J . Chem. SOC., Furudaj) Trans. I , 1989, 85(6), 1303-1313 Excess Molar Enthalpies of Steam-n-Hexane and Steam-n-Heptane up to 698.2 K and 12.6 MPa Nabil Al-Bizreh, Charles N. Colling, Neil M. Lancaster and Christopher J. Wormald* Department of Physical Chemistry, University of Bristol, Bristol BS8 1 TS Flow calorimetric measurements of the excess molar enthalpy, H:, of [xH,O + (1 - x)C,H,,] and [xH,O + (1 - x)C,H,,] are reported. The meas- urements extend over the range 448.2-698.2 K at pressures up to 12.6 MPa. Most of the measurements are at x = 0.5 but the composition dependence was investigated under selected conditions. Whereas previous measurements of HZ for steam with C,-C, n-alkanes at pressures up to 12 MPa could be fitted using the virial equation of state truncated after the third term, the new measurements can only be fitted at lower pressures.This is shown to be because the residual molar enthalpies of n-hexane and n-heptane are much larger than those of the fluids previously studied. Graphs of H: against pressure for (0.5H20 + 0.5C,H,,) exhibit maxima at pressures well below the saturation pressure. It is demonstrated that the maxima are due to the shape of the residual molar enthalpy curves of steam and n-heptane and not to any unusual molecular interaction. Residual molar enthalpies of (0.5H20 + 0.5C7H,,) calculated from the H: measurements lie on smooth monotonic curves. Comparison of the (0.5H20 + 0.5C7H,,) HZ measure- ments with the Peng-Robinson and Patel-Teja equations of state show that neither cubic equation fits the measurements.In previous papers we reported measurements of the excess molar enthalpy HE of mixtures containing steam made using two flow-mixing calorimeters of different design. A low pressure differential flow-mixing calorimeter' has been used to make measurements in the range 353.2-423.2 K at pressures around atmospheric. The mixtures studied include steam-hydrogen,' -nitrogen,, -argon,3 -carbon m~noxide,~ -carbon d i ~ x i d e , ~ C,-C, n-alkane~,~-~ +thene,5 -propene,6 -benzene,, xyclohexane,' -chl~romethane,~ -chloroethaneg and -trichloromethane.'o Analysis of the measure- ments showedg that for pairwise interactions, where there are no specific forces, cross- term second virial coefficients B,, can be calculated using the Stockmayer potential parameters E/kB = 233 K, 0 = 0.312 nm and t* = 1.238 for water, together with the combining rule (1) E l , = r ( E I ' E 2 , ) ~ where 2 ( 4 rJ$ (I' 1,): <=---------- 4 2 (I' +I,> and I is the ionisation energy.In the analysis of HE measurements on steam-argon it was noted3 that B12s calculated using Stockmayer parameters for fluoromethane are not very different from B12s calculated using the above parameters for water. Fluoromethane has the same dipole moment (1.85 Dt) as water, but a smaller reduced dipole moment Using fluoromethane as a homomorph for water in non-associative interactions we suggested a combining rule' which allows the calculation of cross-term third virial t 1 D = 3.33564 x C m. t* = 1.044. 13031304 H: of Steam-n- Hexane and Steam-n-Heptane coefficients from the corresponding states correlation of Orbey and Vera." The combining rule was tested using HE measurements on steam-n-pentane at tem- peratures up to 698.2K and pressures up to 14.0MPa obtained using a high-pressure flow-mixing calorimeter.The experimental HZs were compared with H:s calculated from the virial equation of state using virial coefficients B, C and D for steam, which are consistent with the 1984 NBS/NRC Steam Tables'' of Haar, Gallagher and Kell (HGK), the virial coefficient B for n-pentane calculated from the Kihara potential and C calculated from the Orbey-Vera correlation, the cross-term B,, from eqn (1) and (2), and cross-terms Cll2 and C,,, from our suggested combining rule. Agreement with experiment was to within the uncertainty on the measurements over the full range of temperature and pressure.The virial equation of state also fits all the other HE measurements made at temperatures up to 698.2 K and pressures around 12 MPa. These include mixtures of ~team-nitrogen,'~ -hydrogen,14 -C,-C, n-alkanes,15-17 <thene,I6 -carbon monoxide," and +arbon dioxide.', That the truncated virial equation of state fits the H: measurements on these mixtures so well deserves some comment. It might be expected that the equation would fit the residual volume and enthalpy of a fluid up to moderate densities, but it evidently fits the HZ measurements up to ca. 90% of the saturation pressure of water. This is best explained by examining each of the three terms to which Hg is related: Here HZ is the residual molar enthalpy of the mixture; Hil and H:, are the residual molar enthalpies of steam and n-pentane. For all the mixtures studied so far the maximum pressure to which we have been able to make vapour-phase HE measurements is the saturation pressure of water.Fig. 1 ( a ) shows the vapour pressure of water and of the C,-C, n-alkanes; the curves terminate at critical points. The figure shows that for all measurements on C,-C, n-alkanes and for measurements on (0.5H,O + 0.5C,H1,) above 473.2 K the n-alkane was a supercritical fluid. The figure also shows that at 448.2 K the saturation pressure of water is 0.9 MPa and that of n-pentane is 2.3 MPa. An H: measurement made at 90 % of the saturation pressure of water (0.81 MPa) is therefore at a pressure which is (0.81/2.3) x 100 = 35 Yo of the saturation pressure of n-pentane.For steam, Gallagherg has calculated virial coefficients B, C and D, which are a good fit to the 1984 HGK steam stable residual enthalpies at pressures up to ca. 90% of the saturation pressure, so that H:, in eqn (3) is not significantly in error. For n-pentane at 448.2 K only B and C are known, but at pressures up to 35 YO of saturation two virial coefficients give HZ2 with adequate accuracy. Comparison of H:, for n-pentane at 448.2 K calculated using B and C terms with H:, calculated from the BWRS equation of state shows that up to 2 MPa the difference is negligible. For (0.5H,O + 0.5C,H1,) at 448.2 K the saturation pressure is the dew curve, and this may be crudely approximated to the mean saturation pressure (1.6 MPa) of n-pentane and water.The mixture at 0.8 1 MPa is therefore at ca. 50 YO of the saturation pressure, and H: can be calculated from the mixture virial coefficients with good accuracy. In the temperature range 473.2-698.2 K n-pentane is a supercritical fluid, and comparison with the BWRS equation shows that the virial equation of state with coefficients B and C fits H:, up to pressures around 10 MPa. Using the equation of state described in the following paper the maximum density at which HE measurements on (0,5H,0+0.5C,H1,) were made was calculated to be 0.255 g cm-3 at 598.2 K and 14 MPa. This is ca. 2/3 of the critical density of the mixture. It is worth noting that over the whole 448.2-698.2 K temperature range, HZl of steam is very close to that of n-butane.This can be seen from fig. 1 (b) where HZ, is compared with H:, for the C,-C, n-alkanes at 598.2 K. At this temperature HZs are large and have been measured at pressures close to the saturation pressure 12.06 MPa of steam.N . Al-Bizreh, C. N . Colling, N . M. Lancaster and C. J. Worrnald 1305 573 473 T/K 3 73 0 4 a p l W a 12 Fig. 1. (a) Vapour pressure curves for C,-C, n-alkanes and for water, (-) the vapour pressure of n-alkanes,lS (----) the vapour pressure of water.12 Arrows at the top of the figure indicate temperatures at which the H: measurements were made. (b) Residual molar enthalpies H: at 598.2K of C,-C, n-alkanes and of water. (-) H: of n-alkane calculated from the BWRS equation of state, (----) H: of water." Fig.l ( a ) shows that for steam-n-heptane the maximum pressure at which vapour-phase HZ measurements can be made is the saturation pressure of n-heptane. At 498.2 K and 1.25 MPa steam entering the calorimeter is at 50% of its saturation pressure, but n-heptane is at 85 % of saturation. Fig. 1 (b) shows that H:* of n-heptane is ca. four times bigger than HZ1 of steam. We might therefore expect measurements of HE for steam-n-heptane to be fitted using virial coefficients B and C for n-heptane up to such pressures as the virial equation fails to fit H:2 of n-heptane. We now report HE measurements on steam-n-hexane and steam-n-heptane. Experimental The n-hexane, initially 95 mol% pure n-C,H,,, was treated with oleum to remove benzene, washed with alkali, dried with molecular sieve, and distilled twice.The density1306 HE of Steam-n- Hexane and Steam-n- Heptane Table 1. Experimental excess molar enthalpies H: of (0.5H20 + 0.5C6H1,) and (0.5H20 + 0.5C,H16) measured over a range of pressure 448.3 473.2 498.2 523.2 548.2 573.2 598.2 623.2 648,2 673.2 698.2 448.2 473.2 498.2 523.2 548.2 573.2 598.2 648.2 698.2 HZ HZ HZ HZ HZ p/MPa /J mol-' p/MPa /J mo1-I p/MPa /J mol-1 p/MPa /J rno1-I p/MPa /J mol-' - 0.60 0.76 0.73 1.10 1.18 1.79 1.28 1.98 2.07 2.86 2.01 2.66 3.47 1.13 1.98 2.67 1.03 1.79 2.67 1.05 1.45 1.74 1.12 1.86 2.74 0.4 1 0.38 0.40 0.43 0.79 0.69 1.38 0.86 1.44 0.79 1.44 1.13 2.13 1.10 2.17 466 546 399 65 1 603 1061 574 953 853 1326 748 1037 1427 372 659 908 30 1 536 786 234 334 414 255 365 603 382 323 294 259 507 369 859 389 773 302 649 404 805 288 617 0.76 0.95 1.46 2.62 2.72 3.38 3.64 4.34 4.20 4.98 5.48 3.45 4.1 1 4.91 3.45 4.10 4.87 2.55 3.36 4.1 1 3.39 4.1 1 4.78 0.79 0.79 0.76 1.48 2.17 2.48 3.02 2.84 4.24 2.79 4.24 4.13 6.41 4.27 6.36 (0.5H20 + 0.5C6H1,) 605 695 996 1964 1563 2259 1888 2512 1865 2329 2637 1199 1534 1844 1034 1287 1513 654 870 1115 79 1 987 1160 1.16 1.79 3.17 4.00 4.25 4.9 1 5.40 6.14 6.95 5.58 6.17 6.65 5.75 6.07 6.47 4.87 5.54 6.18 5.42 6.15 6.94 8 60 1336 2926 3080 3443 3086 3449 3082 3459 2168 2388 2666 1862 2022 2171 1352 1584 1746 1328 1526 1757 (0.5H20 + 0.5C,H16) 13515 1.0 13400 792 572 1.13 1000 1160 2.48 9453 2509 2.82 9430 2206 3.55 7242 4729 4.58 7654 2070 5.62 6271 5014 6.00 6259 1576 5.62 4784 3180 7.06 5279 1977 8.53 3937 3218 1373 8.44 2815 2160 1.31 2.26 3.45 4.56 5.00 6.1 1 6.79 7.47 8.34 7.06 7.64 8.29 7.12 7.89 8.58 6.89 7.61 8.25 7.62 8.41 9.14 1.65 3.20 4.58 7.10 7.68 8.44 10.6 10.6 1004 204 1 3879 3979 4548 4019 4352 3717 4013 2857 3056 3309 2373 2646 2830 1996 2191 2363 1901 2097 227 1 9304 9259 7657 6083 5301 5177 4066 3173 2.43 3.79 5.45 7.51 8.13 8.93 9.29 9.02 9.7 1 9.42 10.2 10.1 8.95 9.71 9.97 10.4 10.7 2.13 3.54 5.62 8.44 9.82 11.2 12.5 12.6 2484 5376 5065 4567 4716 4100 41 13 3509 3625 3683 3017 3 143 2536 2666 2807 2402 2520 10865 91 19 7246 5623 4890 4617 3923 3333 of the purified material was 654.98 kg mP3 at 298.1 5 K (literature :19 654.84 kg m-3).The purified material was not less than 99.9mo1°/0 n-C,H,,. The n-heptane, initially 99 mol% pure n-C7H16, was dried with molecular sieve and distilled twice.After purification the density was 697.25 kg m-3 at 298.15 K (literature?' 697.51 kg m-3). The purified n-heptane was not less than 99.8 mol% n-C7Hl,. Steam was generated from ordinary distilled water. Measurements of HZ were made using the apparatus describedN . Al-Bizreh, C. N . Colling, N . M. Lancaster and C. J. Wormald 1307 Table 2. Experimental excess molar enthalpies H: of [xH,O + (1 - x)C,H1,] and [xH,O + (1 - x)C,H,,] measured over a range of composition x HZ H; H; HZ H; x /Jrnol-' x /J mol-' x /Jmol-' x /Jmol-' x /J mol-l [xH,O + (1 - x)C,H1,1 T = 548.2 K 0.299 4296 0.402 4467 0.497 4249 0.602 3709 0.702 2950 T = 598.2 K 0.297 3732 0.399 4165 0.499 4200 0.600 3937 T = 648.2 K 0.303 2925 0.400 3249 0.500 3306 0.599 3136 0.702 2672 p = 4.93 MPa p = 9.41 MPa p = 11.48 MPa txH,O + (1 - x)C,H,,I T = 548.2 K T = 573.2 K T = 598.2 K p = 4.58 MPa p = 6.00 MPa p = 7.68 MPa 0.301 8428 0.400 8351 0.498 7672 0.600 6616 0.701 5318 0.301 6296 0.402 6531 0.499 6263 0.601 5587 0.701 4583 0.300 4780 0.398 5310 0.502 5298 0.601 4833 0.700 4061 4 L E 2 W E 2 2 n 523.2 I--" I 0 0 0 4 8 0 4 8 p/MPa Fig.2. (a) Excess molar enthalpies H; of (0.5H20+0.5C,H,,) plotted against pressure. 0, A, table 1. (-) calculated from the truncated virial equation of state as described in the text. (b) (HE/p) of (0.5H20 + 0.5C,H1,) plotted against pressure. The intercepts are values of the excess isothermal Joule-Thomson coefficient of the mixture given by eqn (6). 0, A, table 1. (-), calculated from the truncated virial equation of state.previo~s1y.l~ Hydrocarbon removed from the apparatus was analysed by g.1.c. to check for decomposition. For each mixture most of the HE measurements were made at x = 0.5, at temperatures up to 698.2 K, and at pressures up to ca. 12 MPa. These measurements are listed in table 1. Measurements were also made over a range of mole fraction x at selected pressures, and these are listed in table 2. Results of the1308 Hz of Steam-n- Hexane and Steam-n- Heptane 8 ‘-473.2 ‘-498.2 p 5 2 3 . 2 6 1 p 698.2 2 I 1 I 1 1 1 C 4 8 12 p/MPa Fig. 3. (a) Excess molar enthalpies H: of (0.5H,0+0.5C7H1,) plotted against pressure. 0, table 1 . (-), drawn with a flexicurve. (b) Excess molar enthalpies HZ of (0.5H,0+0.5C7H1,) at temperatures above the critical temperature 540.2 K of n-heptane.0, table 1 . (-), drawn with a flexicurve. (----), calculated from the truncated virial equation of state. I I X r I I I I 1 0 0.2 0.4 0.6 0.8 1 X Fig. 4. (a) Excess molar enthalpies H: of [xH,O + (1 - x)C6HI4]. (b) Excess molar enthalpies HZ of [xH,O+(l -x)C,H,,]. 0, A, 0, table 2. (-) fitted to the measurements by plotting H:/4x( 1 - x) against x. (----) calculated from the truncated virial equation of state.N . Al-Bizreh, C. N . Colling, N . M. Lancaster and C. J. Wormald 1309 measurements on (0.5H20+0.5C,H,,) are plotted against pressure in fig. 2, and on (0.5H20 + 0.5C,H1,) in fig. 3. Results of the measurements on [xH20 + (1 - x)C,H,,] are plotted against x in fig. 4(a), and on [xH,O+ (1 -x)C,H,,)] in fig.4(b). The accuracy of the steam-n-hexane HE measurements is 2 % at temperatures above the critical temperature 540.2 K of n-heptane, and between 2 and 4% below this temperature. Comparison with the Virial Equation of State It was shown previouslyg that the residual enthalpy H: of a fluid is given by H;(V, T) = I0*[ T($,)v-p]dV+pV-RT. (4) Using the virial equation of state in powers of the density truncated after the fourth term, HE is given by9 where $', w and A are related to the mixture virial coefficients B, C and D and their temperature derivatives. The virial coefficients Bll, C,,, and D,,,, for steam obtained by Gallaghers were fitted to seventh-order polynomials in powers of T-l. Coefficients of the polynomials have been published.20 Differentiation gave #yl, ylll, and Allll for steam.For n-hexane B,, and #i2 were calculated from the Kihara potential with the parameters a = 0.1329 nm, CT = 0.5458 nm, and ElkR = 932 K. For n-heptane the parameters a = 0.1526 nm, CT = 0.5769 nm and ElkB = 1057 K were used. These parameters fit class I virial coefficient measurements on the hydrocarbon.21 Third virial coefficients for the hydrocarbons were calculated from the correlation of Orbey and Vera." Cross-term second virial coefficients B,, and isothermal Joule-Thomson coefficients #;2 were calculated by combining the Kihara potential parameters for the n-alkanes with the parameters of the Stockmayer potential D = 0.3 12 nm, &/kB = 233 K and t* = I .238 for water.g Cross-terms E ~ , were calculated using eqn (1) and (2), a12 and o12 were taken to be the mole fraction weighted arithmetic mean of the pure-component parameters.Cross-term third virial coefficients C,,, and C,,, and their temperature derivatives were calculated from the Orbey-Vera'' correlation together with the combining rules given previously.20 In these combining rules critical parameters for fluoromethane were used, instead of water critical parameters, for those interactions where there was no hydrogen bonding. No cross-term fourth virial coefficients could be calculated. The first test of any set of HE measurements made at high pressures is to check that they are consistent with HEs obtained using our low-pressure flow-mixing calorimeter. At low densities eqn ( 5 ) can be written in the form' limp -+ 0 (HE/p) = x( 1 - x ) (2#y2 - #yl - #&).(6) Values of (HE/p) for (0.5H20 + 0.5C,Hl,) are plotted against pressure in fig. 2(b) where circles and triangles are used alternately to make the isotherms clear. Solid curves shown in the figure should be ignored for the moment. For the Hzs measured over the range 498.2-698.2 K extrapolation of (H:/p) to zero pressure was done graphically. The measurements at 448.2 K and 473.2 K are over too small a pressure range for meaningful extrapolation to be made, and were neglected. Values of limp -+ O(HE/p) are plotted against temperature in fig. 5, where they are compared with values obtained using the low-pressure mixing calorimeter. The upper points in fig. 5 were obtained from a similar analysis of the (0.5H20 + 0.5C,H1,) measurements.Solid curves shown in the figure were calculated from eqn (6) using the Kihara potential for the n-alkane and the Stockrnayer1310 H: of Steam-n- Hexane and Steam-n- Heptane 400 500 600 700 TIK Fig. 5. Zero pressure intercepts of graphs of (H:/p) against p plotted against temperature. The lower curve is for (0.5H,0+0.5C,Hl,) and the upper curve is for (0.5H,0+0.5C7Hl,). 0, from H: measurements obtained using our low-pressure flow mixing cal~rimeter.~-~ 0, from H z measurements listed in table 1. (-) calculated from the truncated virial equation of state. potential for steam with the parameters given above. Fig. 5 shows that the measurements from the low- and high-pressure calorimeters are consistent. The solid curves shown in fig. 2 are H:s for (0.5H20 + 0.5C,H14) calculated from eqn (5).Fig. 1 (a) shows that for this mixture n-hexane vapour entering the calorimeter was a supercritical fluid for the measurements in the range 523.2-698.2 K. The measurements at 498.2 K extend up to 2.43 MPa, 92% of the n-hexane saturation pressure, and these are quite well fitted by eqn (5). Fig. 2(b) shows that the fit to the measurements at pressures below 1.5 MPa is within the uncertainty on the measurements. At higher pressures the calculated HEs are smaller than the experimental values. Fig. 2 shows that the inadequacy of eqn ( 5 ) is most marked at 523.2, 548.2 and 573.2K. At higher temperatures the calculated HE values agree with experiment more closely. This is because the density of the mixture diminishes with increasing temperature, and the non- ideality becomes less.The Hzs for (0.5H20 + 0.5C7H,,) are shown in fig. 3. In fig. 3 (a) the solid curves were drawn with a flexicurve. The smooth curves between 548.2 and 698.2 K are all above the critical temperature 540.2 K of n-heptane. Below T, measurements were made at pressures up to and beyond the saturation pressure. At 448.2 K the saturation pressure is 0.6 MPa, and above this pressure n-heptane enters the calorimeter in the liquid phase. The vertical line drawn in the figure corresponds to the enthalpy of evaporation. The isotherms at 498.2 and 523.2K show smaller vertical sections as the enthalpy of evaporation diminishes with increasing temperature. The HZ values obtained by mixing supercritical n-heptane with subcritical steam are shown on a larger scale in fig.3 (b). The solid curves were again drawn with a flexicurve, and the broken curves were calculated from the virial equation of state as described above. As with the n-hexane mixtures the inadequacy of the virial equation is shown most clearly by the measurements at 548.2-648.2 K. At 698.2 K the fit is slightly better and extends to ca. 6 MPa, whereas at 548.2 K the measurements are fitted up to ca. 3 MPa. The HE measurements on [xH,O + (1 - x)C,HI4] are shown in fig. 4(a) and those on [xH20+(1-x)C7Hl,] are shown in fig. 4(b). Solid curves through the points were constructed by plotting the measurements on graphs of HE/4x(1 -x) against x and drawing the best line through the points. The broken curves were calculated from eqn (5).For both mixtures the calculated curves lie below those obtained experimentally, though the shape is correctly given.N . AI-Bizreh, C. N . Colling, N . M . Lancaster and C. J . Wormald 131 1 24 0 2 L 6 plMPa 0 2 4 6 0 - 0 4 8 12 plMPa Fig. 6. (a) The residual enthalpies H:, of water, HZ2 of n-heptane, and H: of (0.5H20 + 0.5C,H1,) at 548.2 K. (----) the mean of HZl and H:2. 0, calculated from H: listed in table 1, HZl from ref. (12), and HZ2 from the BWRS equation of state. The above terms are related by eqn (3). The figure shows the origin of the maxima in the H: against p graphs in fig. 3. (b) Residual molar enthalpies H: of (0.5H20 + 0.5C,Hl,) calculated using eqn (3). The striking feature of the HE values of (0.5H20+0.5C7Hl,) shown in fig. 3 is the maxima at pressures well below the saturation pressure of n-heptane.These are not due to unusual molecular interactions but are a consequence of the shape of the residual enthalpy curves of n-heptane and steam. This is best made clear by rearranging eqn (3) and calculating the molar residual enthalpy HZ of the mixture from HE and the pure- component residual enthalpies. In fig. 6(a) the broken line is the mean of H:, for steam calculated from the HGK equation of state at 548.2 K and HZ, for n-heptane calculated from the BWRS equation. Circles shown in the figure are values of HZ of (0.5H20 + 0.5C7H,,) calculated by adding the experimental HKs at 548.2 K listed in table 1 to the mean of the pure-component residual enthalpies. The circles lie on a smooth curve of similar shape to H:, for steam.The solid line through the points was drawn with a flexicurve. The difference between this line and the broken line is HE, and the origin of the maximum at 548.2 K in the HE against p graph shown in fig. 3 should now be apparent. HZ for the (0.5H20 + 0.5C7H1,) mixture at other temperatures is shown in fig. 6(b). Cubic Equations of State Robinson2, has used the Peng-Robinson (PR) equation of to calculate liquid/vapour equilibria of binary mixtures containing water and methanol. When their equation is used to calculate vapour phase HEs of steam-hydrocarbon mixtures poor agreement with experiment is found. The combining rule used for the calculation of the cross-term critical temperature q12 is Eqn (7) was used to obtain the cross-term parameter aI2 and hence the value of a for the mixture.Comparison of HEs calculated from the PR equation using < = 0.1 with measurements on (0.5H,0+0.5C7H,,) are shown in fig. 7(a). The value of was chosen to give a reasonable fit to the measurements at 598.2K, but this value does not fit the1312 HE of Steam-n-Hexane and Steam-n-Heptane Fig. 7. Excess molar enthalpies of (0.5H20+ 0.5C,H,,) compared with cubic equations of state. 0, table 1, (-) drawn with a flexicurve. (a) Broken curves calculated from the Peng-R~binson~~ equation of state using 5 = 0.1. (b) Broken curves calculated from the Patel-Teja2* equation of state using < = 0.4. measurements at 548.2 and 698.2 K, although the calculated curves have similar shapes to those obtained experimentally.The failure of the PR equation is partly due to the poor fit to the residual enthalpy of n-heptane and steam, and partly due to the failure of the combining rules to adequately reflect the nature of the water-hydrocarbon interaction. A cubic equation which gives a better fit to the residual enthalpy of the pure components is that of Pate1 and Teja24 (PT) who modified the PR equation by adding a parameter c. It has been shown that the PT equation fits recent measurements of the enthalpy of acetone25 to within a few per cent. Comparison with the HGK tables and the BWRS equation of state shows that the fit to the residual enthalpy of steam and of n-heptane is similar to that for acetone. The fit to HZ, of n-heptane is worst between the critical temperatures 540.2 K and 600 K, and improves with increasing temperature.HEs calculated from the PT equation using c = 0.4 are shown in fig. 6(b). The isotherms are close to those obtained experimentally, although the shape is clearly wrong. The value = 0.4 suggests that the water-hydrocarbon interaction is weaker than that corresponding to the calculated value of the cross-term a,, used in the PT equation. Any equation of state which is to fit the experimental water-hydrocarbon HEs must fit H: of the pure components and take the weak water-hydrocarbon interaction into account. References 1 C. J. Wormald, J. Chem. Thermodyn., 1977, 9, 901. 2 P. Richards, C. J. Wormald and T. K. Yerlett, J . Chem. Thermodyn., 1981, 13, 623. 3 P. Richards and C. J. Wormald, 2. Phys. Chem.N.F., 1981, 128, 35. 4 G. R. Smith and C. J. Wormald, J. Chem. Thermodyn., 1984, 16, 543. 5 N. M. Lancaster and C. J. Wormald, J. Chem. Thermodyn., 1985, 17, 295. 6 N. M. Lancaster and C. J. Wormald, J. Chem. Thermodyn., 1986, 18, 545. 7 G. R. Smith, M. J. Fahy and C. J. Wormald, J . Chem. Thermodyn., 1984, 16, 825.N . Al-Bizreh, C. N . Colling, N . M . Lancaster and C . J . Wormald 1313 8 C. J. Wormald and N. M. Lancater, J. Chem. Thermodyn., 1985, 17, 903. 9 C. J. Wormald and N. M. Lancaster, J. Chem. Soc., Faraday Trans. I , 1988, 84, 3141. 10 N. M. Lancaster and C. J. Wormald, Z . Phys. Chem. N.F., 1981, 128, 43. 11 H. Orbey and J. H. Vera, AZChE J., 1983, 29, 107. 12 L. Haar, J. S. Gallagher and G. S. Kell, NBSINRC Steam Tables (Hemisphere, New York, 1984). 13 C. J. Wormald and C. N. Colling, J . Chem. Thermodyn., 1983, 15, 725. 14 C. J. Wormald and C. N. Colling, J . Chem. Thermodyn., 1985, 17, 437. 15 C. J. Wormald and C. N. Colling, AIChE J., 1984, 30, 386. 16 N. M. Lancaster and C. J. Wormald, J . Chem. Thermodyn., 1987, 19, 89. 17 N. M. Lancaster and C. J. Wormald, J . Chem. Thermodyn., 1987, 19, 1001. 18 C. J. Wormald, N. M. Lancaster and A. J. Sellers, J . Chem. Thermodyn., 1986, 18, 135. 19 API Research Project No. 44., Selected tlalues of properties of hydrocarbons and related compounds 20 N. M. Lancaster and C. J. Wormald, J . Chem. Soc., Faruday Trans. 1, 1988, 84, 3159. 21 J. H. Dymond and E. B. Smith, The virial coeficients of Pure Gases and Mixtures (Clarendon Press, 22 D. B. Robinson, D-Y. Peng and S. Y-K. Chung, Fluid Phase Equilibria, 1985, 24, 25. 23 D-Y. Peng and D. B. Robinson, Znd. Eng. Chem. Fundam., 1976, 15, 59. 24 N. C. Pate1 and A. S. Teja, Chem. Eng. Sci., 1982, 37, 463. 25 T. K. Yerlett and C. J. Wormald, J . Chem. Thermodyn., 1986, 18, 371. (Texas A & M University, 1976). Oxford, 1980). Paper 8/00923F; Receiced 7th March, 1988