Thermodynamic Properties of Aqueous Morpholine and Morpholinium

J. Phys. Chem. B 1997, 101, 409-419

409

Thermodynamic Properties of Aqueous Morpholine and Morpholinium Chloride at Temperatures from 10 to 300 °C: Apparent Molar Volumes, Heat Capacities, and Temperature Dependence of Ionization Peter R. Tremaine,* Dmitri Shvedov, and Caibin Xiao Department of Chemistry, Memorial UniVersity of Newfoundland, St. John’s, Newfoundland, Canada A1C 3X7 ReceiVed: August 13, 1996; In Final Form: October 3, 1996X

Apparent molar heat capacities Cp,φ of aqueous morpholine and morpholinium chloride were determined with a Picker flow microcalorimeter at temperatures from 10 to 55 °C. The apparent molar volumes Vφ have been determined with platinum vibrating tube densitometers at temperatures from 10 to 300 °C and pressures in excess of steam saturation. Values of Vφ for morpholine approach large positive values at elevated temperatures, consistent with a lowering of the critical temperature in the solutions relative to water. The effect in aqueous morpholinium chloride is reversed, confirming the profound effect of ionic charge on the high-temperature thermodynamic properties of aqueous solutes, even for large organic molecules. Standard partial molar heat capacity functions were estimated from the high-temperature Vφ data and low-temperature values of Cp,φ using an empirical model based on the appropriate solvent density derivatives and the revised HelgesonKirkham-Flowers model. The results from both models are consistent with literature values for the heat capacity of ionization determined from high-temperature potentiometric measurements to within the combined experimental uncertainties. The results show that the effects of solvent expansion by the neutral species is significant at elevated temperatures. The effective Born radius of ions containing organic groups could be significantly larger than the radius calculated from the formula for simple cations because of this effect.

1. Introduction In recent years, the properties of aqueous electrolytes and nonelectrolytes at elevated temperatures have been the object of much study, both because of technological interest and because an understanding of the effects of widely varying water properties yields fundamental insights into hydration phenomena. The dramatic changes in the standard partial molar volumes and heat capacities of simple electrolytes at elevated temperatures are now understood to arise from the high degree of long-range solvent polarization that accompanies the approach to the critical temperature and pressure of water at 374 °C and 221 bar.1-5 The behavior of aqueous nonelectrolytes is less well understood. The partial molar properties of simple gases in water display discontinuities that result from critical effects. These are usually in the opposite direction to those observed for electrolytes. Some success has been achieved in describing the high-temperature solvation of gases by the Percus-Yevick equation and by other methods.5,6 Very little work has been done to examine the competing effects of charge and nonelectrostatic interactions with water at high temperatures by larger molecules, for which both effects are significant. Morpholine is of interest in this context because it is a relatively polar cyclic molecule with well-defined geometry and an ionizable secondary amine group. Its critical temperature and pressure are relatively close to those of water, and its thermal stability in aqueous solutions is well established.7 The thermodynamic properties of aqueous morpholine under hydrothermal conditions are also of considerable interest to the electrical power industry, as it is widely used in steam generators as a volatile additive for pH control.8 There are a numerous studies for the ionization equilibria of morpholine in aqueous solutions near ambient temperature.9,10 Mesmer and Hitch11 determined values for the ionization X

Abstract published in AdVance ACS Abstracts, December 1, 1996.

S1089-5647(96)02445-5 CCC: $14.00

constant of morpholine over the temperature range 50-295 °C in dilute KCl media as a function of pressure using a potentiometric technique that employed platinum/hydrogen electrodes in a novel concentration cell with a flowing liquid junction. A critical review of the high-temperature ionization constant and volatility data for a number of industrially important amines has been done by Wetton.12 Low-temperature data for the apparent molar volumes and heat capacities of aqueous morpholine have been determined at 25 °C by Kiyohara et al.13 and from 20 to 55 °C by Cabani et al.14 No studies above 60 °C have been reported in the literature. The purpose of this investigation was to determine the apparent molar volumes of aqueous morpholine and morpholinium chloride at temperatures up to 300 °C , as a means of examining the effect of ionization on hydration and the success of various models used to extrapolate standard partial molar properties to elevated temperatures. The work employed a new high-temperature vibrating tube densitometer recently constructed in our laboratory. Apparent molar heat capacities, measured over the range 10-65 °C in a commercial flow microcalorimeter, are also reported.

2. Experimental Methods Aqueous solutions of morpholine were prepared directly from the commercial product (Fisher, “Certified” A.C.S. grade; refractive index nD20 ) 1.4546 vs literature value nD20 ) 1.4540). Analysis of the commercial product by gas chromatography-mass spectrometry revealed no detectable impurities ( 8 MΩ cm) was used to prepare all solutions. Stock solutions of HCl were obtained by dilution of 15 mol kg-1 concentrated solutions (Fisher “Certified” A.C.S. reagent grade). TRIS (mass fraction: 0.999) was purchased from Aldrich. A Sodev CP-C flow microcalorimeter16 and a Sodev 03D vibrating-tube flow densitometer17 equipped with platinum cells were employed for measurements near ambient conditions. The temperatures of the calorimeter and densitometer were independently controlled by two Sodev CT-L circulating baths to (0.01 °C. The thermistors (Omega, 44107) used to measure the temperatures of the calorimeter and densitometer were calibrated with a Hewlett Packard 2804A quartz thermometer traceable to NBS standards. The densitometer was calibrated daily with pure water and standard 1 mol‚kg-1 NaCl solution. The experimental values of {(cp‚F/(cp,1*F1*)) - 1} for the standard NaCl solution were compared with literature values compiled by Archer18 to correct for a small heat leak effect, according to the method of Desnoyers et al.19 The heat leak correction factors lay in the range 1.005-1.007 at all temperatures studied. High-temperature volumetric measurements were made in a vibrating-tube densitometer, constructed according to the design of Albert and Wood,20 as modified by Corti et al.21 A detailed description of the densitometer is given by Xiao et al.22 Briefly, the densitometer consists of a U-shaped tube (0.90 Pt/0.10 Ir alloy), silver-soldered into a cylindrical brass block. Two inconel rods, mounted on the tube with ceramic adhesive, rest between the poles of a permanent magnet. One of the rods carries the electrical current which drives the vibration of the tube. The other carries the induced current which is measured to sense the frequency of vibration. The temperature is controlled to (0.02 °C by a well-insulated brass oven, with a large thermal mass, that surrounds the densitometer cell. Water was injected continuously from an Isco liquid chromatography pump, and increments of the solutions to be measured were injected by means of a sample loop. The pressure of the flow system was maintained by a nitrogen cylinder and a backpressure regulator (Tescom model 26-1700) connected to the pressurized reservoir at the exit of the densimeter cell. The system pressure was measured by means of an Omega PX951 pressure transducer traceable to NIST standards and an Omega DP41-E process indicator. The accuracy of the pressure measurement was confirmed to be within the manufacturer’s specified error limit by determining the bubble point of water at 300 °C.22 This densitometer was also calibrated daily with pure water and standard 1 mol‚kg-1 NaCl solution, using the standard reference values compiled by Hill23 and Archer,18 respectively. The combined uncertainty in the measured relative densities, (F - F1*), due to the sensitivity limits of the instrument itself and the accuracy of the reference data is estimated to be (0.0002 g cm-3.

3. Results 3.1. Apparent Molar Properties. The experimental values for the relative densities (F - F1*) and heat capacity ratios {(cpF/ (cp,1*F1*)) - 1} of the solutions are listed in Tables 1-4. The tables also tabulate the experimental apparent molar volumes Vφ and heat capacities Cp,φ for aqueous morpholine

Tremaine et al. TABLE 1: Experimental Apparent Molar Volumes VO and Apparent Molar Heat Capacities Cp,O for Morpholine, Where m Denotes Molality, G - G1* Denotes Density Relative to Water Cp,φ,2, m, (F - F*1)103, Vφ , mol‚kg-1 g‚cm-3 cm3‚mol-1 cpF/(c*p,1F*1) - 1 J‚K-1‚mol-1 t ) 10.0 °C, c*p,1 ) 4.1940 J‚K-1‚g-1, F*1 ) 0.999 705 g‚cm-3 1.8037 10.583 6 80.42 -0.049 879 5 204.4 1.2632 7.458 16 80.64 -0.035 413 8 208.5 0.6717 3.976 19 80.90 -0.018 968 2 214.3 0.5024 2.991 45 80.95 -0.014 265 7 215.4 0.4288 2.504 78 81.10 -0.012 092 9 217.6 0.3726 2.085 22 81.38 -0.010 572 8 218.6 0.2454 1.458 39 81.08 -0.007 007 7 217.8 0.1096 0.618 27 81.45 -0.003 100 5 221.8 t ) 25.0 °C, c*p,1 ) 4.1800 J‚K-1‚g-1, F*1 ) 0.997 041 g‚cm-3 1.9122 9.240 57 81.76 -0.045 737 9 225.1 1.8038 8.787 00 81.76 -0.043 547 5 224.9 1.2632 6.210 02 81.92 -0.030 882 2 228.6 0.6716 3.312 75 82.14 -0.016 830 1 231.7 0.6473 3.193 74 82.15 -0.016 232 4 231.9 0.5024 2.477 80 82.21 -0.012 652 1 232.8 0.4288 2.119 06 82.23 -0.010 828 9 233.2 0.2454 1.226 65 82.24 -0.006 143 4 235.6 0.1427 7.204 75 82.24 -0.003 575 5 236.1 0.0496 2.706 88 81.86 -0.001 199 5 237.6 t ) 40.0 °C, c*p,1 ) 4.1773 J‚K-1‚g-1, F*1 ) 0.992 206 g‚cm-3 1.8038 7.135 90 83.19 -0.037 707 1 244.5 1.2632 5.304 59 83.09 -0.027 093 5 245.5 0.6716 2.859 14 83.24 -0.015 004 8 246.5 0.5024 2.158 32 83.26 -0.011 437 6 246.0 0.4288 1.871 40 83.21 -0.009 763 4 246.4 0.2521 1.004 53 83.67 -0.005 868 2 247.5 0.1427 0.595 80 83.51 -0.003 295 5 248.5 0.1096 0.389 79 84.16 -0.002 627 0 247.8 t ) 55.0 °C, c*p,1 ) 4.1809 J‚K-1‚g-1, F*1 ) 0.985 686 g‚cm-3 1.8038 6.716 88 83.98 -0.034 523 5 254.1 1.2632 4.815 00 84.05 -0.025 176 9 254.3 0.6716 2.566 57 84.23 -0.014 472 9 252.0 0.5024 1.971 74 84.18 -0.010 812 6 253.2 0.2454 0.987 76 6 84.16 -0.005 221 6 256.0

and morpholinium chloride, which were calculated from these results using densities and specific heat capacities of pure water taken from Hill’s equation of state.23 By definition

Yφ ) {Y(sln) - 55.509Y1*}/(m2 + m3)

(1)

where Y1* is the molar heat capacity or volume of pure H2O(l) and m2 and m3 are the molalities of the salt and hydrochloric acid, respectively. The excess HCl in our solutions was used to suppress the formation of the neutral species in the morphilinium chloride solutions. The effect of the small amount of excess acid was subtracted by the procedure used by Hovey et al.24,25 Briefly, the contribution of each solute can be described by Young’s rule:26,27

Yφ ){m2/(m2 + m3)}Yφ,2 + {m3/(m2 + m3)}Yφ,3 + δ

(2)

Here, Yφ,2 and Yφ,3 are the values for the hypothetical solution of the pure components with speciation and ionic strength identical to the mixture; δ is an excess mixing term, which usually may be ignored in calculating the properties of the major components where there is a common anion. Both Cp,φ,3 and Vφ,3 from 10 to 75 °C were calculated as functions of ionic strength and temperature from the equations for HCl(aq) reported by Tremaine et al.28 and Hovey et al.25 No similar excess of NaOH was required to suppress the ionization of neutral morpholine at the molalities used here.13 The resulting values of Cp,φ,2 and Vφ,2 for morpholine and morpholinium chloride are tabulated in Tables 1-3. They are plotted as

Properties of Morpholine and Morpholinium Chloride

J. Phys. Chem. B, Vol. 101, No. 3, 1997 411

TABLE 2: Experimental Apparent Molar Heat Capacities Cp,O for {OC4H8NH2Cl+HCl}(aq), F3 ) m(HCl)/[m(OC4H8NH2Cl) + m(HCl)] Cp,φ, J‚K-1‚mol-1

m(OC4H8NH2Cl), mol‚kg-1

m(HCl), mol‚kg-1

0.6313 0.5393 0.3817 0.3246 0.2908 0.1932 0.1233 0.0979

0.0071 0.0068 0.0092 0.0127 0.0160 0.0093 0.0065 0.0037

t ) 10.0 °C, c*p,1 ) 4.1940 J‚K-1‚g-1, F*1 ) 0.999 705 g‚cm-3 -0.046 819 3 61.4 -1.62 -0.040 527 4 58.9 -1.81 -0.029 580 7 53.0 -3.44 -0.025 404 3 51.8 -5.47 -0.023 029 9 49.2 -7.52 -0.015 627 3 42.7 -6.71 -0.010 274 2 32.6 -7.30 -0.008 089 2 38.0 -5.37

63.7 61.5 57.8 59.5 59.9 51.8 42.0 45.1

0.6313 0.6180 0.5393 0.3905 0.3817 0.3246 0.2908 0.1932 0.1233

0.0071 0.0084 0.0067 0.0084 0.0093 0.0127 0.0160 0.0093 0.0065

t ) 25.0 °C, c*p,1 ) 4.1800 J‚K-1‚g-1, F*1 ) 0.997 041 g‚cm-3 -0.043 112 1 92.6 -1.36 -0.042 334 4 91.9 -1.64 -0.037 208 7 91.3 -1.52 -0.027 624 9 86.8 -2.57 -0.027 035 2 86.7 -2.89 -0.023 196 6 85.4 -4.59 -0.021 274 2 79.6 -6.30 -0.014 402 4 74.7 -5.63 -0.009 395 5 74.5 -6.14

95.0 94.8 94.0 91.2 91.8 93.5 90.6 84.3 84.9

0.6313 0.5393 0.3817 0.3246 0.2908 0.2664 0.1981 0.1932 0.1233 0.0979

0.0071 0.0068 0.0093 0.0127 0.0160 0.0051 0.0051 0.0094 0.0065 0.0059

t ) 40.0 °C, c*p,1 ) 4.1773 J‚K-1‚g-1, F*1 ) 0.992 206 g‚cm-3 -0.040 293 6 115.4 -1.25 -0.034 904 7 113.0 -1.39 -0.025 511 7 106.9 -2.65 -0.021 793 9 106.9 -4.21 -0.020 033 3 99.8 -5.78 -0.018 003 3 106.6 -2.14 -0.013 509 5 104.8 -2.85 -0.013 492 3 98.2 -5.17 -0.008 8352 9 89.8 -5.64 -0.006 9327 6 95.6 -6.38

117.9 115.8 112.2 115.4 111.4 110.8 110.5 108.4 100.4 108.1

0.6313 0.5393 0.3817 0.3246 0.2908 0.3292 0.1443 0.0870 0.0582

0.0071 0.0068 0.0093 0.0127 0.0160 0.0071 0.0822 0.0496 0.0331

t ) 55.0 °C, c*p,1 ) 4.1809 J‚K-1‚g-1, F*1 ) 0.985 686 g‚cm-3 -0.036 672 6 133.6 -1.24 -0.033 106 5 129.6 -1.38 -0.024 158 9 123.5 -2.63 -0.021 124 9 115.4 -4.20 -0.018 839 8 118.0 -5.78 -0.021 102 9 120.4 -2.36 -0.013 243 7 41.8 -40.08 -0.007 312 8 50.0 -40.16 -0.004 822 7 40.7 -40.22

136.3 132.6 129.2 124.3 130.6 125.5 128.4 141.6 127.1

0.6039 0.5483 0.4800 0.3850 0.2628

0.0030 0.0050 0.0048 0.0064 0.0109

t ) 65.0 °C, c*p,1 ) 4.1859 J‚K-1‚g-1, F*1 ) 0.980 549 g‚cm-3 -0.411 378 8 151.7 -0.56 -0.461 529 0 143.6 -1.02 -0.525 909 3 137.2 -1.11 -0.614 070 1 139.8 -1.83 -0.727 881 3 127.6 -4.42

153.1 146.0 139.7 144.0 137.5

0.6039 0.5483 0.4401 0.3850

0.0031 0.0050 0.0061 0.0064

t ) 75.0 °C, c*p,1 ) 4.1926 J‚K-1‚g-1, F*1 ) 0.974 847 g‚cm-3 -0.034 399 5 167.8 -0.57 -0.039 860 1 164.3 -1.04 -0.026 578 6 160.7 -1.56 -0.024 398 6 155.5 -1.86

169.2 166.8 164.5 160.0

cpF/(c*p,1F*1) - 1

functions of molality in Figures 1-4. The Debye-Hu¨ckel slope has been subtracted from the values for morpholinium chloride in Figures 3 and 4 to linearize the behavior of apparent molar properties, using procedures discussed below. The experimental results for Vφ,2 from the high-temperature vibrating-tube densitometer are tabulated in Tables 3 and 4 and plotted in Figures 5 and 6. The data were obtained at pressures slightly higher than the steam-saturation pressure at each temperature to avoid bubble formation in the system. In addition, the experimental results for morpholinium chloride at 250 °C were obtained at two pressures, 41 and 101 bar (psat ) 39 bar). These are plotted in Figure 7. The values for Vφ,3 from 10 to 300 °C, needed for the relatively minor Young’s rule correction, were estimated from the approximation Vφ,3(HCl, aq) ≈ V˚(HCl,aq) , using values for V˚(HCl,aq) from the compilation of Shock and Helgeson,29,30 as calculated with the SUPCRT software package.31

F3Cp,φ,3(HCl), J‚K-1‚mol-1

Cp,φ,2(OC4H10NH2Cl), J‚K-1‚mol-1

3.2. Data Treatment. The apparent molar heat capacities and volumes of morpholine over the experimental temperature range could be closely described by the following equations

Cp,φ,2 ) Cp,φ,2∞ + {c4 + c5T + c6T2}m2

(3)

Vφ,2 ) Vφ,2∞ + {V5 + V6T + V7/T}m2

(4)

Cp,φ,2∞ ) c1 + c2/(T - Θ)2 + c3/T3 - qRT(∂R/∂T)p (5) Vφ,2∞ ) V1 + V2/T1/2+ V3/(T - Θ) + V4/T3/2 - qRβ (6) where T/K ) t/°C + 273.15, and Θ ) 228 K is a solventdependent parameter associated with the anomalous behavior of supercooled water.32 Parameters c1-c6 and V1-V8 are adjustable constants, and R and β are the cubic expansion

412 J. Phys. Chem. B, Vol. 101, No. 3, 1997

Tremaine et al.

TABLE 3: Experimental Apparent Molar Volumes VO for {OC4H8NH2Cl+HCl}(aq), F3 ) m(HCl)/[m(OC4H8NH2Cl) + m(HCl)] m{C4H10 NOCl}, mol‚kg-1

m(HCl), mol‚kg-1

0.6313 0.5393 0.3817 0.3246 0.2908 0.1233 0.0979

0.0071 0.0068 0.0093 0.0127 0.0160 0.0065 0.0037

0.6313 0.6180 0.5393 0.3905 0.3817 0.3246 0.2908 0.1932

0.0071 0.0084 0.0068 0.0084 0.0093 0.0127 0.0160 0.0094

0.6313 0.5393 0.3817 0.3246 0.2908 0.2664 0.1932 0.1981

0.0071 0.0068 0.0093 0.0127 0.0160 0.0051 0.0094 0.0051

0.5393 0.3817 0.3246 0.2908 0.1932 0.0979

0.0068 0.0093 0.0127 0.0160 0.0094 0.0059

0.6039 0.5173 0.4800 0.4401 0.3850 0.3104 0.2205 0.0896

0.0031 0.0049 0.0048 0.0061 0.0064 0.0073 0.0095 0.0128

0.6039 0.5483 0.4401 0.3850 0.2205 0.1570

0.0031 0.0050 0.0061 0.0064 0.0095 0.0120

0.6039 0.5483 0.5173 0.4800 0.4401 0.3850 0.3104 0.2205 0.1570 0.0896

0.0031 0.0050 0.0049 0.0048 0.0061 0.0064 0.0073 0.0095 0.0120 0.0128

0.6039 0.5483 0.5173 0.4800 0.4401 0.3850 0.3104 0.2205 0.0896

0.0031 0.0050 0.0049 0.0048 0.0061 0.0064 0.0073 0.0095 0.0128

0.6039 0.5483 0.5173 0.4800 0.4401

0.0031 0.0050 0.0049 0.0048 0.0061

F - F1*, g‚cm-3

Vφ, cm3‚mol-1

t ) 10.0 °C, p ) 1 bar, F1* ) 0.999 705 g‚cm-3 0.018 263 1 92.33 0.015 854 1 92.02 0.011 522 5 91.01 0.009 923 1 89.98 0.009 005 5 88.89 0.004 022 9 87.87 0.003 122 5 89.39 t ) 25.0 °C, p ) 1 bar, F1* ) 0.997 041 g‚cm-3 0.017 317 8 94.04 0.017 019 7 93.83 0.015 015 6 93.78 0.011 165 8 92.90 0.010 931 7 92.73 0.009 426 2 91.66 0.008 522 5 90.66 0.005 784 1 90.65 t ) 40.0 °C, p ) 1 bar, F1* ) 0.992 206 g‚cm-3 0.016 762 9 95.28 0.014 548 6 95.00 0.010 591 7 93.94 0.009 112 6 92.93 0.008 289 2 91.75 0.007 469 4 94.23 0.005 564 0 92.07 0.005 656 2 93.52 t ) 55.0 °C, p ) 1 bar, F1* ) 0.985 686 g‚cm-3 0.014 198 7 96.12 0.010 376 2 94.96 0.009 063 9 93.51 0.008 135 7 92.70 0.005 568 7 92.47 0.002 972 4 90.61 t ) 65.0 °C, p ) 1 bar, F1* ) 0.980 549 g‚cm-3 0.015 810 5 96.92 0.013 689 2 96.57 0.012 716 7 96.60 0.011 785 6 96.18 0.010 389 6 95.94 0.008 401 8 95.65 0.006 098 5 94.18 0.002 687 5 87.39 t ) 75.0 °C, p ) 1 bar, F1* ) 0.974 847 g‚cm-3 0.015 526 9 97.83 0.014 650 5 96.63 0.011 790 0 96.57 0.010 129 8 97.05 0.006 199 4 94.10 0.004 450 3 92.28 t ) 100.2 °C, p ) 5.3 bar, F1* ) 0.958 554 g‚cm-3 0.016 037 4 98.06 0.014 524 8 98.03 0.014 047 1 97.36 0.012 853 2 97.84 0.011 818 2 97.64 0.010 902 8 96.01 0.008 873 3 95.54 0.006 406 0 94.21 0.004 854 0 90.73 0.002 824 8 87.28 t ) 150.2 °C, p ) 5.1 bar, F1* ) 0.917 063 g‚cm-3 0.017 703 9 97.70 0.016 424 0 96.86 0.015 344 7 97.29 0.014 305 3 97.20 0.013 225 9 96.81 0.011 707 1 96.39 0.009 389 1 96.43 0.007 191 3 92.91 0.003 116 0 86.41 t ) 200.1 °C, p ) 19.1 bar, F1* ) 0.865 095 g‚cm-3 0.020 695 3 94.51 0.018 880 5 94.27 0.018 248 9 93.24 0.016 947 6 93.30 0.015 528 0 93.29

F3Vφ,3(HCl), cm3‚mol-1

Vφ,2{OC4H8NH2Cl}, cm3‚mol-1

0.18 0.20 0.40 0.63 0.87 0.84 0.61

93.18 92.96 92.81 92.86 92.22 91.62 92.16

0.20 0.24 0.22 0.38 0.42 0.68 0.93 0.83

94.90 94.87 94.73 94.51 94.54 94.55 94.65 94.17

0.20 0.22 0.43 0.68 0.95 0.34 0.84 0.46

96.15 95.96 95.78 95.86 95.79 95.70 95.65 95.48

0.22 0.42 0.68 0.93 0.83 1.01

97.11 96.83 96.48 96.80 96.08 94.98

0.09 0.16 0.17 0.24 0.29 0.40 0.73 2.20

97.32 97.33 97.40 97.27 97.24 97.49 97.49 97.36

0.09 0.16 0.24 0.28 0.72 1.24

98.24 97.36 97.67 98.38 97.42 98.01

0.08 0.15 0.15 0.16 0.22 0.27 0.38 0.68 1.17 2.07

98.47 98.78 98.13 98.66 98.77 97.34 97.40 97.57 96.41 97.40

0.06 0.11 0.12 0.12 0.17 0.20 0.29 0.52 1.59

98.13 97.63 98.09 98.05 97.98 97.79 98.41 96.38 96.95

0.02 0.04 0.04 0.04 0.05

94.97 95.11 94.08 94.20 94.53



TABLE 3: (Continued) m(HCl), mol‚kg-1

0.3850 0.3104 0.2205 0.1570

0.0064 0.0073 0.0095 0.0120

t ) 200.2 °C, p ) 19.1 bar, F1* ) 0.865 095 g‚cm-3 0.013 951 2 92.08 0.011 073 5 92.76 0.008 353 8 89.28 0.006 186 3 86.16

0.07 0.09 0.18 0.31

93.54 94.85 92.96 92.41

0.6039 0.5483 0.4800 0.4401 0.3850 0.3104 0.2205 0.1570

0.0031 0.0050 0.0048 0.0061 0.0064 0.0073 0.0095 0.0120

t ) 250.2 °C, p ) 100.8 bar, F1* ) 0.805 957 g‚cm-3 0.026 049 0 86.83 0.024 104 7 85.92 0.020 373 2 85.40 0.019 060 5 84.10 0.016 744 3 83.95 0.013 849 7 82.31 0.010 261 1 79.17 0.007 676 1 75.00

-0.07 -0.12 -0.14 -0.18 -0.22 -0.30 -0.53 -0.89

87.35 86.83 86.40 85.46 85.57 84.57 83.15 81.70

0.6582 0.5472 0.3356 0.4192 0.1711

0.0230 0.0257 0.0423 0.0019 0.0126

t ) 250.2 °C, p ) 41.2 bar, F1* ) 0.799 193 g‚cm-3 0.028 349 5 82.84 0.024 513 8 80.27 0.016 960 0 70.64 0.018 896 9 81.93 0.008 904 7 70.48

-0.47 -0.61 -1.37 -0.08 -1.02

86.22 84.67 81.09 82.39 76.76

0.6039 0.5483 0.5173 0.4800 0.4401 0.3850 0.2205 0.0897

0.0031 0.0050 0.0049 0.0048 0.0061 0.0064 0.0095 0.0128

t ) 300.2 °C, p ) 97.9 bar, F1* ) 0.715 615 g‚cm-3 0.035 666 9 54.53 0.033 186 7 51.98 0.031 907 3 49.92 0.029 870 7 49.03 0.027 435 1 49.01 0.024 720 8 45.69 0.011 398 9 31.71 0.007 091 1 21.93

-0.39 -0.68 -0.71 -0.74 -1.02 -1.21 -5.07 -8.88

55.20 53.14 51.11 50.28 50.72 47.68 39.60 35.21

F - F1*, g‚cm-3

Vφ, cm3‚mol-1

F3Vφ,3(HCl), cm3‚mol-1

Vφ,2{OC4H8NH2Cl}, cm3‚mol-1

m{C4H10 NOCl}, mol‚kg-1

Figure 1. Apparent molar heat capacities Cp,φ,2 of morpholine from 10 to 55 °C plotted as a function of molality. Symbols are experimental results, and lines represent the global least-squares fits to eq 3.

Figure 2. Apparent molar volumes Vφ,2 of morpholine from 10 to 100 °C plotted as a function of molality. Symbols are experimental results, and lines represent the global least-squares fits to eq 4.

coefficient and the isothermal compressibility of water, respectively:

q is common to both equations. Values for (∂R/∂T)p and β were calculated from the equation of state of Hill.23 The same equations for the standard partial molar properties were used to fit the apparent molar heat capacities and apparent molar volumes of morpholinium chloride. The excess properties were described adequately by a simple extended Debye-Hu¨ckel equation:

R ) -(∂ ln F1*/∂T)p

(7)

β ) (∂ ln F1*/∂p)T

(8)

The terms containing (∂R/∂T)p and β, which describe the behavior of the standard molar heat capacity and volume at elevated temperatures, are based on the observation by Mesmer et al.2,33 that acid/base equilibrium constants at constant solvent densities are linear functions of temperature over a very wide range. The equations are structured so that the density terms dominate at elevated temperatures. The adjustable parameter

Cp,φ,2 ) Cp,φ,2∞ + AcI1/2 + {c4 + c5T + c6T2}I Vφ,2 ) Vφ,2∞ + AvI1/2 + {V5 + V6T + V7/(T - V8)}I

(9) (10)

Values for the Debye-Hu¨ckel limiting slopes, Ac and Av, were calculated from the formulation reported by Archer and Wang.34


Tremaine et al.

TABLE 4: Experimental Apparent Molar Volumes VO for Morpholine at Elevated Temperatures, Where m Denotes Molality and G - G1* Denotes Density Relative to Water m, mol‚kg-1

(F-F1*)10-3, g‚cm-3

Vφ,2, cm3‚mol-1

m, mol‚kg-1

t ) 150.2 °C, F1* ) 0.917 063 g‚cm 93.84 1.4920 93.72 1.2835 93.70 1.0766 93.55 0.8984 93.52 0.6966 93.44 0.4874

(F-F1*)10-3, g‚cm-3

Vφ,2, cm3‚mol-1

1.623 47 1.513 65 1.354 30 9.559 47 8.762 75 3.983 03

93.54 93.44 93.37 93.64 93.42 93.99

-0.50813 -0.39087 -0.35178 -0.000004 0.35178 0.31135

101.11 101.24 101.27 100.72 99.70 99.28

-3

6.2191 4.6421 4.0587 3.0633 1.9718 1.7732

3.959 77 3.563 76 3.286 55 2.969 72 2.098 69 2.019 46

12.0312 11.3573 9.4028 8.9989 8.0218 6.2191 4.0587

-6.223 98 -6.105 70 -4.215 06 -4.254 55 -3.190 93 -2.08787 -1.55670

t ) 200.2 °C, F1* ) 0.8650 95 g‚cm-3 102.13 1.9718 102.15 1.0766 101.80 0.8984 101.84 0.6966 101.61 0.4874 101.40 0.2992 101.40

1.9718 1.7732 1.4920

4.495 84 4.058 15 3.580 69

t ) 100.2 °C, F1* ) 0.958 554 g‚cm-3 87.99 1.2835 88.02 1.0766 87.95 0.8984

2.904 31 2.387 07 1.790 29

88.16 88.25 88.55

8.9989 8.0218 6.2191 4.6421 3.0633

-9.784 56 -9.085 70 -7.066 78 -5.43607 -3.53351

t ) 250.2 °C, F1* ) 0.799 193 g‚cm-3 111.15 1.9718 111.12 1.4920 110.85 1.0766 110.67 0.6966 110.38 0.4874

-2.446 28 -1.825 00 -1.320 21 -0.893 07 -0.427 11

110.37 110.26 110.19 110.22 109.53

12.0312 8.0218 9.4028 4.0587 1.9718

-30.6827 -24.1167 -26.4538 -14.4135 -7.66130

t ) 300.2 °C, F1* ) 0.715 615 g‚cm-3 132.55 1.4920 132.23 1.0766 132.25 0.8984 131.47 0.4874 130.87 0.2992

-5.96305 -4.30432 -4.58526 -2.92482 -1.38324

130.78 130.48 132.71 134.16 131.17

Figure 3. Apparent molar heat capacities Cp,φ,2 of morpholinium chloride from 10 to 65 °C plotted as a function of ionic strength I after subtracting the Debye-Hu¨ckel limiting law term. Symbols represent experimental results, and lines represent the least-squares global fits to eq 9.

Figure 4. Apparent molar volumes Vφ,2 of morpholinium chloride from 10 to 55 °C plotted as a function of ionic strength I after subtracting the Debye-Hu¨ckel limiting law term. Symbols represent experimental results, and lines represent the least-squares global fits to eq 10.

The isothermal forms of eqs 3-6 were fitted to the experimental results at each temperature by the Marquardt-Levenberg nonlinear least-squares algorithm in the commercial software package SigmaPlot, with identical weighting factors for all the experimental data points. The entire array of values at all temperatures and all molalities was then used to optimize the parameters in eqs 3-10 in order to obtain a global fit to the data. The molality dependance of the apparent molar properties was found to be well represented by this treatment, without a need for additional terms. The results are listed in Tables 5 and 6 and also illustrated in Figures 1-6. The overall standard

deviations of Vφ,2 for morpholine and morpholinium chloride were both ∼0.7 cm-3‚ mol-1. The standard deviations of Cp,φ,2 (OC4H8NH, aq) and Cp,φ,2 (OC4H8NH2Cl, aq) were 1.3 and 4.4 J‚K-1‚mol-1, respectively. We estimate that the combined statistical scatter and systematic errors lead to an uncertainty of no more than (1 cm-3‚ mol-1 in Vφ,2∞ for both species, and (2 and 6 J‚K-1‚mol-1 in Cp,φ,2∞(OC4H8NH, aq) and Cp,φ,2∞ (OC4H8NH2Cl, aq), respectively. 3.3. Standard Partial Molar Properties. By definition, Cp,2° ) Cp,φ,2∞ and V2° ) Vφ,2∞ are the standard partial molar heat capacity and standard partial molar volume of the aqueous



TABLE 5: Global Fitting Equation Parameters for Morpholine OC4H8NH(aq) and Morpholinium Chloride OC4H8NH2Cl(aq) (Eqs 3-10) Vφ,2, cm3‚mol-1

Cp,φ,2, J‚K-1‚mol-1 parameter

OC4H8NH

OC4H8NH2Cl

parameter

OC4H8NH

OC4H8NH2Cl

c1 c2 c3 c4 c5 c6

272.81 -1.83 × 105 -7.97 × 108 -349.94 2.05 -3.00 × 10-3

223.66 1.77 × 105 -2.08 × 109 1.25 × 103 -7.72 1.19 × 10-2

V1 V2 V3 V4 V5 V6 V7 V8 q

227.85 -3.72 × 103 -329.36 3.59 × 105 5.94 -6.12 × 10-3 -1.36 × 103

198.48 -2.02 × 103 8.08 1.50 × 105 0.19 2.59 × 10-2 2.44 × 105 607.63 4.55 × 103

Figure 5. Apparent molar volumes Vφ,2 of morpholine at elevated temperatures plotted as a function of molality. Symbols are experimental results, and lines represent the global least-squares fits to eq 4.

-1.32 × 103

Figure 7. Apparent molar volumes Vφ,2 of morpholinium chloride at 250 °C at 41 and 101 bar plotted as a function of ionic strength (I) after subtracting the Debye-Hu¨ckel limiting law term. Symbols represent experimental results, and lines represent the isothermal leastsquares fits.

TABLE 6: Standard State Properties for Morpholine OC4H8NH(aq) and Morpholinium Chloride OC4H8NH2Cl(aq) from 10 to 300 °C OC4H8NH

Figure 6. Apparent molar volumes Vφ,2 of morpholinium chloride at elevated temperatures plotted as a function of ionic strength (I) after subtracting the Debye-Hu¨ckel limiting law term. Symbols represent experimental results, and lines represent the global least-squares fits to eq 10.

solute, respectively, in the hypothetical 1 mol‚kg-1 standard state. Values for the standard partial molar properties obtained from the least-squares fits to eqs 3-6 are listed in Table 6 and plotted as a function of temperature in Figures 8 and 9. The values of Cp,2° and V2° for morpholine and morpholinium chloride at low temperature are consistent with other similar

t, °C

p, bar

10 25 40 55 65 75 100 150 200 250 250 300

1 1 1 1 1 1 5 5 20 41 101 98

OC4H8NH2Cl

Cp,2°, J‚K-1‚mol-1

V2°, m3‚mol-1

Cp,2°, J‚K-1‚mol-1

V2°, cm3‚mol-1

221.4 236.6 247.9 254.1

81.36 82.23 83.66 84.25 115.53

36.53 72.79 93.80 104.98

91.4 93.5 94.7 94.3 96.74 96.88 95.41 94.67 87.75 63.32 71.07 8.34

88.74 93.50 100.36 109.95 131.63

molecules containing ether and amine groups.5,14,35 Although few temperature-dependent values have been reported, the need to include terms of the type a/(T - Θ)n to describe the temperature dependance below 25 °C is typical of other systems.3,29,30 The experimental values of Cp,φ,2 and Vφ,2 for morpholine and morpholinium chloride in Tables 1-3 at 25 °C agree with those of Kiyohara et al.13 to within experimental error. The results also agree with those of Cabani et al.14 to within the larger experimental scatter associated with adiabatic calorimetry. Our value Cp,2° ) 236 J‚K-1‚mol-1 for aqueous morpholine at 25 °C compares with values of 239 and 234 J‚K-1‚mol-1 from


Tremaine et al.

t

Figure 8. Standard partial molar volumes V2° of morpholine obtained from isothermal fitting to the experimental results at each temperature (shown as solid circles). The extrapolation to elevated temperatures by fitting the HKF model, eq 15, to the entire matrix of results, is shown as a dashed curve. The global fit, eq 6, is shown as the solid curve.

Figure 10. Standard partial molar volume change, ∆rV°, for the ionization of morpholine. The experimental results from Mesmer and Hitch11 are shown as solid circles with error bars. The curves represent our calculations based on the values for standard partial molar volumes of morpholine and morpholinium chloride from our experimental results: dashed line, HKF model; solid line, global fit.

The standard partial molar volume of morpholine chloride V2°(OC4H8NH2Cl, aq) is typical of other aqueous electrolytes which approach a strong negative discontinuity at the critical temperature of water due to the effects of long-range solvent polarization and the corresponding increase of the critical properties in the dilute aqueous solutions. 3.4. Morpholine Ionization. Mesmer and Hitch11 have determined pressure-dependant ionization constants for aqueous morpholine at temperatures up to 295 °C, from which the standard partial molar volume change of reaction ∆rV2° has been determined. These are plotted in Figure 10, along with the more accurate values for ∆rV2° calculated from our data for V2°(OC4H8NH, aq) and V2°(OC4H8NH2Cl, aq). Values of V2° (HCl, aq) for the calculation were taken from the expression reported by Shock and Helgeson29 which is based on data measured by Ellis and Mc Fadden37 from 20 to 200 °C and extrapolated to higher temperatures. The calculations were made for the “isocoulombic” reaction Figure 9. Standard partial molar volumes V2° of morpholinium chloride obtained from isothermal fitting to the experimental results at each temperature (shown as solid circles). The extrapolation to elevated temperatures by fitting the HKF model, eq 14, to the entire matrix of results, is shown as a dashed curve. The global fit, eq 5, is shown as the solid curve.

refs 15 and 16, respectively. Our value V2° ) 82.2 cm3‚mol-1 for aqueous morpholine at 25 °C is in excellent agreement with the value 82.5 cm3‚mol-1 reported by Kiyohara et al.13 The behavior of the standard partial molar volumes for morpholine V2° (OC4H8NH, aq) at elevated temperatures is similar to that observed for the few other aqueous nonelectrolytes that have been studied in this temperature range.5,6,38 The critical properties of morpholine36 (tc,2 ) 345 °C, pc,2 ) 54.7 bar) are lower than those of water (tc,1 ) 374 °C, pc,1 ) 221 bar). Although the critical locus has not been reported, normal type I behavior, in the classification of van Konynenburg and Scott,42 would lower the critical temperature and pressure of dilute aqueous solutions, causing V2° (OC4H8NH, aq) to rise toward a strong discontinuity at tc,1 ) 374 °C at steam saturation pressures.5,6

OC4H8NH(aq) + H+(aq) ) OC4H8NH2+(aq)

(11)

to eliminate the strong effect of the chloride anion. The data from Mesmer and Hitch agree with the more accurate results from the densitometer to within the combined experimental error, except at the low-temperature limit where artifacts from the curve fitting are most likely to occur. The relative contributions of OC4H8NH(aq), OC4H8NH2Cl(aq), and HCl(aq) to ∆rV2° are plotted in Figure 11. There is a significant difference in the high-temperature behavior of V2°(OC4H8NH, aq) and V2°(OC4H8NH2Cl, aq). From the similarity in the plots for V2°(OC4H8NH2Cl, aq) and V2°(HCl,aq), it is clear that much of the difference is due to the contribution of the chloride ion. This observation is confirmed by the small values of ∆rY2° which are almost independent of temperature. The potentiometric values of Mesmer and Hitch13 also provide a means of testing the accuracy of eq 5 for extrapolating lowtemperature Cp,2° data. Experimental values for ∆rCp,2° of reaction 11 are plotted in Figure 12, along with the extrapolated results. The results agree to within the combined experimental errors over the range of experimental data for Cp°(HCl, aq),


t

Figure 11. Contributions to the standard partial molar volume change, ∆rV° for the ionization of morpholine.

Figure 12. Standard partial molar heat capacity change, ∆rCp°, for the ionization of morpholine. The experimental results from Mesmer and Hitch11 are shown as solid circles with error bars. The curves represent our calculations based on the values for standard partial molar heat capacities of morpholine and morpholinium chloride from our experimental results: dashed line, HKF model; solid line, global fit.

10-140 °C. The deviations above 200 °C undoubtedly arise from uncertainties in the HCl data and in the second derivatives of the ionization constants required to calculate ∆rCp,2° from the potentiometric results. 4. Discussion 4.1. Hydration Effects. Standard partial molar volumes have been determined for only a very few simple electrolytes and nonelectrolytes under these conditions.5,29,38 These are the first data for a relatively large neutral molecule and its conjugate acid, for which both solvent polarization and nonelectrostatic solute-solvent interactions might be expected to be important. The standard partial molar heat capacity and standard partial molar volume are thought to contain contributions from solutesolvent interactions and the intrinsic properties of the solute which may be summarized as follows:4,39,40

Y2°(aq) ) Y2°(intr) + [∆hY2°(std state) + ∆hY2°(config)] + ∆hY2°(elec) (12)

J. Phys. Chem. B, Vol. 101, No. 3, 1997 417 Here, Y2°(intr) is the “intrinsic” or “hard core” volume or heat capacity of the isolated solute molecule, assumed to be equal to the value in the crystalline or pure liquid phase, and ∆hY2° is the volume or heat capacity of hydration, i.e. the transfer of the solute from the 1 bar (100 kPa) standard state in the gas to the hypothetical 1 mol kg-1 standard state for the solution. The term ∆hY2°(std state) is associated with the different standard states used for two phases, ∆hY2°(config) is the contribution from perturbations in the hydrogen-bonded structure of water caused by the presence of the solute through dispersion forces and geometric effects, and ∆hY2°(elec) is the electrostatic contribution resulting from the formation of a tightly bound primary solvation sphere about small cations and long-range solvent polarization due to charge-dipole interactions. At low temperatures, ∆hV2°(config) may be positive (“structure making”) when the presence of the solute expands the solvent by reinforcing local regions of hydrogen bonding, or negative (“structure breaking”) when hydrogen bonding disruptions case local solvent collapse as is the case for small cations in the region adjacent to the primary solvation sphere.39 At high temperatures ∆hY2°(config) is the term associated with the lowering or raising of the critical point of the solvent caused by the effect of neutral solutes in the infinite dilution limit. The behavior of Cp,2° and V2° for morpholinium chloride at 25 °C is consistent with group additivity models,35 as are the partial molar properties of morpholine. The agreement is somewhat unexpected because the hydration shell of morpholine is thought to contain one water molecule that acts as a hydrogenbonded bridge between the ether and amine groups, which cannot form in the morpholinium ion.14 The temperature dependance of Cp,2° and V2° for both solutes is unusually small. In aqueous solutions below 25 °C, bulky organic solutes are usually associated with negative values of for (∂Cp,2°/∂T)p and (∂V2°/∂T)p associated with structure making, while electrolytes show the opposite (structure breaking) behavior.39,40 The high-temperature behavior of V2° is described remarkably well by the terms containing (∂R/∂T)p and β in eqs 5 and 6 which dominate at elevated temperatures. The equations correctly predict the magnitude of the pressure dependance of V2°(OC4H8NH2Cl, aq), as discussed in the following section. The physical basis for the success of the “density” model of Mesmer et al.2,33 is inherent in all of the simple hydration models for electrolytes and nonelectrolytes5,39-41 which use Gibbs energy functions of transfer, ∆hG2°(elec), that are inverse functions of solvent density. The specific case of the Born function for ∆hY2°(elec) is discussed below. The magnitude of the hydration effects at elevated temperatures can be illustrated by the simple two-state model proposed by Mesmer et al.2 which considers the volume change in transferring n water molecules from the bulk to a close packed shell of hard spheres in the vicinity of an ion

V2°(aq) ) V2°(intr) + n[V1°(hard sphere water) V1°(bulk water)] (13) Taking the value V1°(hard sphere water) ) 18 cm3‚mol-1 yields a change in hydration number, ∆rn ) 31, for the ionization of morpholine at 300 °C (reaction 11), consistent with values obtained for the ionization of water, ammonia, hydrochloric acid, and sodium chloride which range from 19 to 35. The values obtained from V2°(OC4H8NH2Cl, aq) and V2°(OC4H8NH, aq) for the individual species, n ) 20 and n ) -11, respectively, show that the expansion of the solvent by the neutral species is a significant contribution to ∆rn and hence to the entropic effects that control ionization equilibria at elevated temperatures.2,33 4.2. The Born Equation and the Helgeson-KirkhamFlowers Model. Molecular dynamics calculations1 have shown


Tremaine et al.

TABLE 7: HKF Model Parameters for Morpholine OC4H8NH(aq) and Morpholinium Chloride OC4H8NH2Cl(aq) (Eqs 14 and 15) Cp,2°, J‚K-1‚mol-1

V2°, cm3‚mol-1

parameter

OC4H8NH

OC4H8NH2Cl

parameter

OC4H8NH

OC4H8NH2Cl

c1 c2

249.63 -1.35 × 105

184.84 -3.39 × 105

V1 V2

96.14 -1.03 × 103

103.60 -493.74

that, at elevated temperatures, ∆hY2°(elec) can be represented by the Born equation with remarkable success using an effective radius r > r(intr) to represent the immobilized water in the primary solvation sphere of small cations. The HelgesonKirkham-Flowers model3,30 is based on the Born equation, with a simple empirical function to describe all other terms in eqs 14 and15.

Cp,2° ) c1 + c2/(T - Θ)2 + ωXT

(14)

V2° ) V1 + V2/(T - Θ) - ωQ

(15)

As revised by Tanger and Helgeson,30 the HKF equations take the form at constant pressure. Here, the terms c1, c2, V1, and V2 are species-dependent fitting parameters. The terms ωTX and ωQ are the electrostatic contributions to the standard molar heat capacity and standard molar volume according to the Born equation

Q ) -1(∂ ln /∂p)T

(16)

X ) -1{(∂2 ln /∂T2)p + (∂ ln /∂p)T2}

(17)

ω ) Z2η/r(eff)

(18)

and

where is the static dielectric constant of water, η ) 6.9466 × 10-5‚J‚m-1‚mol-1, Z is the ionic charge, and r(eff) is an effective electrostatic radius of the species {r(eff) ) r(intr) + 0.94Z for cations; r(eff) ) r(intr) for anions}.3,29 In the calculations that follow, values for X and Q were calculated from the SUPCRT software package,31 which incorporates the Haar-GhallagherKell equation of state for water and the dielectric constant formulation of Johnson and Norton.43,44 The pressure dependance of c1, c2, V1, and V2 is small relative to steam saturation pressures3,30 and was ignored. It was not possible to reproduce the partial molar volume function if the hard sphere radius of the morpholinium ion was assumed to be equal to that of the neutral molecule, as calculated from the liquid density at 25 °C {The values r(intr) ) 3.261 Å and r(eff) ) 4.201 Å for the morpholinium ion and r(intr, Cl-, aq) ) 1.81 Å yield ω(OC4H8NH2Cl, aq) ) 5.448 × 105 J‚mol-1‚K-1 ) 5.448 × 106 cm3‚bar‚K-1‚mol-1}. Instead, ω was used as an adjustable parameter and was determined by a least-squares fit to values for V2°(OC4H8NH2Cl, aq), obtained by fitting eq 15 to the experimental apparent molar volumes at each temperature: ω ) 4.2788 × 106 cm3‚bar‚K-1‚mol-1. This value, which corresponds to r(intr) ) 14.7 Å for the morpholinium ion, suggests that the organic group causes significant solvent expansion at elevated temperatures. The values for the species-dependent fitting parameters c1, c2, V1, and V2 are listed in Table 7. The Born equation provides an explanation for the inverse pressure dependance of V2°(OC4H8NH2Cl, aq) at 250 °C plotted in Figure 7. As for other electrolytes at elevated temperatures,1-5,29 the greater compressibilty of water at low pressure enhances the long-range solvent polarization by the ion so that ∆hV2°(elec, psat) , ∆hV2°(elec, p ) 101 bar). The experimental value of (∆V2°/∆p)T at 250 °C is 0.13 cm3‚mol-1‚bar-1. Both

the Born term in eq 8 and the isothermal compressibility term in eq 6 predict (∆V2°/∆p)T ) 0.08 cm3‚mol-1‚bar-1. Finally, we note the significance of the volume of ionization, {V2°(OC4H8NH2+, aq) - V2°(OC4H8NH, aq) - V2°(H+, aq)}, plotted in Figure 11. These negative values (∼-20 cm3‚mol-1 at 200 °C), which are largely due to the difference between the proton in the secondary ammonium group in the mopholinium ring and the free, hydrated proton, are consistent with the large effective radius (r(eff, H+, aq) ) 3.08 Å) used by Ellis and McFadden37 and Tremaine et al.28 to describe V2°(H+, aq) and Cp,2°(H+, aq) by the Born equation over the range of the available experimental data. These extend to only 200 and 140 °C , respectively. In recent years, the HKF equation has been widely applied to aqueous nonelectrolytes, most notably by Shock and coworkers,29 despite the fact that the Born model is entirely without a theoretical basis for describing the solvation of neutral solutes. In effect, these authors use eqs 14 and 15 as fitting equations, which usually produce negative values of ω, implying that Z is a fractional imaginary number. Figure 8 illustrates the results of fitting eq 14 to V2°(OC4H8NH, aq) using the procedure outined above with ω used as an adjustable parameter (ω ) -1.7144 × 106 cm3‚bar‚K-1mol-1). The fitted parameters are listed in Table 7. Although less accurate than eqs 5 and 6, which have more adustable constants for the low-temperature region, the model does in fact reproduce the data adequately. Values for the standard partial molar heat capacity change of the ionization reaction, as calculated from the HKF equation with these “best” parameters, are plotted in Figure 12. Clearly the HKF expression also yields acceptably accurate results for the extrapolated values of ∆rCp°, although eq 5 is more accurate at low temperatures. The explanation lies in the Born term which is derived from a Gibbs energy transfer function that is approximately proportional to the reciprocal density of water. The Born function Q, used in eq 16, is approximately proportional to β over the entire temperature and pressure range used in this work. The proportionality may be expressed as

Q/β ) (F/3)(∂/∂F)T

(19)

Johnson and Norton44 have used the modified UematatsuFranck equation for the static dielectric constant of water to derive the equation

Q/β ) (

∑|Kl(T)Fl)/(∑Kl(T)Fl)2

(20)

where Kl(T) is a temperature-dependant polynomial. The physical basis for this behavior has been explored by Fernandez et al.45 using the Harris-Alder and Onsager-Kirkwood equations for . The tight correlation between Q and β allows the eqs 14 and 15 to be used as an analog to the density model (eqs 5 and 6) with ω as a purely empirical adjustable parameter. 5. Conclusions The measurements reported here for standard partial molar and excess properties of aqueous morpholine and morpholine chloride are consistent with the potentiometric measurements of Mesmer and Hitch.11 Together, the two studies provide quite

Properties of Morpholine and Morpholinium Chloride a complete thermodynamic model for the neutral solute, its conjugate acid, and the ionization of morpholine up to 300 °C. The results show that the effect of solvent expansion by the neutral species is significant at elevated temperatures. The effective Born radius of ions containing organic groups could be significantly larger than the radius calculated from the formula for simple cations because of this effect. Finally, we note that the fitting expressions based on the appropriate solvent density derivatives allow quite accurate estimates of Cp,2° to be made from V2° data at elevated temperatures and pressures. Acknowledgment. This work was supported by the Natural Science and Engineering Research Council of Canada (NSERC) and Memorial University of Newfoundland. References and Notes (1) Wood, R. H.; Carter, R. W.; Quint, J.; Majer, V.; Thompson P. T. J. Chem. Thermodyn. 1994, 26, 225. (2) Mesmer, R. E; Palmer, D. A.; Simonson, J. M. In ActiVity Coefficients in Electrolyte Solutions, 2nd ed.; Pitzer, K. S., Ed.; CRC Press: Boca Raton, FL, 1991; Chapter 8. (3) Shock, E.; Sverjensky, D.; Helgeson, H. J. Chem. Soc., Faraday Trans. 1992, 88, 803. (4) Tremaine, P. R.; Goldman, S. J. Phys. Chem. 1978, 82, 2317. (5) Fernandez-Prini, R. J.; Corti, H. R.; Japas, M. L. High-Temperature Aqueous Solutions: Thermodynamic Properties; CRC Press: Boca Raton, FL, 1992. (6) Levelt Sengers, J. M. H. In Supercritical Fluid Technology; Bruno, J. J., Ely, J. F., Eds.; CRC Press: Boca Raton, FL, 1991; Chapter 1. (7) Gilbert, R.; Lamarre, C. Can. J. Chem. Eng. 1989, 67, 646. (8) ASME Handbook on Thermodynamic Properties of Water; Cohen, P., Ed.; American Society of Mechanical Engineers: New York, 1989. (9) Hetzner, H. B.; Bates, R. G; Robinson, R. A. J. Phys. Chem. 1966, 70, 2869. (10) Czerminski, J. B.; Dickson A. G. J. Solution Chem. 1982, 11, 79. (11) Mesmer, R. B.; Hitch, B. F. J. Solution Chem. 1977, 6, 251. (12) Wetton, E. A. M.; Lewis, G. G. In Water Chemistry for Nuclear Reactor System; BNES: London, 1986; Paper 99. (13) Kiyohara, O. K.; Peron, G.; Desnoyers, J. E. Can. J. Chem. 1978, 53, 2591. (14) Cabani, S.; Conti, G.; Matteoti, E. J. Solution Chem. 1976, 5, 125. (15) Vogel, A. Textbook of QuantitatiVe Chemical Analysis, 5th ed.; Revised by Jeffery, G. H., Bassett, J., Mendham, J., Denney, R. C., Eds.; Bath Press: Avon, 1989. (16) Picker, P.; Leduc, P. A.; Phillys, R. R.; Desnoyers, J. E. J. Chem. Thermodyn. 1971, 3, 631.

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Thermodynamic Properties of Aqueous Morpholine and Morpholinium

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