3036
Ind. Eng. Chem. Res. 1998, 37, 3036-3042
Excess Molar Enthalpies of Nitrous Oxide/Hexane Mixtures in the Liquid and Supercritical Regions Albertina Caban ˜ as, Carlos Menduin ˜ a, Concepcio´ n Pando, and Juan A. R. Renuncio* Departamento de Quı´mica Fı´sica I, Universidad Complutense, E-28040 Madrid, Spain
The excess molar enthalpies HEm of nitrous oxide (N2O)/hexane mixtures were measured in the liquid and supercritical region covering the whole concentration range. The HEm values at 308.15 K and 7.64 and 9.48 MPa and at 318.15 K and 12.27 and 15.00 MPa are moderately positive in the hexane-rich region and moderately negative in the N2O-rich region. The HEm values at 308.15 K and 12.27 and 15.00 MPa are moderately positive over the entire composition range. Large negative HEm values are obtained at 318.15 K and 7.64 and 9.48 MPa. The changes observed in HEm with temperature and pressure are discussed in terms of liquid-vapor equilibrium and critical constants for N2O/hexane. The HEm values for N2O/hexane mixtures are also calculated using cubic equations of state (EOS) and the classical and Wong-Sandler mixing rules. Introduction Nitrous oxide (N2O) is sometimes used in supercritical fluid extraction, and several authors (Alexandrou et al., 1992; Haarhaus et al., 1995; Chang and Huang, 1995; Subra et al., 1997) have reported that N2O is a better solvent than carbon dioxide (CO2) probably because of its dipole moment. The N2O and CO2 molecules are isoelectronic and have the same molar mass and very close critical points. For CO2, the critical temperature (Tc) is 304.21 K and the critical pressure (Pc) is 7.38 MPa, whereas for N2O, Tc is 309.6 K and pc is 7.24 MPa (Reid et al., 1988). The explosion risk reported by Sievers and Hansen (1991) seems to be preventing a wider use of supercritical N2O. Thermodynamic properties such as the excess molar enthalpies (HEm) of mixtures formed by N2O are important in understanding the behavior of these mixtures at supercritical or near critical conditions. Values of HEm in the liquid and supercritical region for the binary mixtures formed by N2O and toluene, cyclohexane, pentane, heptane, or octane have already been reported (Castells et al., 1994a-b; Renuncio et al., 1995; Caban˜as et al., 1997ab; Pittau et al., 1998). Continuing these investigations, the present work reports values of HEm for N2O/hexane at 308.15 and 318.15 K and 7.64, 9.48, 12.27, and 15.00 MPa. Figure 1 is a plot of P versus T for N2O/hexane showing the vapor-liquid equilibrium curve of N2O (Couch et al., 1962), the critical locus in the vicinity of the N2O critical point, and the points at which experimental measurements of HEm have been made. For hexane, Tc is 507.5 K and Pc is 3.01 MPa (Reid et al., 1988). Mixtures at 308.15 K are always liquid, whereas mixtures at 318.15 K may be liquid or supercritical fluid depending on the Tc and Pc of the particular mixture. * To whom all correspondence should be sent. Fax: 3413944135. Phone: +341-3944120. E-mail: Renuncio@ eucmax.sim.ucm.es.
Figure 1. Plot of P versus T for N2O/hexane showing the vaporliquid equilibrium curve (- - -) and critical point (4) of N2O, the critical locus (s) from x ) 1.00 to x ) 0.9715, and (T, P) coordinates (O) where experimental measurements were made.
The HEm values for N2O/hexane mixtures are also calculated using cubic equations of state (EOS) and the resulting HEm values are compared with experimental results. Experimental Section The materials employed were N2O (SEO 99.5 mol % pure) and hexane (Carlo Erba RPE, purity >99 mol %) and they were used without further purification.
S0888-5885(97)00859-2 CCC: $15.00 © 1998 American Chemical Society Published on Web 05/02/1998
Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998 3037 Table 1. Experimental Excess Enthalpies HEm for N2O/Hexane x
HEm (J mol-1)
x
HEm (J mol-1)
x
HEm (J mol-1)
x
HEm (J mol-1)
0.057 0.084 0.136 0.170 0.192 0.277
17 30 51 60 61 39
0.319 0.393 0.469 0.536 0.562 0.577
308.15 K, 7.64 MPa 36 0.623 0.4 0.675 -47 0.728 -104 0.760 -117 0.814 -130 0.840
-193 -270 -323 -343 -407 -446
0.865 0.887 0.929 0.948 0.975 0.992
-460 -453 -427 -403 -290 -133
0.041 0.083 0.098 0.139 0.162 0.231 0.248
34 52 64 86 97 135 147
0.323 0.357 0.396 0.421 0.538 0.601 0.626
308.15 K, 9.48 MPa 162 0.634 167 0.722 167 0.731 166 0.843 147 0.847 122 0.880 105 0.930
100 51 42 -40 -50 -76 -95
0.959 0.976 0.984 0.992
-70 -60 -50 -26
0.043 0.053 0.079 0.096 0.117 0.149 0.240
63 81 114 136 179 198 261
0.299 0.344 0.394 0.489 0.525 0.546 0.581
308.15 K, 12.27 MPa 299 0.646 310 0.695 324 0.748 328 0.779 332 0.790 323 0.802 324 0.848
291 253 214 190 179 174 120
0.895 0.902 0.944 0.977
0.054 0.107 0.131 0.156 0.184 0.201 0.235
70 142 149 181 229 239 292
0.269 0.282 0.343 0.355 0.403 0.468 0.503
308.15 K, 15.00 MPa 320 0.658 325 0.694 348 0.727 348 0.753 355 0.786 369 0.808 368 0.852
361 342 329 301 282 242 211
0.890 0.899 0.920 0.945 0.978 0.986
154 140 111 71 33 30
0.047 0.084 0.181 0.220 0.279 0.318 0.374
-144 -283 -775 -984 -1211 -1418 -1693
0.381 0.466 0.488 0.574 0.619 0.672 0.691
318.15 K, 7.64 MPa -1777 0.720 -2034 0.786 -2248 0.813 -2539 0.825 -2770 0.862 -3119 0.886 -3225 0.907
-3385 -3585 -3765 -3860 -4018 -4031 -4051
0.928 0.966 0.975 0.983
-3884 -3273 -2261 -1128
82 61 19 6.8
0.050 0.092 0.140 0.205 0.288 0.333
-6.1 -4.0 -1.4 -38 -77 -106
0.373 0.424 0.474 0.542 0.580 0.686
318.15 K, 9.48 MPa -127 0.703 -197 0.735 -221 0.765 -311 0.803 -332 0.843 -460 0.866
-478 -531 -571 -627 -677 -697
0.876 0.911 0.940 0.958 0.967 0.975
-693 -687 -623 -538 -477 -394
0.053 0.098 0.148 0.239 0.302 0.342 0.413
34 70 105 144 150 155 157
0.438 0.453 0.513 0.542 0.583 0.605 0.644
318.15 K, 12.27 MPa 151 0.662 155 0.699 132 0.747 126 0.775 100 0.804 90 0.848 59 0.897
40 15 -31 -44 -87 -112 -135
0.916 0.944 0.977 0.985 0.993
-136 -127 -70 -54 -35
0.043 0.063 0.102 0.123 0.175 0.193 0.232 0.284
43 54 96 121 156 180 212 249
0.307 0.404 0.508 0.604 0.644 0.664 0.682 0.698
318.15 K, 15.00 MPa 266 0.712 303 0.747 305 0.761 272 0.791 248 0.814 225 0.850 206 0.873 189 0.884
179 162 150 121 104 72 35 29
0.899 0.916 0.944 0.966 0.985
The measurements were made using a flow mixing calorimeter and the experimental procedure previously described by Castells et al. (1994a). The chemicals were pumped into the calorimeter by two thermostated ISCO pumps (model LC2600). The calorimeter cell was ther-
15 9.1 -12 -23 -11
mostated in a silicon oil bath ((0.0005 K), and the pressure was controlled by a back pressure regulator. A manually controlled piston acts as a fine adjustment of the nitrogen pressure over the back pressure regulator. Oscillations in pressure were smaller than (0.01
3038 Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998
Figure 2. Plot of HEm versus N2O mole fraction for N2O/hexane at 308.15 K as a function of pressure. Key: (9) 7.64 MPa; (b) 9.48 MPa; (2) 12.27 MPa; ([) 15.00 MPa; (s) calculated from eq 1; (- - -) calculated from the SRK EOS and the Wong-Sandler mixing rule.
MPa. All runs were made in the steady-state fixed composition mode. Flow rates were selected to cover the whole mole fraction range. The measurements were carried out at total flow rates of 0.0028 and 0.0056 cm3 s-1. Reproducibility of results was estimated to be ((1 + 0.01HEm) J mol-1. The flow rates, measured in cm3 s-1, were converted to mol s-1 and to mole fractions using the densities of the two materials estimated from pressure-volume isotherms and densities and isothermal compressibilities reported by Couch et al. (1962) and Diaz Pen˜a and Tardajos (1978). Results The HEm values were determined for N2O/hexane over the entire composition range at 308.15 and 318.15 K and 7.64, 9.48, 12.27, and 15.00 MPa. The results are given in Table 1. Figures 2 and 3 are plots of HEm versus N2O mole fraction for the isobars studied at 308.15 and 318.15 K, respectively. Mixtures at 308.15 K and 7.64 and 9.48 MPa show moderately endothermic and exothermic mixing in the hexane-rich and N2O-rich regions, respectively. The exothermic mixing region extends over a very small range of x at 308.15 K and 9.48 MPa, and mixtures at 308.15 K and 12.27 and 15.00 MPa are moderately endothermic. Mixtures at 318.15 K and 7.64 and 9.48 MPa show very exothermic mixing. Mixtures at 318.15 K and 12.27 and 15.00 MPa show moderately endothermic and exothermic mixing in the hexane-rich and N2O-rich regions, respectively. The magnitude of the minimum observed at 318.15 K considerably decreases as pressure increases. Values for the minimum range from -4051 J mol-1 at 7.64 MPa to -23 J mol-1 at 15.00 MPa.
Figure 3. Plot of HEm versus N2O mole fraction for N2O/hexane at 318.15 K as a function of pressure. Key: (9) 7.64 MPa (insert); (b) 9.48 MPa; (2) 12.27 MPa; ([) 15.00 MPa; (s) calculated from eq 1; (- - -) calculated from the SRK EOS and the Wong-Sandler mixing rule.
Values for HEm at each temperature and pressure studied were fitted to the equation:
HEm/(J mol-1) ) x(1 - x)
Cn(2x - 1)n ∑ n)0 1+
∑
(1)
Bk(2x - 1)k
k)1
where x is the N2O mole fraction. The coefficients Cn and Bk are given in Table 2 together with the standard deviations, σ, between experimental and calculated HEm values. The higher value obtained for σ at 318.15 K and 7.64 MPa may be considered adequate if one takes into account that this isobar exhibits a minimum of -4051 J mol-1. As may be also observed in Figures 2 and 3, the HEm values for N2O/hexane change from exothermic to endothermic or become increasingly endothermic as pressure rises for a given temperature and composition. On the other hand, HEm values for N2O/hexane change from endothermic to exothermic or become less endothermic as temperature increases for a given pressure and composition. The temperature and pressure effects on the HEm values are both large and of opposite sign. The pressure effect is more important at 318.15 K, whereas the temperature effect is more important at the lower values of pressure. The combination of both effects leads to great changes in HEm when temperature increases from 308.15 to 318.15 K at 7.64 MPa or when pressure increases from 7.64 to 9.48 MPa at 318.15 K. The changes observed in the HEm with temperature and pressure may be discussed in terms of liquid-vapor equilibrium and critical constants for the N2O/hexane mixtures and the densities of N2O and hexane at the conditions of temperature and pressure of the experi-
Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998 3039 Table 2. Coefficients Cn and Bk and Standard Deviation σ for Least-Squares Representation of -1 HE m (J mol ) for N2O/Hexane by Equation 1 T ) 308.15 K
T ) 318.15 K
parameter
7.64a
9.48a
12.27a
15.00a
7.64a
9.48a
12.27a
15.00a
C0 C1 C2 C3 C4 B1 B2 σ
-279.35 1438.5 -72.757 -144.92
1337.7 132.95 -216.99 619.30
1489.6 -35.136 787.75 -156.71 -1328.9
-9002.7 7049.2 -1841.4 2861.3
-1025.6 1147.2 160.55 757.63 -1136.4 0.81853
551.30 157.05 -267.78
1218.8 1473.2 -453.96 -592.70
0.90699
623.78 970.71 -142.14 -36.588 -290.64 0.77946
0.80226
0.93088
9.7
4.6
7.0
8.3
5.0
6.1
a
9.4
0.22461 -0.67842 49
P/MPa.
Table 3. Densities of N2O and Hexane under the Temperature and Pressure Conditions of the Experiments T, K F(N2O), kg m-3
F(hexane), kg m-3
P, MPa
308.15
318.15
308.15
318.15
7.64 9.48 12.27 15.00
712 748 791 819
253 535 697 754
654 656 659 662
645 647 650 653
ments. With the exception of solubility data reported at atmospheric pressure by Makranczy et al. (1976) and by Patyi et (1978), vapor-liquid equilibrium data and critical locus data are not available for N2O/hexane. The critical locus shown in Figure 1 has been estimated using the procedure developed by Heidemann and Khalil (1980) and the Peng-Robinson EOS (Peng and Robinson, 1976). The densities of N2O and hexane at the conditions of temperature and pressure of the experiments are listed in Table 3. Values for N2O densities were calculated by interpolation of the pressure-volume isotherms reported by Couch et al. (1962). Values for hexane densities were calculated from the densities and isothermal compressibilities reported by Diaz Pen˜a and Tardajos (1978) at 308.15 and 318.15 K. Hexane enters the calorimeter as a liquid because the temperature is lower than the Tc of this component and the pressures are always higher than its Pc. The values for the density of hexane shown in Table 3 are those typical of a liquid and change very little with pressure. At 308.15 K, the N2O also enters the calorimeter as a liquid because the temperature is lower than the Tc of this component and the pressures are always higher than its Pc. The values for the density of N2O at 308.15 K shown in Table 3 are those typical of a liquid and change very little with pressure. At 318.15 K, the N2O enters the calorimeter as a supercritical fluid because the temperature and pressures studied are always greater than those defining its critical point. However, this N2O fluid may be a low-density (gaslike) fluid or a high-density (liquidlike) fluid depending on the pressure. The values for the density of N2O at 318.15 K change as the pressure increases from those typical of a gas at 7.64 and 9.48 MPa to those typical of a liquid at 12.27 and 15.00 MPa. The resulting N2O/hexane mixtures may be liquid, gaslike fluid, or liquidlike fluid, depending on the Tc and Pc of the particular mixture. The critical line predicted by the Peng-Robinson equation (1976) for N2O/hexane goes through a maximum at approximately P ) 10.3 MPa and T ) 375 K and it comes back to the hexane critical point. Because the temperatures and pressures studied are far away from
those defining the critical point of hexane, N2O/hexane mixtures are liquid from x ) 0 to approximately x ) 0.93, and fluid only in a narrow composition range in the N2O-rich region. Due to the transition from a liquid to a fluid mixture, there is also a two-phase region between the liquid and the fluid mixture regions. This region is detected by a high-slope linear section in the N2O-rich region of the 7.64 MPa isobar at 318.15 K. When the states and densities of the pure components and the mixture are similar (liquid or liquidlike fluid N2O and liquid hexane forming a liquid or liquidlike fluid mixture), the values of HEm are moderately negative or positive; this is so for the four isobars at 308.15 K and for the 12.27 and 15.00 MPa isobars at 318.15 K when the values of density are similar for N2O and hexane. When the states and densities of the pure components differ (gaslike fluid N2O and liquid hexane), and the resulting mixture is a liquid, large negative values of HEm are observed; this is so at 318.15 K for the isobars at 7.64 and 9.48 MPa when the density of N2O is much lower than that of hexane. The large negative values of HEm seem to be a consequence of the N2O change of state from that of a low-density fluid to that of a liquid-mixture component. This condensation effect is more important at high x and the minimum HEm values at 318.15 K take place at x ) 0.907 and 7.64 MPa and x ) 0.866 and 9.48 MPa. These results are similar to those previously obtained for other N2O/hydrocarbon binary mixtures (Castells et al., 1994a-b; Renuncio et al., 1995; Caban˜as et al., 1997a-b; Pittau et al., 1998). Calculation of the Excess Molar Enthalpy The excess molar enthalpy of a binary mixture is given by
HEm ) [Hm - H* m]mix -
∑i xi[Hm - H*m]i
(2)
where [Hm - H* m]mix is the residual molar enthalpy of the mixture and [Hm - H*m]i is that of components 1 (N2O) and 2 (hexane), respectively. The residual molar enthalpy is given by
Hm - H* m ) RT(z - 1) +
∂P ∫∞V{T[∂T ]V - P}dV
(3)
where z is the compressibility factor. For pure components, the parameters a and b appearing in the EOS are evaluated in terms of the critical properties and the acentric factor. For mixtures, a and b are calculated using mixing rules. Calculated HEm values result from the balance between two terms adopting similar values: the [Hm - H*m]mix and Σxi[Hm - H*m]i terms of eq 2.
3040 Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998 Table 4. Values for the Binary Adjustable Parameters and the Ratio of the Standard Deviation between Experimental and Calculated HE m Values and the Maximum Absolute Value of E HE m (100 σ/Hmax) Obtained for the N2O/Hexane Mixtures Using Different EOS and Mixing Rules P, MPa 308.15 K EOS SRK SRK PR PR PRSV PRSV
mixing rule classical k12 ) 0.05275 Wong-Sandler k12 ) 0.6807 classical k12 ) 0.03951 Wong-Sandler k12 ) 0.6788 classical k12 ) 0.03972 Wong-Sandler k12 ) 0.6820
parameters
7.64
9.48
δ12 ) -0.03225 A12 ) 1712 J mol-1 A21 ) 410.7 J mol-1
38
17
31
29
36
17
30
31
35
17
30
31
δ12 ) -0.04027 A12 ) 1702 J mol-1 A21 ) 567.4 J mol-1 δ12 ) -0.03904 A12 ) 1687 J mol-1 A21 ) 550.1 J mol-1
Values of pure component residual molar enthalpies depend on the EOS used and are more difficult to evaluate close to the critical point. The same may be said about the mixture residual molar enthalpy, but the [Hm - H*m]mix term has an added flexibility provided by the mixing rule used to calculate the equation parameters. The Wong-Sandler mixing rule (Wong and Sandler, 1992) has been shown to provide accurate HEm values for the binary mixtures formed by N2O and cyclohexane, octane, and heptane and will be used in this study. For comparison purposes, results obtained using the classical mixing rule will be also given. The cubic equations of state used to calculate the HEm values are a modification of the Redlich-Kwong EOS proposed by Soave (1972; SRK EOS), the Peng-Robinson EOS in its original formulation (Peng and Robinson, 1976; PR EOS), and the modification of this equation proposed by Stryjek and Vera (1986; PRSV EOS). The classical van der Waals mixing rules for a and b may be expressed as
a)
b)
∑i ∑j xixjaij;
∑i ∑j xixjbij;
aij ) (aiaj)1/2(1 - kij)
bij )
(bi + bi) 2
(1 - δij)
(4)
(5)
where the subscripts i and j adopt the values 1 and 2 for N2O and hexane, respectively, and kij ) kji and δij ) δji are the binary interaction parameters that are usually determined from experimental binary data. The Wong-Sandler mixing rule defines the mixture parameters a and b as those which simultaneously satisfy the relations
b-
a
)
RT
[
a
]
∑i ∑j xixj b - RT ij
(6)
and
AE∞ CRT
)
a bRT
-
∑i
ai xi biRT
(7)
where C is a numerical constant characteristic of the cubic EOS used and the Helmholtz excess energy AE∞ E (≈Ap)0 ) is described by any of the liquid activity coefficient models proposed for the excess Gibbs energy
318.15 K
12.27
15.00
7.64
9.48
12.27
15.00
18
30
4.3
26
6.3
20
3.7
14
22
17
28
5.0
28
12
18
11
4.2
16
22
17
28
5.0
28
11
18
11
4.1
16
22
17
5.1
9.8
16 5.4 16 5.4
because the two energy terms are indistinguishable at low pressures. In this work, the Wilson model for the excess Gibbs energy (Wilson, 1964) was used:
GEm ) -RT[x1 ln(x1 + Λ12x2) + x2 ln(x2 + Λ21x1)] (8) Λij ) (Vm,j /Vm,i) exp[-Aij /RT]
(9)
For the cross virial coefficient term one may use
[
b-
] [(
a RT
)
ij
) (
)]
ai ai 1 b + bj (1 - kij) 2 i RT RT
(10)
where kij ) kji is a binary parameter. When the WongSandler mixing rule is applied to binary mixtures, the parameter k12 and the parameters A12 and A21 of the excess Gibbs energy model are usually obtained from vapor-liquid equilibrium data. Because these data are not available for N2O/hexane, the Wong-Sandler mixing rule is used in this paper as a mean to correlate HEm values, and values for the parameters are obtained by comparing experimental and calculated HEm values. As was already discussed in the Experimental Section, the uncertainties in temperature, pressure, and composition are smaller than those of the HEm values, and a least-squares procedure was used to minimize deviations between experimental and calculated HEm. Values for the critical constants and the acentric factor were taken from Reid et al. (1988). Because the vapor and liquid equilibrium-phase compositions are unknown for the N2O/hexane mixtures, the HEm values at 7.64 MPa and 318.15 K were calculated only in the one-phase region, and the three data points obtained for x > 0.928 were excluded from the correlation. The binary interaction parameters were adjusted to give the best fit to the complete set of experimental HEm values. Table 4 lists values obtained for the binary interaction parameters, and the percent ratio of the standard deviation between experimental and calculated excess HEm values, σ, and the maximum absolute value of HEm at each of the temperatures and pressures studied. Values for the parameters k12 and δ12 of the classical mixing rule are small, thus leading to a12 and b12 values close to the geometric and arithmetic mean of pure component values, respectively. Values for the parameters k12, A12 and A21 of the Wong-Sandler mixing rule are similar to those reported when vapor-liquid equi-
Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998 3041
librium data are correlated using the Wong-Sandler mixing rule in combination with the Wilson model (Vandana and Teja, 1995; Semar et al., 1995). As could be expected, the results obtained for the PR and PRSV equations are almost coincident. The results obtained for the SRK equation are slightly more accurate than those of the PR and PRSV equations. On the other hand, values for σ/HEm obtained using the Wong-Sandler mixing rule and any of the three EOS used are, for most of the isobars, smaller than those obtained using the classical mixing rule. The dashed-line curves in Figures 2 and 3 are HEm values calculated using the SRK EOS and the Wong-Sandler mixing rule. With the exception of the 7.64 MPa isobar at 308.15 K, the correlations obtained using the SRK, PR, and PRSV equations and the Wong-Sandler mixing rule can be considered accurate. The HEm values calculated at 308.15 K and 7.64 MPa are more exothermic than the experimental values. This result seems to be due to the proximity of conditions of temperature and pressure of experiments to the N2O critical point. Conclusions HEm
values of N2O/hexane were measured in the The liquid and supercritical regions covering the whole concentration range. The HEm values at 308.15 K and 7.64 and 9.48 MPa and at 318.15 K and 12.27 and 15.00 MPa are moderately positive in the hexane-rich region and moderately negative in the N2O-rich region. The HEm values at 308.15 K and 12.27 and 15.00 MPa are moderately positive over the entire composition range. Large negative HEm values are obtained at 318.15 K and 7.64 and 9.48 MPa. The changes observed in the excess enthalpy with temperature and pressure are related to the critical constants for the N2O/hexane mixtures and the densities of N2O and hexane at the conditions of temperature and pressure of the experiments. The large negative values of HEm seem to be a consequence of the N2O change of state from that of a low-density fluid to that of a liquid-mixture component. The SRK, PR, and PRSV EOS used in conjunction with the Wong-Sandler mixing rule reproduce well the great changes with pressure observed in HEm at 318.15 K. The changes observed in HEm with pressure at 308.15 K are small, but correlations at this temperature are more difficult due to the proximity to the N2O critical point, and values of HEm calculated at 308.15 K and 7.64 MPa are more negative than experimental results. It should be also noted that results obtained using the classical mixing rule are not significantly inferior to those obtained using the Wong-Sandler mixing rule. Acknowledgment This work was funded by the Spanish Ministry of Education (DGICYT) Research Project PB-94-0320. We appreciate the aid given to us in estimating the critical locus by Dr. R. A. Heidemann. A.C. acknowledges the Universidad Complutense for its support through a Predoctoral grant. Nomenclature Latin Letters A ) Helmholtz energy
Aij ) Wilson equation coefficient a ) equation of state parameter Bk ) correlation equation coefficient b ) equation of state parameter C ) equation of state numerical constant Cn ) correlation equation coefficient H ) enthalpy J ) joule K ) kelvin k ) binary parameter P ) pressure MPa ) 106 pascal R ) gas constant T ) temperature V ) volume x ) mole fraction z ) compressibility Greek Letters δ ) binary parameter Λ ) Wilson equation coefficient σ ) standard deviation F ) density Superscript E ) excess property Subscripts c ) critical property i, j ) molecular species m ) molar property max ) maximum mix ) mixture 1 ) nitrous oxide 2 ) hexane * ) reference state ∞ ) infinite-pressure state Acronyms EOS ) equation of state PR ) Peng-Robinson PRSV ) Peng-Robinson-Stryjek-Vera SRK ) Soave-Redlich-Kwong
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Received for review November 25, 1997 Revised manuscript received February 12, 1998 Accepted February 13, 1998 IE970859Y
