J. CHEM. SOC. FARADAY TRANS., 1994, 90(18), 2677-2681 Excess Molar Enthalpies of Nitrous Oxide-Toluene in the Liquid and Supercritical Regions R. Cesar Castells,? Carlos Menduifia, Concepcion Pando and Juan A. R. Renuncio Departamento de Quimica Fisica I, Universidad Complutense . E-28040 Madrid, Spain The excess molar enthalpies HEof [xN,O + (1 -x)C,H,CH,] have been measured in the liquid and supercritical regions over the whole concentration range. Mixtures at a temperature of 308.15 K and pressures of 12.27 and 15.00 MPa show moderate endothermic and exothermic mixing in the toluene-rich region and nitrous oxide-rich region, respectively. Mixtures at 308.15 K and 9.49 MPa and at 323.15 K and 12.27 and 15.00 MPa show moderate exothermic mixing. Mixtures at 323.15 K and 7.64 and 9.49 MPa show significant exothermic mixing.The changes observed in the excess enthalpy with temperature and pressure have been discussed in terms of liquid-vapour equilibrium and critical constants for nitrous oxidetoluene. The experimental values of HE at 308.15 and 323.15 K and those previously reported at 313.15 K have been analysed using the Peng-Robinson equation of state. In the last dFade, thermodynamic properties such as the excess molar ebthalpies of carbon dioxide-hydrocarbon mix-tures have been extensively studied in the near critical and supercritical regions because of their anomalous behaviour in the vicinity of tRe critical locus and because of their practical importance in high-pressure technology.'*2 Carbon dioxide has been employed commonly in supercritical fluid extraction because of its low toxicity, safety and low critical tem-perature.It has been reported that N,O is a better solvent than CO, for certain molecule^.^.^ The nitrous oxide and carbon dioxide molecules are isoelectronic and have the same molar mass and very close critical points. For CO, T, is 304.21 K and p, is 7.38 MPa,' while for N,O T, is 309.6 K and p, is 7.24 MPa.6 N20 has a weak dipole moment of 0.166 D,S while CO, has none. This fact seems to be related to the higher affinity shown by N,O to certain molecules. We reported previously measurements of the excess molar enthalpies HEfor carbon dioxide-toluene at temperatures of 308.15, 358.15, and 413.15 K and pressures up to 12.67 MPa' and for nitrous oxide-toluene at 313.15 K and pressures up to 15.00 MPa.' The results for carbon dioxide-toluene could be fitted to the Peng-Robinson equation of state."," This equation is a cubic equation of state of the form RT 4T)p=--v -b V(V + b) + b(u -b) For pure components, a and b are expressed in terms of the critical properties and the acentric factor 0: a( T) = 0.45724a(TXR2T:/p,) (2) b = 0.07780(RTc/p,) (3) a(T)= (1 + ic[l -(T/T,)''2])2 (4) IC = 0.37464 + 1.542260 -0.269920~ (5) For mixtures, a and b are given by a = 11xi xi1 -dij)(Ui Uj)1'Z (6)ij b = 1xibi (7) 1 where dij = dji is the binary interaction parameter which is usually determined from experimental binary data.t Permanent address : Universidad de La Plata-CIDEPINT, Argentina.1 1 D z 3.33564 x C m.Flow calorimetric measurements of HEcovering the whole concentration range for nitrous oxide-toluene at 308.15 and 323.15 K and 7.64, 9.49, 12.27, and 15.00 MPa are reported here. HE for these mixtures are calculated using the cubic equation of state mentioned above and the resulting values are compared with experimental values. The pressure and temperature conditions of the measurements were chosen in order to compare results for nitrous oxide-toluene with those previously obtained for carbon dioxide-toluene.' Experimental The measurements were made using the flow mixing appar- atus and the experimental procedure described previo~sly.~ The chemicals were pumped into the calorimeter by two ther- mostatted ISCO pumps (model LC2600).The calorimeter cell was thermostatted in a silicon oil bath (k0.0005 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. Oscil- lations in pressure were smaller than kO.01 MPa. The materials employed were nitrous oxide (SEO 99.99 mol% pure) and toluene (Merck 99.5 mol% pure) previously dehydrated with sodium. All runs were made in the steady-state fixed composition mode. Flow rates were selected to cover the whole mole frac- tion range. In most cases, the measurements were carried out at a total flow rate of 0.010 cm3 s-'. A few measurements were carried out at a total flow rate of 0.005 cm3 s-'.Flow rates range from 5.0 x lo-' to 2.0 x lop4 mol s-'. The reproducibility of the results was & 1%. The flow rates mea- sured in cm3 s-' were converted to mol s-' and to mole fractions using the densities of the two materials estimated as follows. The densities of N20 at the temperature of the pump and at pressures of 7.64, 9.49, 12.27, and 15.00 MPa were calculated by interpolation of the pressure-volume isotherms of the liquid nitrous oxide measured by Couch et al." The densities of toluene at the temperature of the pump and at pressures of 7.64, 9.49, 12.27 and 15.00 MPa were calculated from the densities and isothermal compressibilities of Garba- josa et ~1.'~and Aicart et ~1.'~ Results Excess molar enthalpies were determined for [xN,O + (1 -x)C,H,CH,] over the entire composition range at 308.15 K and 9.49, 12.27 and 15.00 MPa and at 323.15 K and 7.64, J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 1 Experimental and calculated excess enthalpies HEfor [xN,O + (1 -x)C,H,CH,] HE/(Jmol -') HE/(J mol-') HE/(J mol-') X expt. calc. X expt. calc. X expt. calc. 308.15 K, 9.49 MPa 0.050 1.6 -3.8 0.505 -165 -172 0.822 -425 -430 0.101 -1.4 -7.6 0.551 -223 -211 0.874 -426 -427 0.151 -18 -13 0.601 -271 -257 0.898 -418 -410 0.202 -24 -21 0.649 -298 -301 0.927 -373 -366 0.302 -60 -49 0.701 -359 -350 0.949 -307 -307 0.401 -85 -98 0.749 -386 -389 0.980 -168 -162 (145 1 -120 -131 0.802 -405 -422 308.15 K, 12.27 MPa 0.052 14 17 0.457 16 17 0.851 -200 -200 0.102 32 31 0.504 -5.4 -2.1 0.876 -202 -201 0.153 49 42 0.551 -21 -26 0.900 -194 -195 0.203 44 49 0.606 -54 -58 0.907 -190 -191 0.257 52 52 0.653 -86 -88 0.929 -176 -173 0.308 50 50 0.754 -161 -156 0.950 -142 -144 0.353 46 45 0.761 -163 -160 0.98 1 -69 -72 0.407 32 33 0.805 -184 -185 308.15 K, 15.00 MPa 0.053 32 32 0.463 112 111 0.854 -69 -73 0.104 56 57 0.510 100 101 0.879 -79 -80 0.156 82 79 0.558 86 86 0.890 -81 -81 0.207 92 95 0.612 63 63 0.902 -83 -82 0.262 108 108 0.665 37 35 0.909 -80 -81 0.358 120 119 0.719 -0.1 2.8 0.93 1 -78 -76 0.386 120 119 0.766 -29 -27 0.952 -63 -64 0.413 118 118 0.809 -51 -52 0.98 1 -34 -32 0.438 114 115 323.15 K, 7.64 MPa 0.050 -223 -249 0.496 -2587 -2673 0.798 -4291 -4359 0.099 -580 -535 0.546 -2953 -2960 0.848 -4482 -4561 0.151 -792 -833 0.549 -3016 -2979 0.892 -4435 -4307 0.204 -1142 -1123 0.603 -3354 -3285 0.953 -2099 -2 108 0.252 -1320 -1364 0.649 -347 1 -3534 0.970 -1255 -1258 0.300 -1635 -1604 0.698 -3833 -3798 0.975 -968 -996 0.352 -1872 -1872 0.750 -4125 -4086 0.990 -155 -351 0.399 -2155 -2119 323.15 K, 9.49 MPa 0.05 1 -113 -100 0.405 -850 -884 0.707 -1598 -1595 0.103 -176 -205 0.406 -922 -885 0.754 -1694 -1687 0.154 -338 -313 0.478 -1062 -1059 0.806 -1796 -1764 0.205 -419 -423 0.510 -1126 -1137 0.876 -1718 -1780 0.258 -546 -540 0.547 -1207 -1225 0.929 -1620 -1616 0.306 -668 -651 0.557 -1265 -1251 0.950 -1443 -1433 0.347 -729 -745 0.654 -1474 -1479 0.97 1 -1139 -1114 0.348 -749 -747 323.15 K, 12.27 MPa 0.054 -12 -18 0.464 -305 -300 0.722 -553 -543 0.106 -32 -40 0.468 -300 -304 0.759 -581 -569 0.211 -102 -97 0.504 -358 -338 0.762 -563 -571 0.213 -104 -98 0.515 -340 -349 0.812 -576 -591 0.266 -131 -134 0.516 -341 -350 0.829 -573 -592 0.267 -127 -135 0.562 -396 -395 0.892 -559 -554 0.27 1 -141 -138 0.568 -403 -401 0.900 -561 -543 0.318 -170 -173 0.597 -422 -430 0.949 -444 -405 0.357 -198 -205 0.613 -450 -446 0.952 -385 -388 0.366 -210 -212 0.617 -463 -450 0.982 -195 -198 0.391 -250 -234 0.670 -498 -499 0.990 -118 -117 0.416 -267 -256 0.690 -513 -517 0.99 1 -104 -111 0.418 -249 -257 0.715 -529 -538 323.15 K, 15.00 MPa 0.054 0.3 1.6 0.418 -69 -77 0.857 -316 -320 0.105 1.6 0.8 0.440 -87 -88 0.881 -314 -310 0.106 2.5 0.7 0.444 -85 -90 0.89 1 -302 -303 0.159 -2.8 -3.2 0.465 -110 -102 0.904 -299 -291 0.21 1 -11 -10 0.515 -127 -131 0.932 -256 -250 0.264 -29 -21 0.559 -163 -160 0.935 -240 -243 0.294 -28 -29 0.583 -186 -177 0.936 -236 -241 0.362 -49 -53 0.667 -238 -236 0.972 -142 -138 0.363 -61 -53 0.7 14 -277 -269 0.982 -95 -98 0.387 -62 -63 0.720 -263 -273 0.982 -87 -98 0.390 -66 -65 0.767 -300 -300 0.998 -4.9 -12 0.415 -71 -76 0.812 -312 -318 J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 I-E 30 z -200 -400 0 0.2 0.4 0.6 0.8 1.0 X Fig. 1 Plot of HE against x for [xN,O + (1 -x)C6H,CH3] at 308.15 K as a function of pressure: 0,9.49; A, 12.27;0,15.00MPa; (-) calculated from eqn. (8); (--) calculated from eqn.(1) 9.49, 12.27, and 15.00 MPa. The results are given in Table 1. Values for HEat each temperature and pressure studied were fitted to the equation: 1C,(2x -1)" HE/J mol-I = x(1 -x) 1 +,=' Bk(2x -(8) k= 1 The coefficients C, and Bk are given in Table 2 together with the standard deviations, s, between experimental and calcu- lated HEvalues. Fig. 1 and 2 are plots of HE against x for the isobars studied at 308.15 and 323.15 K, respectively. Fig. 3 is a plot of p against T for [xN,O + (1 -X)C6H,CH3] showing the vapour-pressure equilibrium curve of nitrous oxide,12 the critical locus in the vicinity of the N20 critical point, and the points at which experimental measurements of HE have been made. For toluene T, is 591.8 K and p, is 4.10 MPa.6 Vapour-liquid equilibrium data or critical locus data are not available for [xN,O + (1 -x)C6H,CH3].The critical locus shown in Fig. 3 has been estimated using the procedure developed by Heidemann and Khalil15 and the Peng-Robinson equation of state." The densities of N,O and toluene at the temperatures and pressures of the experiments are listed in Table 3. Values for N,O densities were taken from Couch et a1.' and from Langenfeld et a1.16 Values for toluene densities were calcu- lated from the coefficients of the Tait equation given by Takagi." The toluene enters the calorimeter as a liquid because the temperature is lower than the critical tem-perature of this component and the pressures are always 0 -1 000 I-0 E -20003 z -3000 -4000 0 0.2 0.4 0.6 0.8 1.0 X Fig. 2 Plot of HE against x for [xN20 + (1 -X)C6H,CH3] at 323.15 K as a function of pressure: 0,7.60; 0,9.49; A, 12.27; 0, 15.00 MPa; (-) calculated from eqn. (8); (--) calculated from eqn.(1) higher than its critical pressure. The values of the density of toluene shown in Table 3 are typical of a liquid and change very little with pressure. At 308.15 K the nitrous oxide also enters the calorimeter as a liquid because the temperature is lower than the critical temperature of this component and the pressures are always higher than its critical pressure. The values of the density of nitrous oxide at 308.15 K shown in I ' I ' I ' I ' Ii 00 13 00 I? 11T Q 9 7 0 rlI#I8I,I 300 310 320 330 TIK Fig.3 Plot of p against T for [xN,O + (1 -x)C6H,CH3] showing the vapour-liquid equilibrium curve (---) and critical point (A) of nitrous oxide, the critical locus (-) from x = 1.00 to 0.97, and (T, p) coordinates (0)where experimental measurements were made Table 2 Coefficients and standard deviation, s, for least-squares representation of HE/J mol-' for [xN,O + (1 -x)C,H,CH,] by eqn. (8) T = 308.15 K T = 323.15 K coefficients 9.49" 12.27" 15.00" 7.64" 9.49" 12.27" 15.00" ~~ -672.50 -1.0886 414.66 -10776.7 -4449.1 -1340.7 -487.70 1036.5 895.99 728.85 ,-752.96 820.66 851.63 -199.83 -271.33 -350.32 ----285.19 -329.81 -223.46 ----0.84701 0.73508 0.55148 1.0787 0.92391 0.83657 0.73433 ---0.13777 -------0.43665 -------0.98008 -----I 0.43 122 ------1.24735 ---10 3.2 2.0 83 25 11 5.8 " p/MPa.2680 Table 3 Densities of N,O and toluene under the temperature and pressure conditions of the experiments N*O toluene pjMPa 308.15 K 323.15 K 308.15 K 323.15 K 7.64 -222 -846 9.49 740 437 86 1 848 12.27 790 664 863 850 15.00 819 727 865 852 Table 3 are those typical of a liquid and change very little with pressure. At 323.15 K the nitrous oxide enters the calo- rimeter as a supercritical fluid because the temperature and pressures studied are always greater than those defining its critical point. However, this NzO fluid may be a low-density (gas-like) fluid or a high-density (liquid-like) fluid depending on the pressure.The values of the density of nitrous oxide at 323.15 K change as the pressure increases from those typical of a gas at 7.64 and 9.49 MPa to those typical of a liquid at 12.27 and 15.00 MPa. The resulting [xN,O + (1 -x) C,H,CH,] may be liquid, gas-like fluid, or liquid-like fluid, depending on the critical temperature and pressure of the particular mixture. The phase diagram for [N,O+ C,H,CH3] belongs to class I in the classification of van Konynenburg and Scott.18 The critical locus predicted by the Peng-Robinson equation" for [N,O + C6H5CH,] is similar to the critical locus for the [CO, + C,H,CH,].* The critical line goes through a maximum at p II 17.5 MPa and T 21 435 K and returns to the toluene critical point (T,= 591.8 K, p, = 4.10 MPa).Since the temperatures and pressures studied are far from those defining the critical point of toluene, [xN,O + (1 -X)C,H,CH,] is a liquid from x = 0 to x N 0.95, and is a fluid only in a narrow composition range in the N,O-rich region. Owing 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 is detected by a high-slope linear section in the N,O-rich region of the isobars shown in Fig. 1 and 2. Unfortunately, the vapour and liquid equilibrium-phase compositions cannot be determined from these plots. When the states and densities of the pure components and the mixture are similar (liquid or liquid-like fluid nitrous oxide and liquid toluene forming a liquid or liquid-like fluid mixture), the values of HE are negative or slightly positive.This is so at 308.15 K for isobars at 9.49, 12.27 and 15.00 MPa and at 323.15 K for isobars at 12.27 and 15.00 MPa when the density values are similar for N,O and toluene. When the states and densities of the pure components differ (gas-like fluid nitrous oxide and liquid toluene), and the resulting mixture is a liquid, large negative values of HE are observed. This is so at 323.15 K for the isobars at 7.60 and 9.49 MPa when the density of N,O is much lower than that of toluene. The shape of the isobars in Fig. 1 and 2 denotes behav- iour similar to that previously reported for [xCO, + (1 -x)C,H,CH,].* The critical point of carbon dioxide is very close to that of nitrous oxide and the [xCO, + (1 -X)C6H5CH3]and [xN,O + (1 -X)C6H5CH,]critical loci are very similar.The temperature and pressures at which experimental measurements have been made for [XCO, + (1 -X)C,H,CH,] and [xNZO + (1 -x)C,H,CH,] have a similar position with respect to the critical locus in the p against T plot. This may be seen by comparing the plot of Fig. 2 with a similar one shown for [XCO, + (1 -x)C,H,CH3] in Fig. 3 of ref. 8. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Calculationof the Excess Molar Enthalpy The excess molar enthalpy of a binary mixture is given by HE= [H -H*lmiX-1xi[H -H*li (9) I where [H -H*lmiXis the residual molar enthalpy of the mixture and [H -H*li is that of components 1 and 2, respectively. The residual molar enthalpy is given by H -H* = RT(z -1) + JI{T[z]"-p} dv (10) where z is the compressibility factor.For a fluid which follows the Peng-Robinson equation of state, eqn. (10) becomes -da7'--a H-H*=RT(z-l)+ dT In [z + 2.414Bj (11)2312b z -0.414B where B is given by B=--b RT Comparison of the Peng-Robinson Equation of State with Experiment Excess enthalpies for the nitrous oxide-toluene system were calculated at 308.15, 313.15 and 323.15 K from 7.60 to 15.00 MPa using the expressions given in the previous section. The experimental values of HE at 313.15 K were reported in a previous paper and are shown in Fig. 4. The values used for the critical constants are those already given.Values for the acentric factor were taken from Reid et aL6 The binary inter- action parameter was adjusted to give the best fit to the experimental HE values at 308.15, 313.15 and 323.15 K. A value of 0.1018 was obtained for a,, . Since the vapour and liquid equilibrium-phase compositions are unknown, HE values were calculated only in the one-phase region. The curves of long dashes shown in Fig. 1, 2 and 4 are HEvalues calculated using this value for a,, . Although better results could be obtained if a,, was adjusted to give the best fit at each temperature, we prefer to make comparison with experi- ment using a single value for the interaction parameter. For the 9.49, 12.27 and 15.00 MPa isobars at 308.15, 313.15 and 323.15 K the mean deviation of the calculated values of HE from experiment is 80 J mol-'.For the 7.64 MPa isobar at 323.15 K the mean deviation is 100 4 mol-'. This is in good agreement if we take into account the fact that this isobar loo0 -1 000 I-0 E -2000 0002'-3000 -4000 0 0.2 0.4 0.6 0.8 1.0 X Fig. 4 Plot of HE against x for [xN,O + (1 -x)C,H,CH,] at 313.15 K as a function of pressure: 0,7.60; 0,9.49; A, 12.27; 0, 15.00 MPa; (--) calculated from eqn. (1) J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 268 1 exhibits a minimum of -4500 J mol-'. The agreement is not ninger, M. Radosz, M. A. McHugh and V. J. Krukonis, Elsevier, good for the 7.60 MPa isobar at 313.15 K which exhibits a minimum of -2300 J mol-' (the mean deviation is 600 J mol -').This discrepancy between experimental measure-ments and the calculated curve seems to arise from the failure of the Peng-Robinson equation of state to give the correct value for the compressibility factor of nitrous oxide under these 3 4 5 6 Amsterdam, 1985. K. Sakaki, J. Chem. Eng. Data, 1992,37,249. N. Alexandrou, M. J. Lawrence and J. Pawliszyn, Anal. Chem, 1992,64,30 1. Carbon Dioxide, IUPAC Thermodynamic Tables of the Fluid State, Pergamon, Oxford, 1976. R. C. Reid, J. M. Prausnitz and B. E. Poling, The Properties of conditions of temperature and pressure. Couch et aI.12 reported experimental values for the nitrous oxide compress- ibility factor for a wide range of temperature and pressure. The agreement between these values for z and those calcu- lated by means of the Peng-Robinson equation or by means of the Kubic equation" is good except at 7.60 MPa and 7 8 9 10 Gases and Liquids, McGraw-Hill, Singapore, 1988.D. E. Stogryn and A. P. Stogryn, Mol. Phys., 1966,11,371. C. Pando, J. A. R. Renuncio, R. S. Schofield, R. M. Izatt and J. J. Christensen, J. Chem. Thermodyn., 1983, 15, 747. R. C. Castells, C. Menduiiia, C. Pando and J. A. R. Renuncio, J. Chem. Thermodyn., 1994,26,641. D-Y. Peng and D. B. Robinson, Ind. Eng. Chem. Fundam., 1976, 313.15 K when we are in the vicinity of the nitrous oxide critical point. Wormald and c~-workers~~-~~ have sucessfully used the Kubic equation of state to fit excess enthalpies of several binary mixtures at high pressures.HE data for the [N,O-C,H,CH, J system were also analysed using this equa- 11 12 13 15, 59. A. G. Casielles, C. Pando and J. A. R. Renuncio, Thermochim. Acta, 1989, 154, 57. E. J. Couch, L. J. Hirth and K. A. Kobe, J. Chem. Eng. Data, 1962,6, 229. G. Garbajosa, G. Tardajos, E. Aicart and M. Diaz Peiia, J. Chem. Thermodyn., 1982,14,671. tion. Results from this calculation are not reported in this paper because values for the deviation between experimental and calculated HE are higher than those obtained for the Peng-Robinson equation of state. 14 15 16 E. Aicart, G. Tardajos and M. Dim Peiia, J. Solution Chem., 1982, 11, 557. R. A. Heidemann and A. M. Khalil, AIChE J., 1980,26,769. J. J. Langenfeld, S. B. Hawthorne and D. J. Miller, Anal. Chem., 1992,64,2263.This work was funded by the Spanish Ministry of Education 17 18 T. Takagi, Rev. Phys. Chem. Jpn., 1978,48, 17. P. H. Van Koynenberg and R. L. Scott, Phil. Trans. R. SOC., (DGICYT) Research Project PB-9 1-0392. We appreciate the aid given to us by Dr. R. A. Heidemann in estimating the critical locus. R.C.C. acknowledges the Universidad Com- plutense of Madrid for a visiting research professorship at the Department of Physical Chemistry. 19 20 21 1980,298,495. W. L. Kubic, Fluid Phase Equilibria, 1982,9, 79. C. N. Colling, N. M. Lancaster, M. J. Lloyd, M. Masucci and C. J. Wormald, J. Chem. SOC., Faraday Trans., 1993,89,77. M. Masucci and C. J. Wormald, J. Chem. SOC.,Faraday Trans., 1993,89,1345; 3375. 22 M. Masucci, C. J. Wormald and L. Yan, J. Chem. SOC.,Faraday References 23 Trans., 1993,89,4193. C. J. Wormald and C. N. Colling, J. Chem. Thermodyn., 1993, 1 Supercritical Fluid Technology, ed. T. J. Bruno and J. F. Ely, CRC Press, Boca Raton, FL, 1991. 2 G. Morrison, J. M. H. Levelt Sengers, R. F. Chand and J. J. 24 25, 599. C. J. Wormald and M. J. Lloyd, J. Chem. Thermodyn., 1993, 26, 101. Christensen, Supercritical Fluid Technology, ed. J. M. L. Pen- Paper 4/0206 1 H ; Received 6th April, 1994