Isochoric heat capacity measurements for H2O + CH3OH mixture in the near-critical and supercritical regions

Fluid Phase Equilibria 252 (2007) 33–46

Isochoric heat capacity measurements for H2O + CH3OH mixture in the near-critical and supercritical regions N.G. Polikhronidi a , I.M. Abdulagatov b,∗ , G.V. Stepanov a , R.G. Batyrova a a

Institute of Physics of the Dagestan Scientific Center of the Russian Academy of Sciences, 367003 Makhachkala, M. Yaragskogo Str.94, Dagestan, Russia b Institute for Geothermal Problems of the Dagestan Scientific Center of the Russian Academy of Sciences, 367030 Makhachkala, Shamilya Str.39, Dagestan, Russia Received 24 August 2006; received in revised form 5 December 2006; accepted 5 December 2006 Available online 13 December 2006

Abstract The isochoric heat capacity of two (0.5004 and 0.5014 mole fraction of methanol) H2 O + CH3 OH mixtures has been measured in a range of temperatures from 371 to 579 K and densities between 214 and 394 kg m−3 . Measurements were made with a high-temperature, high-pressure, nearly constant-volume adiabatic calorimeter. The measurements were performed in the one- and two-phase regions including the coexistence curve, and in the near-critical and supercritical regions. Temperatures at the phase transition curve TS (ρ) for each of the measured densities and the critical parameters (TC and ρC ) for the 0.4996H2 O + 0.5004CH3 OH mixture were obtained using the method of quasi-static thermograms. The uncertainty of the heat-capacity measurements is estimated to be 2%. Uncertainties of the density, temperature and concentration measurements are estimated to be 0.15%, 15 mK and 5 × 10−5 mole fraction, respectively. The derived values of the critical parameters, together with published data, were used to calculate the value of the Krichevskii parameter. The near-critical isochoric heat capacity behavior for the 0.4996H2 O + 0.5004CH3 OH mixture was studied using the principle of isomorphism of the critical phenomena in binary mixtures. © 2006 Elsevier B.V. All rights reserved. Keywords: Adiabatic calorimeter; Coexistence curve; Critical point; Isochoric heat capacity; Krichevskii parameter; Methanol; Water

1. Introduction In recent years, methanol and water + methanol mixtures under supercritical conditions have attracted the attention of different research groups due to their industrial and technological applications. However, we do not yet have a sufficient understanding of the microscopic structural properties of supercritical aqueous alcohol mixtures including the nature of hydrogen bonding, which is responsible for the unusual thermodynamic behavior in the near-critical and supercritical conditions. The thermodynamic properties of H2 O + CH3 OH mixture are vital to a fundamental understanding, on the molecular level, of important physical and chemical phenomena that occur in near-critical and supercritical fluids and fluid mixtures. These phenomena include hydrogen bonding (association) and chemical reac∗ Corresponding author. Present address: Physical and Chemical Properties Division, National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, U.S.A. Tel.: +1 303 497 4027; fax: +1 303 497 5224. E-mail address: [email protected] (I.M. Abdulagatov).

0378-3812/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2006.12.005

tions (thermal decomposition) which both affect the structure and thermodynamic properties of near-critical and supercritical fluids [1,2]. Aqueous alcohol solutions contain H-bonded molecular associations that lead to anomalies in thermodynamic and structural properties. In mixtures, hydrogen bonding interactions can occur between molecules of the same species (self-association) or between molecules of different species (solvation). Therefore, the structural and thermodynamic properties of aqueous alcohol solutions are governed by the hydrogen bonding. Unfortunately, statistical mechanics (calculation of the structural and thermodynamic properties of a fluid from knowledge of the intermolecular interactions) can give inaccurate or even physically impossible results when applied to hydrogen bonded fluids. Experimental and theoretical studies of the thermodynamic and structural properties of aqueous alcohol mixtures at supercritical conditions can thus provide clues to a better understanding of the unusual thermodynamic behavior of supercritical aqueous solutions on a microscopic level. Furthermore, it can improve our grasp of supercritical fluid technologies and chemical reactions in supercritical media [3,4]. In

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mixtures in which alcohol is one of the components, the thermodynamic properties may exhibit anomalies due to the presence of H-bonded molecular associations. Alcohol molecules strongly affect water structure; therefore, mixtures of water + alcohol show anomalies in various physical properties [4]. Due to their high polarity, water and alcohol are complicated liquids and are a challenge to study both experimentally and theoretically. Their mixtures form a quite complex liquid system. In contrast to physical interactions, chemical interactions (hydrogen-bonding) are short-ranged and highly directional. A deeper understanding of the structure and nature of supercritical aqueous systems will lead to marked improvements in important practical applications for environmental, mechanical, chemical, biological and geothermal industries, and new thermodynamic data for aqueous solutions at near-critical and supercritical conditions are of great consequence. Measurements of the thermodynamic properties of the H2 O + CH3 OH mixture in the near-critical and the supercritical regions are scarce. A heat capacity (CV VTx) experiment is both a powerful and a structurally sensitive means to study structural changes (phase transition and critical phenomena). Precise experimental (CV VTx) data will also prove useful for the development of a physico-chemical model of the thermodynamic properties of strong hydrogen-bonding mixtures in the near-critical and supercritical conditions and to study the effect of supercritical media (supercritical water) on the Hbonding mechanism [1]. There are no (CV VTx) measurements for aqueous methanol mixtures in the near-critical and supercritical regions. This is due to considerable experimental difficulties involving their polarity (unstable molecules of methanol at high temperatures) and severe (experimental difficulties due to high temperature and high pressure) supercritical condition. Previously, the isochoric heat capacity of H2 O + CH3 OH mixture at low temperatures (below 420 K) and at pressures up to 30 MPa were measured by Kuroki et al. [5], Kitajima et al. [6] and Aliev et al. [7]. Measurements were made with a twin-cell adiabatic calorimeter. The uncertainty of the heat capacity measurements is within 1.0–2.2%. Abdulagatov et al. [8] reported (CV VTx) measurements for H2 O + CH3 OH mixture in the critical and supercritical regions (at temperatures from 435 to 645 K and at densities from 250 to 450 kg m−3 ) at a concentration of 0.5 mass fraction. The uncertainty in (CV VTx) measurements is 4.5% in the critical and supercritical regions. Recently, Bulemela et al. [9] measured of the volumetric behavior of a H2 O + CH3 OH mixture in the vicinity of the critical region with a vibrating-tube densimeter. Bazaev et al. [10] used constant-volume piezometer to measure PVTx properties of 0.64H2 O + 0.36CH3 OH mixture in the critical and supercritical regions. The uncertainty in density measurements is 0.16%. They also extracted the values of the critical parameters (TC , PC , ρC ) for this concentration using the isochoric P–T and isothermal P–ρ break point technique near the critical point. The uncertainties of the derived values of the critical temperature, the critical pressure and the critical density are 0.6 K, 0.4 MPa and 10 kg m−3 , respectively. Xiao et al. [11] used a vibrating-tube densimeter to measure the density of H2 O + CH3 OH mixtures at temperatures from 323 to 573 K and at pressures between 7 and 13.5 MPa. The val-

ues of the critical temperature and the critical pressure were determined from analysis of the experimental behavior of the excess molar volumes. Hynˇcica et al. [12] reported densities for dilute aqueous solutions of methanol and derived partial molar values at infinite dilution in the temperature range from 298.15 to 573.15 K and at pressures up to 30 MPa. Measurements were made with a high-temperature and high-pressure flow vibrating-tube densimeter. The uncertainty in the density measurements is about 10−3 kg m−3 . Simonson et al. [13] reported excess molar enthalpies for this mixture at temperatures from 298 to 573 K and at pressures up to 40 MPa. Wormald et al. [14] used a new high temperature and high pressure differential flow mixing calorimeter to measure the excess enthalpies of H2 O + CH3 OH mixtures over the temperature range from 423 to 523 K at pressures up to 20 MPa. Five sources (Bazaev et al. [10], Xiao et al. [11], Marshal and Jones [15], Griswold and Wong [16] and Wormald and Yerlett [17]) of data for the critical parameters were found in the literature for the H2 O + CH3 OH mixture. Marshall and Jones [15] measured the liquid + vapor critical temperatures of H2 O + CH3 OH mixtures over the entire composition range with a precision of ±0.4 K using a visual method. Only three data points, reported by Bazaev et al. [10], Xiao et al. [16] and Griswold and Wong [16], for the critical pressure of the H2 O + CH3 OH mixture were found in the literature. Only one data point reported by Bazaev et al. [6] is available for the critical density of the 0.64H2 O + 0.36CH3 OH mixture. Thus, the major objective of this paper is to provide accurate isochoric heat capacity data (CV VTx) and phase boundary (TS , ρS , x) properties for H2 O + CH3 OH mixtures in the critical and supercritical regions. Previously, we have measured the isochoric heat capacity of the pure components H2 O and CH3 OH near the critical and supercritical regions [18–22]. The same apparatus was used to measure CV VTx for H2 O + CH3 OH mixtures. To check and confirm the accuracy of the method, the isochoric heat capacity measurements at the critical isochore 321.96 kg m−3 (IAPWS accepted values of the critical density is 322 kg m−3 ) for pure water were compared with the IAPWS fundamental equation of state [23]. The agreement of measured and calculated values of the isochoric heat capacity along the critical isochore is within 3–4%. 2. Experimental The experimental apparatus used for isochoric heat capacity measurements for the H2 O + CH3 OH mixture is the same as that used previously for measurements on pure fluids (H2 O, D2 O, CO2 , CH3 OH, C2 H5 OH, C2 H6 , C3 H8 , C7 H16 , C10 H22 , N2 O4 ) and fluid mixtures (H2 O + D2 O, H2 O + C2 H5 OH, CO2 + C10 H22 , C2 H6 + C3 H8 ) [18–22,24–31]. A complete description of the apparatus and the method is provided in earlier publications [32–34], and thus only a brief discussion of them will be given here. The isochoric heat capacities were measured with a high-temperature, high-pressure, adiabatic and nearly constant-volume calorimeter, with an uncertainty of 2–3% in the critical and supercritical regions. The volume of the calorimeter, approximately 105.126 ± 0.05 cm3

N.G. Polikhronidi et al. / Fluid Phase Equilibria 252 (2007) 33–46

(at atmospheric pressure and 297.15 K), is a function of temperature and pressure. The values of calorimeter volume were determined using the highly accurate, IAPWS accepted PVT values for pure water calculated from the Wagner and Pruß equation of state [23]. The uncertainty in the determination of volume at any T and P in our experiment is about 0.05%. The mass of the sample was measured using a weighing method with an uncertainty of 0.05 mg. Therefore, the uncertainty in the measurements of density ρ = m/V(P,T) is about 0.06%. The heat capacity was obtained from the measured quantities m, Q, T and C0 . The thermometer was calibrated on the ITS-90 scale. The uncertainty of temperature measurements was less than 15 mK. The heat capacity of the empty calorimeter C0 was determined experimentally using a reference substance (helium4) with well-known heat capacities [35], in the temperature range up to 1000 K at pressures up to 30 MPa. The uncertainty in the heat capacity data used for calibration of C0 is 0.2%. The correction related to the non-isochoric behavior during heating was determined to an uncertainty of about 4.0–9.5% depending on the density. The absolute uncertainty in CV is 0.013 kJ K−1 due to difficulties maintain the adiabatic condition. The combined standard uncertainty related to the indirect character of CV measurements did not exceed 0.16%. Based on the detailed analysis of all sources of uncertainties likely to affect the determination of CV with the present system, the combined standard uncertainty (at a coverage factor of two) of measuring the heat capacity with allowance for the propagation of uncertainty related to the non-isochoric conditions of the process was 2%. Heat capacity was measured as a function of temperature at nearly constant density. The calorimeter was filled at room temperature, sealed off and heated along the quasi-isochore. Each run for heat capacity was normally started in the twophase region and completed in the one-phase (liquid or gas depending on the filling factor) region. This method enables one to determine, to a high accuracy, the transition temperature TS of the system from the two-phase to a single-phase state (i.e., to determine TS and ρS data corresponding to the phase-coexistence curve), the jump in the heat capacity CV , and reliable CV data in the one- and two-phase regions (see refs. [32,34,36]). The method of quasi-static thermograms (temperature versus time, T–τ plot) is used to accurately determine the location of the liquid–vapor (L–V) phase transition boundary for the H2 O + CH3 OH mixture near the critical point. The details and basic idea of the method of quasi-static thermograms and it application to complex thermodynamic systems are described in detail elsewhere [36,38–40]. The method of quasi-static thermograms makes it possible to obtain reliable data up to temperatures of TC ± 0.01 K with an uncertainty of 0.02 K. The water was triply distilled and degassed and had an electric conductivity of about 10−4 −1 m−1 . The purity of CH3 OH was 99.95 mole%. 3. Results and discussion Measurements of the isochoric heat capacity for two mixtures (0.5004 and 0.5014 mole fraction) H2 O + CH3 OH were performed along 10 liquid and vapor isochores: 214.42, 235.00,

35

244.77, 252.54, 251.44, 259.50, 269.50, 290.78, 342.10 and 394.80 kg m−3 . The temperature range was 371–579 K. The measurements were made in the one- and two-phase regions including near- and supercritical conditions. A total of 20 values of CV and TS were measured on the coexistence curve near the critical point. The experimental one- and two-phase isochoric heat capacity data for H2 O + CH3 OH mixtures are given in Table 1 and shown in Figs. 1 and 2 in the CV –T and CV –ρ projections along the various near-critical isochores (Fig. 1a and b) and supercritical isotherms (Fig. 2). In Fig. 1a and b, the temperature dependence of CV along each measured isochores near the phase transition temperatures TS shows discontinuous behavior (jumpily decreases or increases) on passing through the phase transition points. Fig. 2 demonstrates that the CV –ρ curve along the near-critical isotherm of 562.63 K exhibits a noticeable maximum at a density between 260 and 275 kg m−3 . As temperature increases (when moving away from the critical isotherm), the maximum of CV is sharply decreases. 3.1. Isochoric heat capacities and densities of H2 O + CH3 OH mixture at saturation The isochoric heat capacity experiments described above also allow simultaneous measurements of one- and two-phase CV , temperatures TS and densities ρS at saturation (at the phase transition boundary). The measured values of CV , TS and ρS at saturation are given in Table 2. Fig. 3 demonstrates the temperature dependence of the one-phase (right) and two-phase (left) isochoric heat capacities for the saturated liquid H2 O + CH3 OH mixture. As one can see from Fig. 3, the measured values of CV monotonically increases as the temperature approaches the critical point without any criticality as is exhibited for pure components. The measured values of saturated density derived by using the quasi-static thermogram method are presented in Fig. 4 together with the values for pure components calculated from the IAPWS [23] and the IUPAC [37] equations of state. Fig. 4 include also the values of saturated density reported by other authors in the range far from the critical point. As one can see, the agreement between the present values and the data reported by other authors for the saturation densities is fairly good, within 0.5–1.0%. 3.2. Critical parameters of H2 O + CH3 OH mixture Fig. 5 illustrates the temperature dependence of the liquid (CV = CV 2 − CV 1 , where CV 2 , CV 1 are the two- and one-phase liquid isochoric heat capacities at saturation, respectively) and vapor (CV = CV 2 − CV 1 , where CV 2 , CV 1 are the two- and one-phase vapor isochoric heat capacities at saturation, respectively) isochoric heat capacity jumps of the H2 O + CH3 OH mixture at saturation. As one can see from Fig. 5, both CV –T and CV –T curves cross at the critical point of TC = 562.51 ± 0.5 K, where the liquid and vapor phases become identical, providing the temperature of the critical points of the mixture. One can note in Fig. 5 that isochoric heat capacity jumps do not diverge as the temperature approaches the critical point as is observed for pure fluids and some binary mixtures (see

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Table 1 Experimental values of the one- and two-phase isochoric heat capacities of H2 O + CH3 OH mixtures ρ = 394.80 (kg m−3 )

ρ = 342.10 (kg m−3 )

ρ = 290.78 (kg m−3 )

T (K)

CVX (kJ kg−1 K−1 )

T (K)

CVX (kJ kg−1 K−1 )

T (K)

CVX (kJ kg−1 K−1 )

371.885 372.108 372.554 415.668 446.086 446.399 455.501 455.800 456.098 494.623 494.909 495.290 531.163 531.344 531.528 535.206 535.573 535.756 547.438 547.619 547.800 547.982 555.681 555.774 555.853 556.012 556.123 556.213 556.392 556.452 556.547 556.632 556.785 556.803 556.816 556.816 556.884 556.974 557.066 557.154 557.923 558.193 558.376 558.463 558.643 558.829 559.002 559.182 562.593 562.772 562.861 562.951 563.130 571.434 571.612 571.701 571.878

3.540 3.527 3.534 4.149 4.107 4.193 4.624 4.708 4.655 4.913 4.982 4.847 6.405 6.475 6.568 6.499 6.549 6.517 6.839 6.903 6.895 6.790 7.688 7.837 7.835 7.858 7.849 7.878 7.958 7.899 7.844 7.922 7.915 7.894 7.922 4.538 4.517 4.519 4.531 4.603 4.490 4.494 4.531 4.466 4.420 4.403 4.447 4.389 4.221 4.219 4.194 4.109 4.067 4.049 3.928 3.958 3.967

531.530 531.712 531.896 531.988 551.607 551.788 551.969 552.059 558.875 558.964 559.143 559.324 559.414 559.480 559.480 559.482 559.572 559.663 559.750 559.844 559.932 561.337 561.516 561.607 564.831 565.010 565.189 565.279 565.368 574.100 574.188 574.455 574.633 – – – – – – – – – – – – – – – – – – – – – – – –

6.921 6.897 6.963 7.112 7.671 7.664 7.565 7.642 9.302 9.351 9.406 9.530 9.756 9.768 5.640 5.634 5.634 5.502 5.582 5.498 5.487 4.930 4.971 4.857 4.595 4.539 4.510 4.431 4.428 4.173 3.975 3.964 4.007 – – – – – – – – – – – – – – – – – – – – – – – –

531.528 531.712 531.896 532.086 549.887 550.068 550.249 550.430 558.823 559.002 559.187 559.365 559.499 559.589 559.631 559.768 559.858 559.990 560.080 560.171 560.278 560.369 560.457 560.544 560.637 560.729 560.817 560.874 560.874 560.896 560.917 560.934 561.022 561.118 561.204 561.298 562.772 562.951 563.131 563.220 567.870 568.048 568.226 568.316 577.734 577.912 578.089 578.177 578.266 – – – – – – – –

7.510 7.683 7.662 7.731 7.998 8.019 7.978 7.997 9.843 9.992 10.04 10.08 10.01 10.10 10.07 9.990 10.00 10.10 10.12 10.14 10.23 10.26 10.42 10.41 10.53 10.61 10.54 10.54 6.455 6.427 6.419 6.370 6.375 6.288 6.260 6.208 5.465 5.305 5.201 5.194 4.869 4.819 4.741 4.691 4.289 4.262 4.228 4.177 4.127 – – – – – – – –

N.G. Polikhronidi et al. / Fluid Phase Equilibria 252 (2007) 33–46

37

Table 1 (Continued ) ρ = 269.50 (kg m−3 )

ρ = 259.50 (kg m−3 )

ρ = 251.44 (kg m−3 )

T (K)

CVX (kJ kg−1 K−1 )

T (K)

CVX (kJ kg−1 K−1 )

T (K)

CVX (kJ kg−1 K−1 )

551.064 551.155 551.336 551.428 551.517 551.608 560.619 560.709 560.889 560.978 561.068 561.158 561.226 561.316 561.403 561.403 561.490 561.580 561.675 566.888 566.066 566.245 566.424 578.089 578.266 578.354 578.531 578.620 – – – – – – – – – –

8.648 8.517 8.445 8.520 8.504 8.626 10.34 10.29 10.27 10.34 10.49 10.60 10.86 10.69 10.86 6.803 6.816 6.776 6.559 4.864 4.777 4.653 4.647 4.193 4.165 4.168 4.096 4.136 – – – – – – – – – –

503.829 504.018 504.207 504.396 522.003 522.281 522.467 522.652 522.838 532.080 532.174 532.356 532.540 544.801 545.074 545.347 551.426 551.607 551.786 551.968 560.786 560.966 561.056 561.235 561.415 561.504 561.597 561.673 561.673 561.772 561.863 562.234 562.503 562.682 562.774 570.989 571.256 571.523

6.612 6.534 6.597 6.607 7.093 7.144 7.070 7.193 7.140 7.398 7.290 7.317 7.383 7.739 7.810 7.811 8.600 8.572 8.570 8.579 10.37 10.52 10.32 10.42 10.47 10.65 10.79 10.95 6.916 6.840 6.793 5.745 5.508 5.324 5.262 4.458 4.483 4.364

516.975 517.162 517.348 517.535 536.490 536.673 536.857 536.948 537.040 552.149 552.240 552.423 552.605 552.696 556.933 557.113 557.295 557.474 557.561 557.653 560.648 560.828 560.917 561.009 561.097 561.276 561.458 561.635 561.725 561.797 561.797 561.815 561.905 562.084 562.174 572.342 575.608 575.874

7.104 7.006 7.019 7.043 7.814 7.825 7.819 7.799 7.804 8.709 8.700 8.771 8.804 8.764 9.000 9.094 9.007 9.080 9.097 9.067 10.36 10.50 10.55 10.56 10.79 10.85 10.71 10.91 10.92 11.05 7.029 6.830 6.135 5.961 5.917 4.440 4.361 4.295

ρ = 235.00 (kg m−3 )

ρ = 214.42 (kg m−3 )

ρ = 252.54a (kg m−3 )

T (K)

CVX (kJ kg−1 K−1 )

T (K)

CVX (kJ kg−1 K−1 )

T (K)

CVX (kJ kg−1 K−1 )

554.589 554.678 554.767 554.951 555.040 555.131 560.350 560.530 560.709 560.883 561.068 561.271 561.362 561.450 561.544 561.690 561.709 561.709 561.720 561.809 561.903

9.406 9.376 9.685 9.451 9.517 9.566 9.947 9.980 10.14 10.31 10.57 10.81 10.77 10.96 10.96 11.07 11.09 6.952 6.937 6.383 6.090

495.862 496.052 496.247 496.339 496.433 531.804 531.988 532.264 532.449 540.334 540.608 540.882 550.611 550.793 550.974 551.194 559.812 559.991 560.260 560.440 560.967

7.080 7.119 7.187 7.160 7.090 8.543 8.510 8.590 8.603 8.765 8.748 8.749 9.400 9.415 9.473 9.398 10.80 10.82 10.82 10.83 10.86

540.790 540.973 541.196 541.338 550.702 551.245 558.823 559.182 559.362 561.158 561.337 561.519 561.607 561.786 561.876 561.966 561.966 561.991 562.080 562.170 562.259

8.300 8.339 8.331 8.290 8.483 8.506 9.692 9.613 9.684 10.71 10.67 10.80 10.76 10.89 10.87 10.94 6.957 6.459 6.235 6.051 5.993

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Table 1 (Continued ) ρ = 235.00 (kg m−3 ) T (K) 562.052 562.231 562.410 562.593 562.772 562.951 571.335 571.523 571.612 571.783 571.878 572.059

ρ = 214.42 (kg m−3 ) CVX (kJ kg−1 K−1 ) 6.147 5.919 5.795 5.793 5.729 5.500 4.794 4.626 4.616 4.501 4.603 4.595

ρ = 252.54a (kg m−3 )

T (K)

CVX (kJ kg−1 K−1 )

T (K)

561.248 561.337 561.478 561.494 561.494 561.542 561.632 561.811 561.991 562.170 – –

10.75 10.89 10.90 10.95 6.601 6.170 5.729 5.534 5.604 5.401 – –

562.346 562.794 568.227 568.673 577.292 577.735 578.089 578.354 578.531 – – –

CVX (kJ kg−1 K−1 ) 5.916 5.770 4.755 4.701 4.388 4.341 4.354 4.300 4.282 – – –

ρ = 244.77a (kg m−3 ) T (K)

CVX (kJ kg−1 K−1 )

T (K)

CVX (kJ kg−1 K−1 )

503.168 503.357 503.735 513.236 513.704 513.892 522.188 522.560 522.745 531.864 531.988 532.080 532.264 540.608 540.973 541.156 541.338 550.159 550.340 550.521 550.883 550.974 555.401 555.581 555.852

7.019 6.955 6.980 7.503 7.477 7.480 7.630 7.654 7.675 8.203 8.289 8.300 8.294 8.333 8.350 8.394 8.403 8.483 8.505 8.554 8.634 8.639 8.913 9.093 9.070

556.032 560.350 560.529 560.709 560.978 561.105 561.284 561.367 561.468 561.644 561.733 561.825 561.913 561.944 561.944 562.071 562.161 562.250 562.344 568.941 569.119 569.297 569.476 – –

9.104 10.51 10.49 10.40 10.48 10.64 10.79 10.84 10.84 10.72 10.75 10.92 10.84 10.90 6.933 6.820 6.678 6.546 6.346 4.914 4.818 4.745 4.688 – –

a

x = 0.5014 mole fraction of methanol.

also Section 3.4). Fig. 2 demonstrates that the maximum of the CV –ρ curve along the selected near-critical isotherm of 562.63 K occurs at a density between 260 and 275 kg m−3 . As was shown in our previous publication (Abdulagatov et al. [41]), the curve of the loci of the isothermal maxima of CV in the T–ρ plane starts at the critical point and then moves (shifts) to lower densities down to approximately ρ ≈ 0.9ρC and then turns to higher densities until it joins with the isothermal CV minima curve at temperature of about T ≈ 1.35TC . Therefore, the maximum of CV –ρ curve along the critical isotherm (TC = 562.51 ± 0.5 K) occurs at a density above 275 kg m−3 , i.e. the critical density for this mixture ρC > 275 kg m−3 . Our estimated value of the critical density (by extrapolating to the critical isotherm of TC = 562.51 ± 0.5 K) is ρC = 280 ± 5 kg m−3 . The derived values of the critical parameters for 0.4994H2 O + 0.5004CH3 OH are plotted in Fig. 6 in the TC –x,

ρC –x and PC –x projections along with the values reported by other authors from the literature [10,11,15–17]. The critical temperature and density obtained are in fair agreement with the data reported by other authors (see Fig. 6). Our value of TC = 562.51 ± 0.5 K is in satisfactory (difference is 1.19 K) agreement with the interpolated value of TC = 563.7 ± 0.4 K at x = 0.5004 mole fraction calculated from the data by Marshall and Jones [15], but is significantly lower (by 3.49 K) than the value (566.0 K) reported by Wormald and Yerlett [17] for the concentration of 0.5 mole fraction. The value of the critical pressure estimated by the relation recommended by Reid et al. [42] using the derived value of the critical temperature of 562.51 K is PC = 12.34 MPa. As one can see from Figs. 6 and 7, this value of the critical pressure is slightly (by 0.46 MPa) lower than interpolated value. This is still acceptable because the value is within the uncertainty of the prediction technique.

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Fig. 1. (a and b) Experimental one- and two-phase isochoric heat capacities of H2 O + CH3 OH mixtures as a function of temperature along the near-critical isochores.

Figs. 4, 6 and 7 demonstrate the behavior of the critical lines of the H2 O + CH3 OH mixture in the TC –x, ρC –x, PC –x, TC –ρC and TC –PC projections. As one can see from Fig. 6, the agreement between the critical temperature data reported by various authors is satisfactory, except the value reported by Griswold and Wong [16]. The value of the critical temperature and pressure reported by Griswold and Wong [16] for the concentration of x = 0.79 mole fraction is significantly (by 8 K) lower than other published data. As Fig. 6 demonstrates, the critical curves for H2 O + CH3 OH in TC –x, PC –x and ρC –x projections shows a slightly negative deviation from ideal mixture behavior.

The PC –TC and ρC –TC projections of the critical locus of H2 O + CH3 OH mixture together with vapor pressure and coexistence curve for pure components are presented in Figs. 4 and 7. As one can see from these figures, the critical curves of the H2 O + CH3 OH mixture are continuous and connect the critical points of both pure components (H2 O and CH3 OH) without any anomalies (without maximum and minimum). As Fig. 7 shows, the critical line for the H2 O + CH3 OH mixture in the PC –TC projection almost linearly connects the critical points of both pure components (with a very slight negative deviation from ideal mixture behavior). In the P–T diagram (see Fig. 7), the critical

40

N.G. Polikhronidi et al. / Fluid Phase Equilibria 252 (2007) 33–46 Table 2 Isochoric heat capacities of H2 O + CH3 OH mixture at saturation TS (K)

ρS (kg m−3 )

CV 2 (kJ kg−1 K−1 )

x = 0.5004 mole fraction of CH3 OH 556.816 394.80 7.992 559.480 342.10 9.768 560.874 290.78 10.540 561.403 269.50 10.864 561.673 259.50 10.950 561.797 251.44 11.051 561.709 235.00 11.090 561.494 214.42 10.948 TS (K)

ρS (kg m−3 )

CV2 (kJ kg−1 K−1 )

x = 0.5014 mole fraction of CH3 OH 561.966 252.54 10.937 561.944 244.77 10.903

CV 1 (kJ kg−1 K−1 ) 4.538 5.640 6.455 6.803 6.916 7.029 6.952 6.600 CV1 (kJ kg−1 K−1 ) 6.957 6.933

Fig. 2. Experimental isochoric heat capacities of 0.4996H2 O + 0.5004CH3 OH as a function of density along the near- and supercritical isotherms.

line is the envelope of the (P,T) loops and the two-phase region is limited by both coexistence curves and the critical line.The present derived critical property data for the H2 O + CH3 OH mixture together with published data were fitted to an empirical polynomial function as a function of composition TC (x) = (1 − x)TC1 + xTC2 + x(1 − x) × [T1 + (1 − 2x)T2 + (1 − 2x)2 T3 ],

(1)

3.3. Shape of the critical lines and Krichevskii parameter of H2 O + CH3 OH mixture

PC (x) = (1 − x)PC1 + xPC2 + x(1 − x) × [P1 + (1 − 2x)P2 + (1 − 2x)2 P3 ],

(2)

ρC (x) = (1 − x)ρC1 + xρC2 + x(1 − x) × [ρ1 + (1 − 2x)ρ2 + (1 − 2x)2 ρ3 ],

where TC1 = 647.096 K, PC1 = 22.064 MPa, ρC1 = 322.0 kg m−3 (IAPWS [23] accepted values), TC2 = 512.6 K, PC1 = 8.1035 MPa and ρC1 = 275.56 kg m−3 (IUPAC [37] accepted values). The derived values of fitting (empirical) parameters (Ti , Pi and ρi , i = 1, 3) are given in Table 3. These equations were used to calculate the Krichevskii parameter (see Section 3.3) and characteristic parameters, K1 , K2 , τ 1 , τ 2 , ρ1 and ρ2 (see Section 3.4) for the 0.4996H2 O + 0.5004CH3 OH mixture.

(3)

The Krichevskii parameter plays a very important role in near-critical solution thermodynamics [43–52], particularly in determining the behavior of dilute solutions near the solvent’s critical point. In general, the thermodynamic behavior

Fig. 3. Experimental values of one-phase liquid (CV 1 ) and two-phase liquid (CV 2 ) isochoric heat capacities of 0.4996H2 O + 0.5004CH3 OH at saturation as a function of temperature near the critical point.

N.G. Polikhronidi et al. / Fluid Phase Equilibria 252 (2007) 33–46

Fig. 4. The experimental liquid and vapor densities at saturation for H2 O + CH3 OH mixtures and their pure components from CV experiments together with values reported by other authors. (—) Pure H2 O [23] and pure CH3 OH [37]; (䊉 and ) Bazaev et al. [10] (0.36 mole fraction); (×) Shakhverdiev and Safarov [88] (x = 0.36 mole fraction, interpolated data); () Yokoyama and Uematsu [87] (0.36 mole fraction); () Osada et al. [89] (0.5 mole fraction); () Shakhverdiev and Safarov [88] (0.5 mole fraction); (♦) this work (0.5004 mole fraction); () critical point of mixture (this work); () critical parameters of pure components; (– – – –) experimental critical line; (– · – · – · –) linear interpolation of the critical line.

41

Fig. 5. Measured liquid (CV ) and vapor (CV ) isochoric heat capacity jumps at saturation near the critical point.

of infinitely dilute mixtures near the solvent’s critical point can be completely characterized by the Krichevskii parameter, which is equal to the derivative (∂P/∂x)∞ TC VC calculated at the critical point of the pure solvent. Using the concept of the Krichevskii parameter, Levelt Sengers [43] proposed a description of thermodynamic behavior of dilute near-critical solutions based on the derivative (∂P/∂x)∞ TV (Krichevskii function J [62,63]). Therefore, the Krichevskii parameter governs

Fig. 6. Reported values of the critical temperature, the critical density and the critical pressure of 0.4996H2 O + 0.5004CH3 OH mixture as a function of concentration. (䊉) Marshall and Jones [15]; () Xiao et al. [11]; () Bazaev et al. [10]; () Wormald and Yerlett [17]; () Griswold and Wong [16]; (♦) this work; (– – – –) for ideal mixture (linear interpolation); (–) calculated from the correlations (1) to (3). Table 3 The values of parameters in Eqs. (1)–(3) T1

T2

T3

P1

P2

P3

ρ1

ρ2

ρ3

−67.2407

−8.5144

20.5444

−8.5801

−3.3456

−4.5547

−67.2412

−11.3503

19.4766

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N.G. Polikhronidi et al. / Fluid Phase Equilibria 252 (2007) 33–46

lines and the derivative (∂P/∂x)C TC VC .  C       ∂P ∂TC C ∂PC C dPS C = − ∂x VC TC ∂x CRL dT CXC ∂x CRL       dTC C dPC C dPS C = − (4) dTC CRL dx CRL dT CXC

Fig. 7. PC –TC projection of the critical line of 0.4996H2 O + 0.5004CH3 OH mixture together with vapor–pressure curves of pure components calculated with reference equation of states [23,37]. (♦) This work; () Bazaev et al. [10]; () Xiao et al. [11]; (– – – –) critical line for ideal mixture (linear interpolation); (–·–·–·–) critical line for real mixtures; (—) vapor–pressure curves for the pure components (1, water [23] and 2, methanol [37]).

the thermodynamic properties of a solute in the vicinity of the critical point of a pure solvent (water). For example, in the limit of infinite dilution many partial molar properties of the solute ¯ ∞ ), which are related to the Krichevskii parame¯ ∞, C (V¯ 2∞ , H 2 p2 ter, are strongly divergent at the solvent’s critical point [53–61] (see also below Eq. (5)). The vapor–liquid distribution coefficient KD of solute at infinite dilution between vapor and liquid 2 )[ρ(l) − ρ ], is also directly solvent, RT ln KD ≈ −(2J/ρC1 C1 related to the Krichevskii function, J = (∂P/∂x)∞ TV [53–73]. The limiting slope of RT ln KD as a function of the liquid phase density [ρ(l) − ρC1 ], as the system approaches the critical point, 2 is also given by Krichevskii parameter as −2(∂P/∂x)∞ TC VC /ρC1 , Henry’s constant KH near the critical point [48,64] (T ln(KH /f1 ), and T ln E (where E = y2 P/P2sub is the enhancement factor, P, y2 , P2sub are the pressure, solubility and sublimation pressure, respectively) are linear in the solvent density, with a slope given by Krichevskii parameter. The Krichevskii parameter also determines the shape of the dew-bubble curves, isothermal in P–x space and isobaric in T–x space [43–45]. The Krichevskii function, J = (∂P/∂x)∞ TV , has a simple physical means and a straight forward connection to total and direct correlation function integrals (TCFI and DCFI) [65–71] and takes into account the effects of the intermolecular interactions between solvent and solute molecules that determine the thermodynamic properties of dilute solutions. The values of (∂P/∂x)∞ TV associated also with the behavior of the microstructure parameters of dilute supercritical solutions (cluster size, NClus ), are measure of the finite microscopic rearrangement of the solvent structure around the infinitely dilute solute relative to the solvent structure in an ideal solution. The Krichevskii parameter can be estimated from the initial slopes, dTC /dx and dPC /dx, of the TC (x) and PC (x) critical lines of the solutions and the values of vapor–pressure curve slope (dPS /dT )C CXC of pure water at the critical point. Krichevskii [72] derived the relation between the initial slopes of the critical

where “CXC” and “CRL” subscripts are related to the vapor–pressure and critical line curves, respectively. The regimes of the near-critical dilute solution behavior depends strongly on the signs and magnitudes of the initial slopes of the critical curves TC (x), PC (x) and on the slope of the vapor–pressure curve (dPS /dT )C CXC at the critical point of pure solvent, i.e. the magnitude and sign of the Krichevskii parameC ter, (∂P/∂x)C TC VC The value of the derivative (dPS /dT )CXC = 0.2682 MPa K−1 for pure water is calculated with the vapor–pressure equation (IAPWS formulation, Levelt Sengers [73]), and the slopes of the critical lines TC (x) and PC (x) from correlations (1) and (2). The values of (∂PC /∂TC )CRL for most aqueous salt solutions at the critical point of pure water are lower than the slope of the vapor–pressure curve (dPS /dT )C CXC for water at the critical point (see Levelt Sengers [44] and Anisimov et al. [54]). Therefore, as one can see from Eq. (4), the values of the Krichevskii parameter for aqueous salt solutions is negative (the values of the derivative (dTC /dx)CRL > 0 is positive). The values of the derivatives (dTC /dx)x=0 = −189.71 K and (dPC /dx)x=0 = −30.44 MPa at infinite dilution (x → 0) calculated from Eqs. (1) and (2) were used to determine the value of the Krichevskii parameter for the H2 O + CH3 OH mixture. Our result for the Krichevskii parameter calculated with Eq. (4) is 20.44 MPa. Fig. 8 (left) shows the concentration dependence of the pressure of the mixture H2 O + CH3 OH along the critical isotherm–isochore of pure water reported by Bazaev et al. [10]. The experimental limiting (x → 0) slope of the P–x curve is the experimental Krichevskii parameter. Unfortunately, there is only one single data point (P, T, ρ, x) at pure water’s critical isotherm–isochore for the H2 O + CH3 OH mixture at x = 0.36 mole fraction, reported by Bazaev et al. [10]. The estimated value of the experimental Krichevskii parameter from the P–x data reported by Bazaev et al. [10] is 21.83 MPa. This acceptable agreement, within 6.8% between the present value of the Krichevskii parameter and directly measured value, confirms the reliability and accuracy of the calculated values of the derivatives, dTC /dx and dPC /dx, from Eqs. (1) and (2). This is also good confirmation of the reliability of the shape of the critical curves TC (x) and PC (x) for this mixture. Therefore, the Krichevskii parameter, (∂P/∂x)∞ TC VC , for the H2 O + CH3 OH mixture is positive. This means that the addition of a small amount of solute (methanol) at constant temperature and density increases the pressure of the dilute H2 O + CH3 OH mixture. As one can see from Fig. 7, the projection of the critical line in the P–T plane lies on the low-temperature side of the vapor–pressure curve of the pure water or its smooth extension (the critical isochore of pure water), (∂PC /∂TC )CRL < (dPS /dT )C CXC and (dTC /dx)x=0 < 0. Therefore, according to Eq. (4), (∂P/∂x)C T,V > 0. This is typical for most aqueous solution of volatile compounds.

N.G. Polikhronidi et al. / Fluid Phase Equilibria 252 (2007) 33–46

43

Fig. 8. The limiting slope (the Krichevskii parameter) of the P–x dependence (left) and Vm –x plot (right) for H2 O + CH3 OH mixture along the pure water’s critical isochore–isotherm and the critical isotherm–isobar. (䊉) Bazaev et al. [10].

For infinitely dilute mixtures (x → 0), the partial molar volume of solute V¯ 2∞ can be calculated using the concentration derivatives of pressure (∂P/∂x)∞ TV (Krichevskii function) as [44,65,66,74–76]   ∞  ∂P V¯ 2∞ = ρ0−1 KT +1 (5) ∂x TV where KT > 0 is the compressibility of pure solvent (water) and ρ0 is the density of pure solvent (water). As one can see from Eq. (5), adding a solute (methanol) which will likely raise the pressure, (∂P/∂x)C TV > 0, will cause the partial molar volume V¯ 2∞ to approach +∞. This anomaly is caused by the critical effects due to the divergence of the isothermal compressibility KT of the pure solvent (water) and is common to all dilute nearcritical mixtures [44,45,53,77,78]. Near the critical point of pure water (x → 0, infinite dilution), the Krichevskii function in Eq. (5), (∂P/∂x)TV , approaches the Krichevskii parameter and the isothermal compressibility strongly diverges at the critical point of the solvent (water) KT ∝ (T − TC )−γ → +∞; consequently, the partial molar volume V¯ 2∞ will also diverge strongly. The sign of the V¯ 2∞ divergence is dependent on the sign of the Krichevskii parameter. Our previous PVTx measurements for the H2 O + CH3 OH mixture (Bazaev et al. [10]) showed that experimental values of molar volume Vm as a function of composition along the pure water’s critical isotherm–isochore increases with concentration. As Fig. 8 (right) shows, along water’s critical isotherm–isobar in the limit as the pressure approaches water’s critical pressure PC the tangent (slope (∂Vm /∂x)∞ pT → +∞ is infinite at the water’s critical point) approaches the vertical and therefore the values of the derivative (∂Vm /∂x)∞ pT become positively infinite. Since the partial molar volume V¯ 2∞ of solute (methanol) is obtained from the tangent (∂Vm /∂x)∞ pT , the partial molar volume of an infinitely dilute H2 O + CH3 OH mixture near the critical point of pure water tends to plus infinity V¯ 2∞ → +∞.

For some solutes (relatively involatile), the partial molar volume tends to minus infinity V¯ 2∞ → −∞ (for example, for most salt solutions). For these types of mixtures the Krichevskii parameter, therefore, is negative. The calculated values with Eq. (5) of the partial molar volumes V¯ 2∞ at infinite dilution near the critical point of pure water as a function of density along the near- and supercritical isotherms are given in Fig. 9. 3.4. Isomorphic near-critical behavior of the isochoric heat capacity of H2 O + CH3 OH mixture The Krichevskii parameter also governs the thermodynamic behavior (isomorphism of the critical behavior of mixtures) of fluid mixtures near the critical point of one of the components.

Fig. 9. Partial molar volumes of infinite dilution H2 O + CH3 OH mixture along the near-critical and supercritical isotherms as a function of pure solvent (water) density calculated with Eq. (5), using the crossover equation of state for pure water [90]. (1) 648.0 K; (2) 648.5 K; (3) 649.0 K; (4) 650.0 K; (5) 652.0 K.

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N.G. Polikhronidi et al. / Fluid Phase Equilibria 252 (2007) 33–46

A comprehensive analysis of the consequences of the isomorphism principle to the critical behavior of mixtures has been presented by Anisimov et al. [79–82]. According to the isomorphism principle, the near-critical behavior of binary fluids (CV and other thermodynamic properties) is controlled by two characteristic parameters K1 and K2 [83] that are determined by the initial slopes (x → 0) of the critical curves (TC –x) and (PC –x) or by the shape of the critical curves. The parameter K1 controls strongly divergent properties such as the isothermal compressibility KT and the isobaric heat capacity CP . The parameter K2 is responsible for the deformation of the weak divergence of CV and defines the range of Fisher renormalization of the critical exponent α [84]. The parameter K1 and the corresponding characteristic temperature difference τ 1 and characteristic density difference ρ1 are defined by     x(1 − x) dPC dPS c dTC K1 = − , ρC RTC dx dT CXC dx  1/γ Γ0+ K12 β τ1 = and ρ1 = B0 τ1 (6) x(1 − x) The isochoric heat capacity behavior of a binary mixture will exhibit the same behavior as those of the pure components in the range of temperature τ τ 2 [83], where  1/α K22 x(1 − x) dTC + τ2 = A0 , K2 = , x(1 − x) TC (x) dx τ=

T − TC , T

ρ =

ρ − ρC , ρC

β

ρ2 = B0 τ2

(7)

The values of the derivative dTC /dx = −130.2 K and dPC /dx = 12.29 MPa are calculated from Eqs. (1) and (2), the critical temperature for composition x = 0.5004 mole fraction of CH3 OH is TC = 563.04 K, the critical amplitudes A+ 0 = 31.6, B0 = 1.98 and Γ0+ = 0.058 of the power laws for isochoric heat capacity, coexistence curve and isothermal compressibility for pure water, respectively, are from references [30,85], and the universal critical exponents for CV , α = 0.11 and for the coexistence curve β = 0.324 are from reference [86]. Along the critical isochore in the one-phase region all properties of a binary fluid mixture will exhibit the same behavior as those of a pure fluid in the range of temperatures τ τ 1 and τ τ 2 . At τ 2 < τ < τ 1 properties that exhibit strong singularities in onecomponent fluids (associated with critical exponent γ) will reach a plateau, however, weakly singular properties (associated with critical exponent α) will continue to grow. At τ < τ 2 , those properties that diverse weakly in one-component fluids will be saturated and all critical exponents will be renormalized by a factor 1/(1 − α). In term of density, along the critical isotherm the behavior of all properties will be one-component-like at densities |ρ| ±ρ1 and Fisher renormalization occurs at |ρ| ±ρ2 [84]. The values of characteristic parameters K1 , τ 1 , ρ1 , K2 , τ 2 and ρ2 calculated from Eqs. (6) and (7) for the 0.4996H2 O + 0.5004CH3 OH mixture are given in Table 4. Fig. 10 shows the concentration dependence of the

Table 4 The values of characteristic parameters for H2 O + CH3 OH mixture x (mole fraction)

K1

K2

τ1

τ 2 × 104

ρ1 × 107

ρ2

0.5004

0

−0.0578

0

3.984

2.15

0.1555

Fig. 10. Characteristic temperature τ 2 and density ρ2 differences as a function of concentration calculated from the critical lines data, Eq. (7).

characteristic parameters τ 2 and ρ2 . As one can see, the values of τ 2 at concentrations between 0.12 and 0.65 mole fraction shows a maximum, while the characteristic temperature difference τ 1 is zero over the whole concentration range. Therefore, Fisher renormalization (mixture-like behavior) of the critical exponent for weakly singular properties such as CV along the critical isochore can be experimentally observed at temperatures τ < τ 2 (for the mixture H2 O + CH3 OH x = 0.5004 mole fraction, τ < 0.00039 or T < 563.74 K, see Table 4), while all properties that exhibit strong singularities in one-component fluids exhibit pure-like behavior. In terms of density, along the critical isotherm, CVX exhibits mixture-like behavior at densities |ρ| 0.245. Fig. 11 shows a CV –log10 τ plot of the isochoric heat capacity of the 0.4996H2 O + 0.5004CH3 OH

Fig. 11. Isochoric heat capacity CV of pure water and 0.4994H2 O + 0.5004CH3 OH mixture as a function of log10 τ along their critical isochores. (1) Pure water calculated from the crossover model by Kiselev and Friend [90]; (2) the present measurements for the mixture along the near-critical isochore of 290.78 kg m−3 ; (– – – –), is the parallel line to the pure water CV behavior.

N.G. Polikhronidi et al. / Fluid Phase Equilibria 252 (2007) 33–46

mixture and pure water along their critical densities. As this figure demonstrates, the mixture exhibits mixture-like behavior (renormalization) as the critical point is approached at temperatures about τ < 0.00036, which is very close to the value (τ = 0.00039) predicted by critical properties data (see Table 4). In the concentration range from 0 to 0.12 and from 0.65 to 1.0 mole fraction the weakly singular properties (CV ) exhibit pure-like behavior (τ 2 = 0, CV ∝ τ −α ). Unfortunately, there is no CVX data for the mixture at these concentration ranges to check the pure-like behavior of isochoric heat capacity along the critical isochore. However, it is physically obvious that as the concentration approaches the pure component limits (x → 0 and x → 1) the pure components in the mixture dominate the critical effects, displaying behavior, which is typical for pure fluids. Therefore, in the concentration ranges x < 0.12 and x > 0.65 mole fractions the crossover from mixture-like to pure-like behavior of CVX is observed along the critical isochore. This means that CVX , which diverges weakly for pure H2 O (x = 0) and pure CH3 OH (x = 1) with an exponent α = 0.110, CV ∝ τ −α along the critical isochore, will be renormalized by the factor 1/(1 − α)(−α ⇒ α/(1 – α)), CVX ∝ τ α/(1−α) for the 0.4996H2 O + 0.5004CH3 OH mixture at concentrations between (0.12 and 0.65) mole fraction of methanol at temperatures below τ 2 = 0.00039 (see Fig. 10). A cusp (liquid–vapor critical point) was observed in the temperature CV –T dependence of the measured isochoric heat capacities along the near-critical isochores (see Fig. 1a and b) and along the saturation curve (see Fig. 3) for the mixture. As Figs. 1 and 3 shows, CV increases monotonically with T up to the cusp (critical point) without any criticality as exhibited for pure components. At this cusp, the liquid and vapor become identical, providing the temperature and the density of the critical points of the mixture. Fig. 5 also demonstrates that the isochoric heat capacity jumps near the critical point do not exhibit any criticality, i.e. CV monotonically decreases as temperature approaches TC , while for pure fluids and some binary mixtures CV exhibits a singularity as CV ∝ τ −α . Therefore, the present isochoric heat capacity measurements for the 0.4996H2 O + 0.5004CH3 OH mixture confirm the prediction (renormalization critical behavior of CVX ) by the critical curves data and the Krichevskii parameter. 4. Conclusions The isochoric heat capacity of two (0.5004 and 0.5014 mole fraction) H2 O + CH3 OH mixtures was measured using a hightemperature and high-pressure adiabatic calorimeter in a range of temperatures from 371 to 579 K and densities between 214 and 394 kg m−3 . The value of the Krichevskii parameter (20.44 MPa) was calculated using critical curves data. The derived value of the Krichevskii parameter satisfactorily agrees with the value of 21.83 MPa estimated from the direct experimental slope of P–x measurements along the critical isotherm–isochore of pure water. The isochoric heat capacity of the 0.4996H2 O + 0.5004CH3 OH mixture exhibits pure-like behavior (CV ∝ τ −α ) along the critical isochore at concentrations x > 0.65 and x < 0.12 mole fraction, while all strongly divergent properties such as the isothermal compressibility KT and the

45

isobaric heat capacity CP exhibit pure-like behavior over the whole concentration range. In the concentration range from 0.12 to 0.65 mole fraction along the critical isochore at temperatures and at temperatures τ < 0.00039 (or T < 563.74 K) CVX exhibits mixture-like behavior (Fisher renormalization of the critical behavior, α → 1/(1 − α), is taking place). In terms of density, along the critical isotherm CVX exhibits mixture-like behavior at densities |ρ| 0.245. Acknowledgements The authors are thankful to Dr. J.W. Magee for interest in this work and useful discussion of the results. One of us (I.M.A.) thanks the Physical and Chemical Properties Division at the National Institute of Standards and Technology for the opportunity to work as a Guest Researcher at NIST during the course of this research. The authors would also like to thank Dr. M. Huber for his assistance in improving the manuscript. This work was also supported by the Grants of RFBR 05-08-18229 and 06-08-08136 and IAPWS International Collaboration Project Award. References [1] A.A. Chialvo, P.T. Cummings, J. Chem. Phys. 101 (1994) 4466–4469. [2] Y. Marcus, Phys. Chem. Chem. Phys. 1 (1999) 2975–2983. [3] P.A. Webley, J.W. Tester, Supercritical Fluid Science and Technology, ACS, 1989, pp. 259–275, Chapter 17. [4] P.E. Savage, R. Li, J.T. Santini Jr., J. Supercritical Fluids 7 (1994) 135–144. [5] T. Kuroki, N. Kagawa, H. Endo, S. Tsuruno, J.W. Magee, J. Chem. Eng. Data 46 (2001) 1101–1106. [6] H. Kitajima, N. Kagawa, H. Endo, S. Tsuruno, J.W. Mage, J. Chem. Eng. Data 48 (2003) 1583–1586. [7] M.M. Aliev, J.W. Magee, I.M. Abdulagatov, Int. J. Thermophys. 24 (2003) 1551–1579. [8] I.M. Abdulagatov, V.I. Dvoryanchikov, M.M. Aliev, A.N. Kamalov, in: P.R. Tremaine, P.G. Hill, D.E. Irish, P.V. Balakrishnan (Eds.), Proceeding of the 13th International Conference Prop., Water and Steam, NRC Research Press, Ottawa, 2000, pp. 157–164. [9] E. Bulemela, P. Tremaine, Sh. Ikawa, Fluid Phase Equilib. 245 (2006) 125–133. [10] A.R. Bazaev, I.M. Abdulagatov, J.W. Magee, E.A. Bazaev, A.E. Ramazanova, A.A. Abdurashidova, Int. J. Thermophys. 25 (2004) 804–838. [11] C. Xiao, H. Bianchi, P.R. Tremaine, J. Chem. Thermodyn. 29 (1997) 261–286. [12] P. Hynˇcica, L. Hn˘edkovsk´y, I. Cibulka, J. Chem. Thermodyn. 36 (2004) 1095–1103. [13] J.M. Simonson, D.J. Bradley, R.H. Busey, J. Chem. Thermodyn. 19 (1987) 479–492. [14] C.J. Wormald, L. Badock, M.J. Lloyd, J. Chem. Thermodyn. 28 (1996) 603–613. [15] W.L. Marshall, E.V. Jones, J. Inorg. Nucl. Chem. 36 (1974) 2319– 2323. [16] J. Griswold, S.Y. Wong, Chem. Eng. Prog. Symp. Ser. 48 (1952) 18–34. [17] C.J. Wormald, T.K. Yerlett, J. Chem. Thermodyn. 32 (2000) 97–105. [18] I.M. Abdulagatov, V.I. Dvoryanchikov, A.N. Kamalov, J. Chem. Eng. Data 43 (1998) 830–838. [19] I.M. Abdulagatov, B.A. Mursalov, N.M. Gamzatov, in: H. White, J.V. Sengers, D.B. Neumann, J.C. Bellows (Eds.), Proceedings of the 12th International Conference Prop., Water and Steam, Begell House, New York, 1995, pp. 94–102. [20] N.G. Polikhronidi, I.M. Abdulagatov, J.W. Magee, G.V. Stepanov, Int. J. Thermophys. 22 (2001) 189–200.

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