G.; Origlia, M. L.; Stark, M. A.; Woolley, E. M. J. Chem. Thermodynamics 2000, 32, 499–516. (Received 27 September 2000; in final form 2 January 2001)
WE-266
Apparent molar volumes and apparent molar heat capacities of aqueous solutions of N,N-dimethylformamide and N,N-dimethylacetamide at temperatures from 278.15 to 393.15 K and at the pressure 0.35 MPa M. L. Origlia, B. A. Patterson, and E. M. Woolleya Department of Chemistry and Biochemistry, Brigham Young University, Provo, UT 84602-5700, U.S.A.
Apparent molar heat capacities C p,φ and apparent molar volumes Vφ were determined for aqueous solutions of N ,N -dimethylformamide and N ,N -dimethylacetamide at temperatures from 278.15 to 393.15 K and at the pressure 0.35 MPa. The molalities investigated ranged from 0.015 mol·kg−1 to 1.0 mol · kg−1 . We used a vibrating-tube densimeter (DMA 512P, Anton PAAR, Austria) to determine the densities and volumetric properties. Heat capacities were obtained using a twin fixed-cell, power-compensation, differentialoutput, temperature-scanning calorimeter (NanoDSC 6100, Calorimetry Sciences Corporation, Spanish Fork, UT, U.S.A.). The results were fit by regression to equations that describe the surfaces (Vφ , T, m) and (C p,φ , T, m). Infinite dilution partial molar volumes V2o and heat capacities C op,2 were obtained over the range of temperatures by extrapolation c 2001 Academic Press of these surfaces to m = 0. KEYWORDS: apparent molar volume; apparent molar heat capacity; N ,N -dimethylformamide; N ,N -dimethylacetamide
1. Introduction In this paper, we have focused our attention on aqueous solutions of two nonionic solutes, N ,N -dimethylformamide (DMF) and N ,N -dimethylacetamide (DMA). Both DMF and DMA are used as solvents for many organic reactions and industrial applications. Because of their high polarity and electrical permitivity, they have been used extensively in binary systems with water to examine the enthalpies of solution of different solutes, especially alkali and tetraalkylammonium halides. (1,2) The physical and chemical properties of DMF allow it to be used widely as a solvent in many industrial, electrolytic, and petroleum processes. It is used in the manufacture of resins, polymers, acrylic fibers, and synthetic leathers. Salt solutions of DMF are used in a To whom correspondence should be addressed (E-mail: earl [email protected]).
0021–9614/01/080917 + 11 $35.00/0
c 2001 Academic Press
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M. L. Origlia, B. A. Patterson, and E. M. Woolley
electrolytic capacitors and electroplating baths. DMF, either pure or in solution, is used to extract aromatics from petroleum mixtures, and it also finds uses as a paint stripper and cleaner for machinery, moldings, and gas pipelines. DMA is a high boiling, polar solvent that readily dissolves gases and numerous organic and inorganic substances. It is a colorless liquid and is miscible with water and many common organic solvents. DMA has applications as a polar solvent for the manufacture of films and fibers; as a booster solvent in coating and adhesive formulations; as a reaction medium for the manufacture of pharmaceuticals, agricultural products, wetting agents, and plasticizers; and as a purification and crystallization solvent for aromatic dicarboxylic acids and extraction agent for gases and oils. (3) Our purpose in this work is to investigate the apparent molar volumes Vφ and apparent molar heat capacities C p,φ for DMF and DMA in water from 0.015 mol·kg−1 to 1.0 mol·kg−1 , at temperatures T from 278.15 K to 393.15 K, and at the pressure 0.35 MPa. We have fit by regression the (Vφ , T, m) and (C p,φ , T, m) surfaces, and we have obtained values of V2o and C op,2 by extrapolation to the m = 0 plane. Values of Vφ were calculated from densities obtained using a vibrating-tube densimeter (DMA 512P, Anton PAAR, Austria) at 278.15 < T /K < 368.15. A twin fixed-cell, powercompensation, differential-output, temperature-scanning calorimeter (NanoDSC 6100, Calorimetric Sciences Corp., Spanish Fork, UT, U.S.A.) was used to measure the heat capacities of the solutions at 278.15 < T /K < 393.15 from which values of C p,φ were obtained. (4–6) All experiments were performed at the pressure 0.35 MPa.
2. Experimental The DMF (Spectrum Quality Products, Inc., Gardena, CA, U.S.A., lot NG0090, 0.999 mass fraction, molar mass = 73.09 g · mol−1 ) and the DMA (Sigma-Aldrich, St Louis, MO, U.S.A., lot BU 12545MS, 0.999 mass fraction, molar mass = 87.12 g · mol−1 ) were used as received. The purity of the DMA and DMF were found by NMR spectroscopy (INOVA 500, Varian Inc., Palo Alto, CA, U.S.A.) to be 0.9994 mole fraction (mole fraction of total H due to DMA and DMF). Thus, we have used the 0.999 mass fraction from the manufacturers in our calculations of solution compositions. All solutions were made by mass, and buoyancy corrections were applied. We assumed that the only impurity in the solutes was water. Water used to prepare all solutions was distilled, deionized, autoclaved, and then degassed. The densimeter was thermostatted with a temperature controller–circulator (PolyScience 9510, Niles, IL, U.S.A.) which was programmed to be isothermal at each of several temperatures as described previously. (6) The period of vibration τ and temperature of the densimeter cell were recorded for at least 800 s while the period was stable. The pressure inside the densimeter cell was monitored and controlled with a pressure transducer (PX120-100GV, Omega Engineering, Stamford, CT, U.S.A.). With this system, the temperature of the densimeter was controlled within an average standard deviation of 0.0022 K, with a maximum deviation of ±0.004 K at all temperatures studied, and the pressure was controlled within ±0.001 MPa. For all solutions investigated and at all
Thermodynamics of N ,N -dimethylformamide and N ,N -dimethylacetamide
919
temperatures, the period of vibration τ of about 4 ms had an average standard deviation of 0.7 ns and a maximum standard deviation of 2 ns. Densities were calculated by equation (1): ρs = ρw + {kρ · (τs2 − τw2 )}.
(1)
In equation (1), ρs is the density of the solution; ρw is the density of water; τs and τw are the periods of vibration of the vibrating tube when it contains the solution of interest and when it contains water, respectively; and kρ is the temperature- and pressure-dependent calibration constant. The values of kρ were determined from measurements at the same temperatures and pressure with water (7) and 1.0 mol · kg−1 NaCl(aq). (8) Measurements with water were repeated every few days to determine and compensate for possible drift in the cell characteristics and to verify the reproducibility of measurements. The values of τ were determined for rounded temperatures as described previously. (6) Densities of the solutions obtained with this system were reproducible to within ±7 µg·cm−3 for both compounds at all T and m. The calorimeter was calibrated and used as described previously. (4–6) Measurements were recorded at a scan rate r of 16.6667 mK · s−1 for both heating and cooling at 273.15 < T /K < 398.15 and at the pressure p = 0.350 ± 0.015 MPa. Data were collected for at least 4 scans up and 4 scans down for each solution. The massic heat capacity is given by equation (2): c p,s = {kc · (1Ps − 1Pw )/(r · ρs )} + (c p,w · ρw /ρs ).
(2)
In equation (2), c p,s and c p,w are the massic heat capacities of the solution of interest and of water, respectively; 1Ps is the difference in power applied to the heaters on the two calorimetric cells to maintain them at the same temperature when the reference cell contains water and the sample cell contains the solution of interest; and 1Pw is that same (very small) difference in power when both cells contain water. In equation (2), kc is the temperature- and pressure-dependent calibration constant of the calorimeter which was obtained from measurements with water (7) and 1.0 mol · kg−1 NaCl. (8) Experiments with water were performed every few days in order to account for small changes in the baseline signal of the calorimeter. Apparent molar volumes and heat capacities of DMF(aq) and DMA(aq) were obtained by equations (3) and (4): Vφ = (M2 /ρs ) − {1000 · (ρs − ρw )/(ρs · ρw · m)}, C p,φ = (M2 · c p,s ) + {1000 · (c p,s − c p,w )/m}.
(3) (4)
In equations (3) and (4), M2 is the molar mass of the solute and m is the molality of the solute in the solution.
3. Results and discussion Apparent molar volumes Vφ for DMF(aq) and DMA(aq) are given in tables 1 and 2. Figures 1 and 2 show these (Vφ , m, T ) results for the two solutes, where the regressed
920
M. L. Origlia, B. A. Patterson, and E. M. Woolley
TABLE 1. Apparent molar volumes Vφ for DMF(aq) at p = 0.35 MPa. The ± uncertainties are standard deviations from 20 or more consecutive readings of the vibration period during at least 800 s m mol · kg−1
Vφ /(cm3 · mol−1 ) T = 278.15 K
T = 288.15 K
T = 298.15 K
T = 308.15 K
T = 318.15 K
0.0148
76.34 ± 0.18
76.48 ± 0.17
76.83 ± 0.16
76.28 ± 0.17
76.67 ± 0.28
0.0301
74.54 ± 0.09
74.31 ± 0.08
74.42 ± 0.07
74.97 ± 0.09
74.89 ± 0.09
0.0603
73.51 ± 0.05
74.39 ± 0.05
74.93 ± 0.04
75.63 ± 0.05
75.87 ± 0.08
0.1002
72.68 ± 0.03
73.59 ± 0.02
74.33 ± 0.03
75.17 ± 0.02
75.95 ± 0.07
0.2008
72.88 ± 0.01
73.65 ± 0.01
74.31 ± 0.01
75.23 ± 0.01
75.99 ± 0.01
0.4012
72.69 ± 0.007
73.56 ± 0.005
74.31 ± 0.007
75.10 ± 0.006
75.87 ± 0.007
0.7019
72.49 ± 0.003
73.39 ± 0.004
74.19 ± 0.004
75.00 ± 0.005
75.79 ± 0.004
1.0045
72.33 ± 0.002
73.26 ± 0.003
74.09 ± 0.003
74.91 ± 0.002
75.75 ± 0.005
T = 328.15 K
T = 338.15 K
T = 348.15 K
T = 358.15 K
T = 368.15 K
0.0148
77.11 ± 0.17
78.67 ± 0.18
78.42 ± 0.21
80.44 ± 0.22
80.03 ± 0.19
0.0301
76.28 ± 0.08
77.33 ± 0.07
78.13 ± 0.10
78.77 ± 0.10
79.60 ± 0.10
0.0603
77.19 ± 0.05
77.81 ± 0.04
78.24 ± 0.05
79.24 ± 0.05
80.09 ± 0.04
0.1002
76.64 ± 0.03
77.62 ± 0.03
78.20 ± 0.03
79.16 ± 0.03
80.09 ± 0.04
0.2008
76.74 ± 0.01
77.48 ± 0.01
78.38 ± 0.01
79.31 ± 0.01
80.35 ± 0.02
0.4012
76.64 ± 0.008
77.47 ± 0.007
78.36 ± 0.007
79.26 ± 0.007
80.26 ± 0.01
0.7019
76.58 ± 0.003
77.44 ± 0.004
78.30 ± 0.004
79.25 ± 0.004
80.25 ± 0.004
1.0045
76.52 ± 0.003
77.38 ± 0.002
78.27 ± 0.003
79.25 ± 0.003
80.25 ± 0.003
Average experimental values of ρs can be obtained with equation (3) and with ρw given in reference 12.
surfaces are for the empirical function given in equation (5): Vφ = v0 + (v1 · T 2 ) + (v2 · m).
(5)
The regression was performed with weighting factors equal to the reciprocal of the estimated uncertainties in Vφ from tables 1 and 2. The regression parameters vi for equation (5) are given in table 3. The largest deviations from the regression surfaces occur at the lowest m where the uncertainty in Vφ is greatest, corresponding to the smallest differences between ρ s and ρ w . Our Vφ results show a significant dependence on T for both amides, with (∂ Vφ /∂ T ) p ∼ 0.09 cm3 · mol−1 · K−1 . A small negative dependence of Vφ on m is evident. The magnitude of the dependence of Vφ on m and T is only slightly larger for DMA(aq) than it is for DMF(aq). This could be the result of the larger surface area of exposed hydrophobic moiety being exposed to the aqueous environment in for DMA. The DMF(aq) and DMA(aq) regression surfaces show the same trends, with a nearly constant difference between them at all T and m. The difference [Vφ {DMA(aq)}–{Vφ {DMF(aq)}] = (15.25 ± 1.0) cm3 · mol−1 is consistent with that expected for the -CH2 - functional group at T = 298.15 K and p = 0.1 MPa. (9)
Thermodynamics of N ,N -dimethylformamide and N ,N -dimethylacetamide
921
TABLE 2. Apparent molar volumes Vφ for DMA(aq) at p = 0.35 MPa. The ± uncertainties are standard deviations from 20 or more consecutive readings of the vibration period during at least 800 s m mol · kg−1
Vφ /(cm3 · mol−1 ) T = 278.15 K
T = 288.15 K
T = 298.15 K
T = 308.15 K
T = 318.15 K
0.0151
87.19 ± 0.19
88.95 ± 0.14
88.02 ± 0.19
89.63 ± 0.13
92.57 ± 0.39
0.0307
89.42 ± 0.09
89.15 ± 0.07
89.58 ± 0.10
90.31 ± 0.09
92.03 ± 0.12
0.0604
89.02 ± 0.04
89.43 ± 0.05
89.97 ± 0.03
90.49 ± 0.04
90.94 ± 0.04
0.0987
88.93 ± 0.03
89.30 ± 0.02
89.84 ± 0.03
90.34 ± 0.02
90.82 ± 0.03
0.2009
87.94 ± 0.02
88.69 ± 0.01
89.46 ± 0.01
90.18 ± 0.01
91.23 ± 0.02
0.4008
87.65 ± 0.006
88.51 ± 0.006
89.32 ± 0.005
90.11 ± 0.007
90.99 ± 0.007
0.6999
87.19 ± 0.003
88.07 ± 0.003
88.96 ± 0.003
89.82 ± 0.005
90.70 ± 0.004
1.0010
86.91 ± 0.002
87.84 ± 0.002
88.76 ± 0.003
89.65 ± 0.003
90.55 ± 0.003
T = 328.15 K
T = 338.15 K
T = 348.15 K
T = 358.15 K
T = 368.15 K
0.0151
91.27 ± 0.15
91.99 ± 0.18
92.71 ± 0.20
94.49 ± 0.20
94.49 ± 0.29
0.0307
91.80 ± 0.10
91.71 ± 0.08
93.06 ± 0.09
94.14 ± 0.09
95.39 ± 0.12
0.0604
92.40 ± 0.04
92.69 ± 0.04
93.59 ± 0.06
94.60 ± 0.06
95.41 ± 0.05
0.0987
91.53 ± 0.03
92.38 ± 0.03
93.21 ± 0.02
94.20 ± 0.03
95.11 ± 0.03
0.2009
92.05 ± 0.01
92.75 ± 0.01
93.66 ± 0.01
94.70 ± 0.01
95.70 ± 0.01
0.4008
91.86 ± 0.006
92.81 ± 0.006
93.71 ± 0.007
94.74 ± 0.006
95.91 ± 0.009
0.6999
91.64 ± 0.005
92.58 ± 0.003
93.60 ± 0.004
94.68 ± 0.004
95.87 ± 0.003
1.0010
91.51 ± 0.002
92.49 ± 0.002
93.54 ± 0.003
94.63 ± 0.003
95.81 ± 0.003
Average experimental values of ρs can be obtained with equation (3) and with ρw given in reference 12.
Values of C p,φ for DMF(aq) and DMA(aq) are given in tables 4 and 5. Figures 3 and 4 show the results for each solute and the regression surfaces obtained by equation (6): C p,φ = c0 + (c1 · T ) + (c2 · T 2 ) + {c3 + c4 /(T − 270)} · m.
(6)
The regressions used weighting factors equal to the reciprocal of the estimated uncertainties in C p,φ from tables 4 and 5. The regression parameters for equation (6) are given in table 6. As was noted with the regressions for Vφ using equation (5), the largest deviations from the regression surfaces using equation (6) occur at the lowest m where the uncertainty in C p,φ is greatest, corresponding to the smallest differences between c p,s and c p,w . The C p,φ and C op,2 values for both the amides are large and positive, and they increase with increasing temperature. The increase in C p,φ and C op,2 with temperature is approximately linear, with (∂C p,φ /∂ T ) p ∼ 0.5 J · K−2 · mol−1 . Our regression surfaces for both Vφ and C p,φ show parallel behavior. The large and positive values of C p,φ and C op,2 for aqueous DMF and DMA are undoubtedly related to the formation of an ordered water structure (“icebergs”) around these molecules. As
922
M. L. Origlia, B. A. Patterson, and E. M. Woolley
82
–1 3 Vφ /(cm . mol )
80 78 76 74 380 360
72 1.0 0.6 m/(m ol . k 0.4 g –1 )
320
T/ K
340
0.8 300 0.2
280 0.0
FIGURE 1. Apparent molar volumes Vφ for DMF(aq) at p = 0.35 MPa plotted against temperature and molality. , Experimental values from table 1; , reference 9, T = 298.15 K, p = 0.1 MPa. The surface was generated from regression parameters in table 3 with equation (5).
◦
TABLE 3. Regression parameters of equation (5) for the apparent molar volumes Vφ of aqueous DMF and DMA. The ± values for each parameter are chosen to reproduce the generated Vφ values to within ±0.01 cm3 · mol−1 at m 6 1.0 mol · kg−1 and at 278.15 6 T /K 6 393.15 Parameter
DMF(aq)
DMA(aq)
ν0 /(cm3 · mol−1 )
62.894 ± 0.006
76.722 ± 0.006
104 · ν1 /(cm3 · mol−1 · K−2 )
1.2974 ± 0.0004
1.4326 ± 0.0004
ν2 /(cm3 · mol−2 · kg)
−0.386 ± 0.006
−0.665 ± 0.006
1a /(cm3 · mol−1 )
0.74
0.61
a Standard deviations from the regression.
was the case with the Vφ , the DMF(aq) and DMA(aq) regression surfaces for C p,φ show the same general trends, with a nearly constant difference between them at all T and m. The magnitude of the dependence of C p,φ on m is only slightly larger for DMA(aq)
Thermodynamics of N ,N -dimethylformamide and N ,N -dimethylacetamide
923
TABLE 4. Apparent molar heat capacities C p,φ for DMF(aq) at p = 0.35 MPa. The ± uncertainties are standard deviations for the average values obtained from a total of at least 8 total scans at both increasing and decreasing T m mol · kg−1
C p,φ /(J · K−1 · mol−1 ) T = 278.15 K T = 283.15 K T = 288.15 K T = 293.15 K T = 298.15 K T = 303.15 K
0.0148 0.0301 0.0603 0.1002 0.2008 0.4012 0.7019 1.0045
207.4 ± 10.0 208.4 ± 6.8 209.3 ± 2.9 208.3 ± 1.2 211.1 ± 1.0 204.4 ± 0.8 201.2 ± 0.7 198.3 ± 0.5
213.4 ± 9.4 214.1 ± 6.5 214.8 ± 2.8 214.0 ± 1.1 216.8 ± 0.9 210.7 ± 0.7 208.0 ± 0.6 205.4 ± 0.5
218.0 ± 9.2 218.7 ± 6.5 219.4 ± 2.7 218.7 ± 1.1 221.5 ± 0.8 215.8 ± 0.7 213.5 ± 0.6 211.2 ± 0.4
222.4 ± 9.9 222.8 ± 6.6 223.3 ± 2.7 222.8 ± 1.0 225.6 ± 0.9 220.3 ± 0.7 218.2 ± 0.6 216.2 ± 0.4
225.7 ± 10.1 226.1 ± 6.6 226.8 ± 2.6 226.4 ± 0.9 229.2 ± 0.8 224.2 ± 0.7 222.3 ± 0.6 220.5 ± 0.5
229.6 ± 9.5 229.8 ± 6.5 230.2 ± 2.6 229.8 ± 0.9 232.6 ± 0.8 227.8 ± 0.7 226.1 ± 0.6 224.4 ± 0.5
T = 308.15 K T = 313.15 K T = 318.15 K T = 323.15 K T = 328.15 K T = 333.15 K 0.0148 0.0301 0.0603 0.1002 0.2008 0.4012 0.7019 1.0045
232.8 ± 9.6 233.1 ± 5.9 233.2 ± 2.7 233.0 ± 0.9 235.7 ± 0.8 231.1 ± 0.7 229.5 ± 0.6 227.9 ± 0.5
235.8 ± 10.2 236.1 ± 6.8 236.2 ± 2.8 236.1 ± 0.9 238.7 ± 0.8 234.2 ± 0.7 232.7 ± 0.6 231.2 ± 0.6
238.9 ± 10.4 238.9 ± 6.9 239.0 ± 3.0 238.9 ± 1.0 241.4 ± 0.8 237.1 ± 0.7 235.7 ± 0.7 234.2 ± 0.6
241.7 ± 10.4 241.6 ± 6.9 241.7 ± 3.0 241.7 ± 1.0 244.1 ± 0.8 239.9 ± 0.7 238.5 ± 0.7 237.0 ± 0.6
245.1 ± 10.4 244.5 ± 6.8 244.5 ± 3.2 244.4 ± 1.0 246.7 ± 0.8 242.5 ± 0.7 241.2 ± 0.7 239.7 ± 0.7
248.2 ± 10.7 247.3 ± 6.8 247.3 ± 3.3 247.0 ± 1.1 249.3 ± 0.8 245.2 ± 0.7 243.8 ± 0.8 242.4 ± 0.8
T = 338.15 K T = 343.15 K T = 348.15 K T = 353.15 K T = 358.15 K T = 363.15 K 0.0148 0.0301 0.0603 0.1002 0.2008 0.4012 0.7019 1.0045
250.9 ± 10.8 249.9 ± 6.7 249.9 ± 3.4 249.6 ± 1.2 251.8 ± 0.8 247.7 ± 0.8 246.3 ± 0.8 244.9 ± 0.8
253.8 ± 11.1 252.2 ± 6.5 252.4 ± 3.5 252.0 ± 1.3 254.1 ± 0.8 250.0 ± 0.8 248.6 ± 0.8 247.2 ± 0.9
256.3 ± 11.4 254.5 ± 6.4 254.7 ± 3.7 254.3 ± 1.5 256.4 ± 0.7 252.3 ± 0.7 250.9 ± 0.9 249.4 ± 0.9
259.3 ± 12.0 257.2 ± 6.2 257.3 ± 3.7 256.6 ± 1.8 258.6 ± 0.7 254.6 ± 0.7 253.1 ± 0.9 251.6 ± 1.0
262.0 ± 12.7 259.8 ± 6.4 259.5 ± 3.9 258.9 ± 2.1 260.7 ± 0.8 256.7 ± 0.7 255.2 ± 0.9 253.7 ± 1.0
263.8 ± 13.9 262.0 ± 6.8 261.6 ± 4.2 261.0 ± 2.6 262.8 ± 0.9 258.7 ± 0.7 257.2 ± 0.9 255.7 ± 1.0
T = 368.15 K T = 373.15 K T = 378.15 K T = 383.15 K T = 388.15 K T = 393.15 K 0.0148 0.0301 0.0603 0.1002 0.2008 0.4012 0.7019 1.0045
266.4 ± 15.3 264.2 ± 7.8 263.6 ± 4.6 263.0 ± 3.3 264.7 ± 1.1 260.7 ± 0.7 259.1 ± 0.9 257.5 ± 1.0
268.1 ± 17.8 266.4 ± 9.8 265.6 ± 5.5 265.0 ± 4.2 266.5 ± 1.5 262.5 ± 0.7 261.0 ± 0.9 259.3 ± 1.0
270.7 ± 21.4 268.7 ± 13.2 267.4 ± 6.8 266.7 ± 5.5 268.2 ± 2.2 264.2 ± 1.0 262.6 ± 0.8 260.9 ± 1.0
273.1 ± 25.6 271.2 ± 17.6 269.4 ± 8.6 268.4 ± 7.2 269.8 ± 3.2 265.8 ± 1.4 264.3 ± 0.7 262.6 ± 0.9
274.4 ± 30.9 273.8 ± 23.4 271.1 ± 11.1 270.0 ± 9.3 271.3 ± 4.4 267.3 ± 2.1 265.9 ± 0.5 264.1 ± 0.7
277.3 ± 38.7 277.3 ± 31.3 272.8 ± 14.4 271.6 ± 11.8 273.0 ± 5.4 268.8 ± 3.3 267.5 ± 0.8 265.7 ± 0.5
Average experimental values of c p,s can be obtained with equation (4) and with c p,w given in reference 12.
924
M. L. Origlia, B. A. Patterson, and E. M. Woolley
TABLE 5. Apparent molar heat capacities C p,φ for DMA(aq) at p = 0.35 MPa. The ± uncertainties are standard deviations for the average values obtained from a total of at least 8 total scans at both increasing and decreasing T m mol · kg−1
C p,φ /(J · K−1 · mol−1 ) T = 278.15 K T = 283.15 K T = 288.15 K T = 293.15 K T = 298.15 K T = 303.15 K
0.0151 0.0307 0.0604 0.0987 0.2009 0.4008 0.6999 1.0010
277.7 ± 12.6 279.8 ± 5.9 281.0 ± 1.4 280.8 ± 2.0 278.8 ± 0.6 275.3 ± 0.2 268.4 ± 0.1 263.0 ± 0.1
281.4 ± 12.3 284.0 ± 5.7 284.9 ± 1.5 285.0 ± 2.1 283.4 ± 0.7 280.6 ± 0.1 274.7 ± 0.1 269.9 ± 0.06
284.9 ± 11.9 287.4 ± 5.5 288.5 ± 1.6 288.6 ± 2.1 287.3 ± 0.8 285.0 ± 0.2 279.8 ± 0.1 275.6 ± 0.07
288.1 ± 11.9 290.3 ± 5.4 291.8 ± 1.5 291.9 ± 2.0 290.9 ± 0.8 288.9 ± 0.2 284.2 ± 0.1 280.6 ± 0.05
290.9 ± 11.9 293.3 ± 5.3 294.8 ± 1.5 295.1 ± 2.0 294.2 ± 0.7 292.5 ± 0.2 288.2 ± 0.1 284.9 ± 0.06
293.7 ± 11.4 295.8 ± 4.9 297.7 ± 1.5 298.1 ± 1.9 297.4 ± 0.7 295.8 ± 0.2 291.9 ± 0.2 288.9 ± 0.1
T = 308.15 K T = 313.15 K T = 318.15 K T = 323.15 K T = 328.15 K T = 333.15 K 0.0151 0.0307 0.0604 0.0987 0.2009 0.4008 0.6999 1.0010
296.8 ± 10.6 298.7 ± 4.6 300.6 ± 1.5 301.1 ± 1.8 300.4 ± 0.6 299.1 ± 0.2 295.4 ± 0.1 292.5 ± 0.1
299.2 ± 11.5 301.5 ± 5.1 303.6 ± 1.6 304.0 ± 1.8 303.5 ± 0.6 302.2 ± 0.2 298.7 ± 0.2 295.9 ± 0.2
301.8 ± 11.6 303.8 ± 5.2 306.4 ± 1.6 306.8 ± 1.8 306.3 ± 0.6 305.0 ± 0.2 301.6 ± 0.3 299.0 ± 0.2
304.2 ± 12.2 306.7 ± 5.1 309.1 ± 1.6 309.5 ± 1.8 309.1 ± 0.6 307.9 ± 0.3 304.5 ± 0.3 302.0 ± 0.3
306.9 ± 12.5 309.3 ± 5.1 311.8 ± 1.6 312.3 ± 1.8 311.8 ± 0.6 310.6 ± 0.4 307.3 ± 0.4 304.8 ± 0.4
309.7 ± 13.0 312.3 ± 5.2 314.5 ± 1.7 315.0 ± 1.7 314.5 ± 0.6 313.2 ± 0.5 310.0 ± 0.5 307.5 ± 0.4
T = 338.15 K T = 343.15 K T = 348.15 K T = 353.15 K T = 358.15 K T = 363.15 K 0.0151 0.0307 0.0604 0.0987 0.2009 0.4008 0.6999 1.0010
312.4 ± 13.4 315.1 ± 5.3 317.1 ± 1.9 317.6 ± 1.7 317.1 ± 0.6 315.8 ± 0.6 312.6 ± 0.6 310.1 ± 0.5
315.0 ± 14.1 317.4 ± 5.5 319.6 ± 2.0 320.1 ± 1.7 319.5 ± 0.6 318.2 ± 0.6 315.0 ± 0.6 312.5 ± 0.5
317.4 ± 14.8 320.2 ± 5.7 322.0 ± 2.2 322.4 ± 1.8 321.8 ± 0.6 320.5 ± 0.6 317.3 ± 0.7 314.7 ± 0.6
319.7 ± 15.3 322.5 ± 6.0 324.2 ± 2.3 324.8 ± 1.9 324.1 ± 0.6 322.7 ± 0.7 319.5 ± 0.7 316.9 ± 0.7
321.7 ± 15.7 324.8 ± 6.3 326.3 ± 2.6 327.0 ± 1.9 326.3 ± 0.7 324.9 ± 0.8 321.6 ± 0.8 319.0 ± 0.7
323.9 ± 16.1 327.1 ± 6.4 328.4 ± 2.8 329.0 ± 2.1 328.3 ± 0.8 326.8 ± 0.8 323.5 ± 0.9 320.9 ± 0.8
T = 368.15 K T = 373.15 K T = 378.15 K T = 383.15 K T = 388.15 K T = 393.15 K 0.0151 0.0307 0.0604 0.0987 0.2009 0.4008 0.6999 1.0010
326.0 ± 16.7 328.9 ± 6.5 330.4 ± 2.9 330.9 ± 2.1 330.2 ± 0.9 328.7 ± 0.9 325.3 ± 0.9 322.7 ± 0.9
328.2 ± 17.7 331.0 ± 6.9 332.2 ± 3.0 332.7 ± 2.2 332.0 ± 0.9 330.4 ± 1.0 327.1 ± 1.0 324.4 ± 1.0
329.2 ± 18.6 332.3 ± 7.2 333.6 ± 3.2 334.4 ± 2.2 333.6 ± 1.0 332.0 ± 1.0 328.6 ± 1.0 325.8 ± 1.0
329.8 ± 20.1 333.8 ± 7.4 335.0 ± 3.5 336.1 ± 2.2 335.2 ± 1.1 333.6 ± 1.1 330.1 ± 1.1 327.3 ± 1.1
331.4 ± 20.1 335.3 ± 7.7 336.4 ± 3.8 337.6 ± 2.2 336.6 ± 1.1 335.0 ± 1.1 331.5 ± 1.1 328.7 ± 1.2
332.2 ± 19.9 336.1 ± 8.2 338.0 ± 4.5 339.3 ± 2.3 338.2 ± 1.0 336.5 ± 0.8 333.0 ± 0.8 330.1 ± 1.0
Average experimental values of c p,s can be obtained with equation (4) and with c p,w given in reference 12.
Thermodynamics of N ,N -dimethylformamide and N ,N -dimethylacetamide
925
99
Vφ /(cm3 . mol – 1)
96
93
90
87 380
1.0
360
0.8
340
0.6 m/( mo l .k
320
0.4
g
–1
)
300
0.2 0.0
T/
K
280
FIGURE 2. Apparent molar volumes Vφ for DMA(aq) at p = 0.35 MPa plotted against temperature and molality. , Experimental values from table 2; , reference 9, T = 298.15 K, p = 0.1 MPa; H, reference 10, T = 298.15 K, p = 0.1 MPa; N, reference 11, T = 298.15 K, p = 0.1 MPa. The surface was generated from regression parameters in table 3 with equation (5).
◦
than it is for DMF(aq), but there is no statistically significant difference between the dependence of C p,φ on T for DMA(aq) and DMF(aq). The difference [C p,φ {DMA(aq)}– C p,φ {DMF(aq)}] = (67.4 ± 2.6 ) J · K−1 · mol−1 is consistent with that expected for the -CH2 - functional group at T = 298.15 K and p = 0.1 MPa. (9) The V2o and C op,2 values obtained in this investigation are in good agreement with values reported in the literature. Values of V2o reported by Cabani et al. (9) at T = 298.15 K and p = 0.10 MPa differ from ours by 0.07 cm3 · mol−1 and −1.05 cm3 · mol−1 for DMF(aq) and DMA(aq), respectively. Values of V2o , reported by Assarsson and Eirich (10) and by De Visser et al. (11) for DMA(aq) at T = 298.15 K and p = 0.10 MPa differ from those of this study by 0.56 cm3 · mol−1 and by −0.19 cm3 · mol−1 , respectively. The value of C op,2 given by Cabani et al. (9) for DMF(aq) at T = 298.15 K and p = 0.10 MPa differs by 2.6 J · K−1 · mol−1 from our results. All these differences are within the total uncertainties we expect, given the standard deviations in tables 1 to 6.
926
M. L. Origlia, B. A. Patterson, and E. M. Woolley
270
1 mol – )
240
Cp,φ/(J . K
250
–1
260
230 220 210 380 200
360
1.0 0.6 m/(m 0.4 ol . k g –1 )
320
T/
0.8
K
340
300 0.2
280 0.0
FIGURE 3. Apparent molar heat capacity C p,φ for DMF(aq) at p = 0.35 MPa plotted against temperature and molality. , Experimental values from table 4; , reference 9, T = 298.15 K, p = 0.1 MPa. The surface was generated from regression parameters in table 6 with equation (6).
◦
TABLE 6. Regression parameters of equation (6) for the apparent molar heat capacities C p,φ of aqueous DMF and DMA. The ± values for each parameter are chosen to reproduce the generated C p,φ to within ±0.1 J · K−1 · mol−1 at m 6 1.0 mol · kg−1 and at 278.15 6 T /K 6 393.15. Parameter c0 /(J · K−1 · mol−1 ) c1 /(J · K−2 · mol−1 ) 104 · c2 /(J · K−3 · mol−1 ) c3 /(J · K−1 · mol−2 · kg) c4 /(J · kg · mol−2 ) 1a /(J · K−1 · mol−1 )
DMF(aq) −196.30 ± 0.04 2.1544 ± 0.0001 −24.556 ± 0.002 −5.20 ± 0.04 −80.8 ± 0.3 1.6
a Standard deviations from the regression.
DMA(aq) −82.50 ± 0.04 1.8913 ± 0.0001 −20.828 ± 0.002 −7.57 ± 0.04 −103.2 ± 0.3 2.1
Thermodynamics of N ,N -dimethylformamide and N ,N -dimethylacetamide
927
Cp,φ/(J . K
–1
1 mol – )
330
315
300
285 380 360
270 320
0.8 0.6 m/(m ol . k
300
0.4
g – 1)
T/K
340 1.0
0.2
280 0.0
FIGURE 4. Apparent molar heat capacity C p,φ for DMA(aq) at p = 0.35 MPa plotted against temperature and molality m. , Experimental values from table 5. The surface was generated from regression parameters in table 6 with equation (6).
◦
REFERENCES 1. De Visser, C.; Somsen, G. J. Chem. Thermodynamics 1972, 4, 313–319. 2. De Visser, C.; Somsen, G. J. Solution Chem. 1974, 3, 847–854. 3. Eberling, E. L. Kirk-Othmer Encyclopedia of Chemical Technology: 3rd edition, Vol. 11. Grayson, M.: editor. John Wiley and Sons: New York. 1980, 263–267. 4. Woolley, E. M. J. Chem. Thermodynamics 1997, 29, 1377–1385. 5. Ballerat-Busserolles, K.; Origlia, M. L.; Woolley, E. M. Thermochimica Acta 2000, 347, 3–7. 6. Ballerat-Busserolles, K.; Ford, T. D.; Call, T. G.; Woolley, E. M. J. Chem. Thermodynamics 1999, 31, 741–762. 7. Hill, P. G. J. Phys. Chem. Ref. Data 1990, 19, 1233–1274. 8. Archer, D. G. J. Phys. Chem. Ref. Data 1992, 21, 793–829. 9. Cabani, S.; Gianni, P.; Mollica, V.; Lepori, L. J. Solution Chem. 1981, 10, 563–595. 10. Assarsson, P.; Eirich, F. R. J. Phys. Chem. 1968, 72, 2710–2719. 11. De Visser, C.; Heuvelsland, W. J. M.; Dunn, L. A.; Somsen, G. J. Chem. Soc. Faraday Trans. I 1978, 74, 1159–1169. 12. Ford, T. D.; Call, T. G.; Origlia, M. L.; Stark, M. A.; Woolley, E. M. J. Chem. Thermodynamics 2000, 32, 499–516. (Received 27 September 2000; in final form 2 January 2001)
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