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Excess enthalpies and excess volumes for (ethane + propan-1-ol) at the temperatures (298.15, 323.15, and 348.15) K and at the pressures (5, 10, 12.5, and 15) MPa
O-582 J. Chem. Thermodynamics 1995, 27, 1033–1045
Excess enthalpies and excess volumes for (ethane+propan-1-ol) at the temperatures (298.15, 323.15, and 348.15) K and at the pressures (5, 10, 12.5, and 15) MPa J. B. Ott, a L. R. Lemon, J. T. Sipowska, b and P. R. Brown Department of Chemistry, Brigham Young University, Provo, UT 84602 , U.S.A.
(Received 6 February 1995; in final form 31 March 1995) Excess molar enthalpies HmE and excess molar volumes VmE have been determined for {xC2 H6+(1−x)CH3(CH2 )2OH} at T=(298.15, 323.15, and 348.15) K and p=(5, 10, 12.5, and 15) MPa. The HmE s were measured with a high-temperature high-pressure flow calorimeter. The VmE s were measured simultaneously with a vibrating-tube densitometer inserted in the flow line of the calorimeter past the mixing chamber. (Vapor+liquid) equilibrium is present at p=5 MPa and T=(323.15 K and 348.15 K). The value of the pressure coefficient (1HmE /1p)T , which is large at all three temperatures, is calculated from VmE and (1VmE /1T )p . The results are in good agreement with the values obtained directly from the change in HmE with pressure. 7 1995 Academic Press Limited
1. Introduction In this paper, we report the excess enthalpies H E and excess volumes V E for (ethane+propan-1-ol). The measurements were made at pressures p=(5, 10, 12.5, and 15) MPa and temperatures T=(298.15, 323.15, and 348.15) K. The critical pressure pc and critical temperature Tc are 4.91 MPa and 305.50 K for ethane,(1) and 5.17 MPa and 536.71 K for propan-1-ol.(2) Figure 1 compares the (p,T ) conditions where experimental measurements were made with the (vapor+liquid) equilibrium lines for the two components. It is apparent that the propan-1-ol is a liquid at all the experimental temperatures, while the ethane is a liquid at the lowest temperature and a supercritical fluid at the two higher temperatures. We have not found (fluid+fluid) equilibria reported in the literature for this system and, hence, no critical locus is shown in figure 1, but at the two higher temperatures, (vapor+liquid) equilibrium is likely at p=5 MPa. This paper continues our study of (alkane+alkanol) mixtures. In previous papers, we reported HmE results for (ethane+methanol,(3) + ethanol,(4) and + butan-1-ol(5) ); a
Author to whom correspondence should be sent. Present address: Department of Chemistry, 566 MSB, University of Michigan-Flint, Flint, MI 48502-2186, U.S.A. b
0021–9614/95/091033+13 $12.00/0
7 1995 Academic Press Limited
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FIGURE 1. Q, (p,T ) conditions for measurements of HmE reported in this paper for {xC2 H6+(1−x)CH3(CH2 )2OH}. q, Critical points for ethane (A) and propan-1-ol (B). ——, The vapor pressures of the pure components.
(propane+methanol,(6, 7) + ethanol,(8) + propan-1-ol,(9) and + butan-1-ol(10) ); and (butane+methanol,(11) and + butan-1-ol(12) ). Results for VmE have been reported for (butane+ethanol,(13) and + butan-1-ol(12) ). For these two mixtures, we calculated the pressure coefficient (1HmE /1p)T from VmE and (1VmE/1T )p using the equation: (1HmE /1p)T=VmE −T(1VmE/1T )p ,
(1)
and obtained excellent agreement with results obtained directly from HmE . The effect of pressure on HmE of (butane+ethanol) and (butane+butan-1-ol) is small at the (p,T ) conditions where we made our measurements. We reported in earlier papers(3, 4) that (1HmE /1p)T is large for liquid (ethane+methanol,(3) and +ethanol(4) ) at T=298.15 K, which is 7.35 K below the critical temperature of ethane. Similarly, a large (1HmE /1p)T is expected for (ethane+propan-1-ol) at the same temperature. The pressure coefficient may also be large at T=323.15 K and T=348.15 K, where the ethane is a supercritical fluid. Both VmE and (1VmE/1T )p are small for the (alkane+alkanol) systems we have studied so far,(12, 13) but may become large when (1HmE /1p)T is large because of the relation given by equation (1).
2. Experimental Ethane (Matheson, mass fraction q0.99) and reagent-grade propan-1-ol (Mallinckrodt, mole fraction q0.99) were used without further purification. The propan-1-ol was stored over 0.3 nm molecular sieves to remove water. The densities at T=293.15 K and p=(5, 10, 12.5, and 15) MPa used to calculate the mole fractions
H E and V E for (ethane+propan-1-ol)
1035
x were respectively (358.8, 395.6, 407.2, and 416.0) kg·m−3 for ethane, and (807.3, 811.2, 813.2, and 815.2) kg·m−3 for propan-1-ol. The values for ethane were calculated from the modified BWR equation with 32 parameters given by Younglove and Ely.(1) The densities of the propan-1-ol were based on a density of 803.5 kg·m−3 ,(14) at ambient pressure and T=293.15 K, corrected to the pressures of the measurements using a value of 0.964 GPa−1 for the isothermal compressibility. The HmE measurements were made with the isothermal flow calorimeter that we have designated as calorimeter (1 and described earlier.(15) The VmE measurements were made with an Anton-Paar Model DMA 60 vibrating-tube densitometer with a Model DMA 512 measuring cell inserted into the flow line of the calorimeter between the exit tube and the back-pressure regulator. Details of the operation of this cell have been given previously.(16) Bath temperatures, controlled to 20.001 K, were monitored with a platinum resistance probe connected to a Hart Scientific Model 1006 thermometer calibrated with a Rosemount resistance thermometer (ITS-90). Pressures were measured with a Sensotec strain-gauge transducer connected to a Model 450D meter calibrated against a dead-weight gauge. Pressures and temperatures were measured with an accuracy better than 20.1 MPa and 20.02 K. We estimate the HmE s and VmEs to be accurate to 20.010·HmE and 20.015·VmE , if phase separation does not occur. The uncertainty in HmE increases to 20.02·HmE at the extremes of x and in the regions of x where phase equilibrium is present. When phase separation occurs, an HmE resulting from the mixing of two fluids is not measured. Rather, a value is obtained which is an average of HmE for the two mixtures in equilibrium, and this apparent HmE varies linearly with x.
3. Results and discussion Values of HmE and VmE for {xC2 H6+(1−x)CH3(CH2 )2OH} at each of the (p,T ) conditions are given in tables 1 and 2. To avoid round-off errors, the results are given to one more significant figure than is justified by the accuracy of the measurements. The results where phase separation is absent were fitted to the equation: n
XmE =x(1−x) s aj (1−2x) j/{1−k(1−2x)},
(2)
j=0
where XmE is either HmE /(J·mol−1 ) or VmE/(cm3·mol−1 ). The parameters aj , skewing parameter k, and the standard deviation s, are given in tables 3 and 4 for HmE and VmE . Deviations dHmE and dVmE of the experimental results from equation (2) are given in tables 1 and 2. The results of measurements of HmE at T=323.15 K and T=348.15 K in the composition range where phase equilibrium is present were fitted to the equation: HmE /(J·mol−1 )=b0+b1 x,
(3)
where b0 and b1 are parameters summarized in table 5. Values of VmE could not be obtained under these (p,T ) conditions; the measurement of VmE with the vibrating-tube densitometer is very sensitive to the changes in phase when incomplete
1036
J. B. Ott et al.
TABLE 1. Experimental excess molar enthalpies HmE for {xC2 H6+(1−x)CH3(CH2 )2OH}; dHmE is the deviation of the experimental results from equation (2) with the parameters given in table 3 or from equation (3) with the coefficients given in table 5 x
HmE J·mol−1
dHmE J·mol−1
0.0447 0.0899 0.1356 0.1818 0.2130 0.2443 0.2759 0.3077 0.3398 0.3721
−53.7 −109.1 −157.1 −204.8 −239.1 −268.2 −299.2 −330.5 −356.1 −375.5
2.6 −1.3 0.2 1.0 −1.3 0.8 −0.2 −2.9 −2.0 2.6
0.0326 0.0652 0.0978 0.1305 0.1797 0.2125 0.2454 0.2949 0.3279 0.3776
−15.6 −31.3 −45.2 −59.0 −80.3 −91.7 −99.5 −112.6 −118.1 −124.7
−0.4 −1.0 −0.2 0.3 −1.3 −0.9 1.7 1.4 2.0 1.0
0.0167 0.0500 0.0834 0.1334 0.1667 0.2168 0.2501 0.2834 0.3334
−12.0 −18.6 −32.3 −44.6 −56.9 −62.4 −69.1 −72.4 −74.5
−5.1 1.0 −1.2 1.4 −2.5 2.3 0.6 0.9 1.0
0.0340 0.0680 0.1019 0.1357 0.1695 0.2033 0.2539 0.2875 0.3379 0.3715
−7.1 −13.0 −16.8 −22.6 −25.1 −30.6 −30.4 −31.9 −32.7 −26.0
−0.2 −0.4 0.9 −0.5 0.8 −1.7 1.4 0.5 −2.0 1.7
0.0297 0.0597 0.0899 0.1356 0.1664 0.2130 0.2443 0.2918 0.3398 0.3721
−170.4 −340.0 −519.9 −772.1 −960.5 −1271.2 −1432.7 −1692.6 −1956.2 −2172.6
8.3 −0.5 −14.0 7.4 11.5 −14.4 3.3 −0.3 3.7 −2.1
x
HmE J·mol−1
dHmE J·mol−1
T=298.15 K, p=5 MPa 0.4047 −399.1 0.2 0.4375 −414.2 2.8 0.4706 −434.3 −3.0 0.5040 −438.3 3.3 0.5376 −446.7 1.4 0.5715 −449.2 1.3 0.6056 −448.0 0.8 0.6574 −446.8 −8.2 0.6922 −428.5 −2.1 0.7273 −412.6 −3.4 T=298.15 K, p=10 MPa 0.4107 −128.0 −1.3 0.4439 −125.5 −0.1 0.4939 −120.6 −1.7 0.5272 −113.6 −2.0 0.5774 −97.5 −1.4 0.6109 −82.1 0.8 0.6444 −67.9 −0.3 0.6948 −39.4 1.3 0.7285 −20.0 0.7 0.7622 25.1 1.9 T=298.15 K, p=12.5 MPa 0.3668 −76.2 −1.3 0.4168 −71.5 −0.9 0.4501 −67.1 −1.7 0.4835 −56.8 1.3 0.5335 −45.0 −1.2 0.5668 −31.7 0.2 0.6168 −11.6 −0.5 0.6501 5.2 0.5 0.6834 22.4 0.9 T=298.15 K, p=15 MPa 0.4049 −23.3 −0.3 0.4551 −12.5 0.0 0.4885 −4.4 −1.1 0.5385 14.8 1.0 0.5717 27.5 0.4 0.6049 41.9 0.0 0.6547 65.4 −0.6 0.6878 82.2 −0.5 0.7373 108.7 1.0 0.7703 122.2 −1.2 T=323.15 K, p=5 MPa 0.4047 −2211.4 48.2 0.4541 −2091.6 −36.0 0.4873 −1908.0 10.5 0.5376 −1710.1 0.7 0.5715 −1583.2 −12.4 0.6056 −1431.6 −1.6 0.6574 −1212.0 4.2 0.6922 −1087.9 −15.4 0.7273 −935.8 −8.3 0.7627 −793.7 −12.3
x
HmE J·mol−1
dHmE J·mol−1
0.7627 0.8164 0.8525 0.8889 0.9256 0.9441 0.9627 0.9813 0.9860 0.9888
−380.5 −332.6 −289.1 −230.3 −156.9 −107.2 −49.0 12.7 23.6 32.5
5.6 4.7 2.7 1.1 −5.2 −4.4 −1.4 2.5 0.5 3.1
0.7960 0.8299 0.8638 0.8978 0.9318 0.9488 0.9659 0.9829 0.9872
24.7 44.7 69.0 87.3 107.2 115.6 118.8 114.5 110.1
1.8 −1.0 0.6 −2.6 −1.6 −0.4 −1.1 0.8 2.8
0.7334 0.7668 0.8167 0.8501 0.8834 0.9334 0.9667
49.9 65.6 92.6 105.9 119.6 130.1 127.8
1.7 −0.5 0.6 −1.5 −0.5 −0.8 1.2
0.8197 0.8526 0.8854 0.9018 0.9346 0.9510 0.9673 0.9837
146.0 155.1 160.2 162.8 164.5 159.1 151.9 129.4
1.8 0.2 −1.8 −1.1 1.5 0.0 1.2 −1.3
0.8164 0.8525 0.8889 0.9256 0.9627 0.9819 0.9863 0.9890
−565.7 −410.6 −261.3 −104.3 53.7 127.6 153.5 165.5
−6.0 0.1 −1.0 4.5 9.3 3.9 11.7 0.0
1037
H E and V E for (ethane+propan-1-ol) TABLE 1—continued x
HmE J·mol−1
dHmE J·mol−1
0.0326 0.0652 0.0978 0.1305 0.1797 0.2125 0.2454 0.2949 0.3279 0.3776
−22.8 −45.4 −74.4 −89.4 −123.9 −145.4 −155.2 −177.9 −186.1 −200.2
2.5 3.6 −3.0 3.1 −2.0 −5.7 0.9 −0.7 2.6 1.4
0.0167 0.0500 0.0834 0.1334 0.1667 0.2168 0.2501 0.2834 0.3334
−6.7 −23.8 −26.5 −42.0 −47.0 −57.5 −60.3 −63.1 −59.3
0.1 −5.0 2.5 −0.1 1.9 −0.5 0.3 −0.6 2.7
0.0340 0.0680 0.1019 0.1357 0.1695 0.2033 0.2539 0.2875 0.3379 0.3715
−3.3 −7.0 −6.2 −5.6 −4.4 −0.5 4.8 8.6 22.5 33.8
−0.5 −2.1 0.0 0.8 0.9 2.3 0.9 −1.8 −0.8 −0.3
0.0297 0.0597 0.0899 0.1356 0.1664 0.2130 0.2443 0.2918 0.3398 0.3721 0.4047
−162.0 −309.6 −453.4 −698.9 −885.5 −1092.6 −1266.3 −1371.8 −1270.1 −1167.9 −1022.8
−3.6 −1.0 7.5 2.6 −17.8 18.8 −7.8 6.8 −26.2 −14.7 39.0
0.0652 0.0978 0.1305 0.1797 0.2125 0.2454 0.2949 0.3279 0.3776
−85.3 −135.4 −165.3 −226.3 −263.4 −313.4 −351.8 −397.7 −430.2
2.1 −6.5 4.0 2.1 3.4 −9.0 6.5 −5.8 7.4
x
HmE J·mol−1
dHmE J·mol−1
T=323.15 K, p=10 MPa 0.4107 −204.0 3.1 0.4439 −208.2 1.7 0.4939 −210.4 −1.6 0.5272 −208.3 −3.8 0.5744 −189.3 4.1 0.6109 −186.7 −6.0 0.6444 −165.0 0.9 0.6948 −141.7 −4.1 0.7285 −112.0 2.5 0.7791 −71.3 1.2 T=323.15 K, p=12.5 MPa 0.3668 −64.1 −4.8 0.4168 −48.4 2.7 0.4501 −46.5 −3.7 0.4835 −28.5 3.8 0.5335 −14.6 −2.0 0.5668 1.6 −1.5 0.6168 30.6 0.7 0.6501 52.5 2.9 0.6834 71.2 0.6 T=323.15 K, p=15 MPa 0.4049 46.8 0.3 0.4551 68.0 −0.1 0.4885 82.8 −1.6 0.5385 113.4 2.2 0.5717 130.6 0.2 0.6049 148.6 −1.7 0.6547 183.3 2.0 0.6878 201.4 −0.6 0.7373 235.0 2.6 0.7703 248.9 −2.6 T=348.15 K, p=5 MPa 0.4541 −919.0 4.2 0.4873 −831.6 −1.6 0.5376 −688.4 0.4 0.5715 −600.0 −6.2 0.6056 −500.7 −2.7 0.6574 −353.3 −0.6 0.6922 −257.0 −2.0 0.7273 −151.1 5.4 0.7627 −60.8 −3.7 0.8164 91.3 −2.3 0.8525 211.3 16.5 T=348.15 K, p=10 MPa 0.4107 −467.5 −3.7 0.4439 −487.9 −1.8 0.4939 −516.2 −5.0 0.5272 −513.3 8.3 0.5774 −527.8 −0.5 0.6109 −519.8 4.3 0.6444 −521.6 −7.0 0.6948 −488.4 −1.0 0.7285 −463.2 −4.7
x
HmE J·mol−1
dHmE J·mol−1
0.8130 0.8468 0.8706 0.8978 0.9148 0.9318 0.9488 0.9659 0.9829 0.9872
−28.6 −0.4 21.2 67.4 90.9 128.0 141.6 156.7 165.1 147.9
10.2 −0.2 −9.1 −1.0 −2.8 8.5 −2.4 −6.3 5.9 0.2
0.7334 0.7668 0.8167 0.8501 0.8834 0.9334 0.9667 0.9833
106.0 122.9 160.8 179.3 207.4 234.3 231.1 190.8
2.3 −3.6 −0.1 −4.4 2.0 3.1 2.8 −4.8
0.8197 0.8526 0.8854 0.9018 0.9182 0.9346 0.9510 0.9673 0.9837
275.6 289.4 302.9 303.2 302.3 297.7 292.1 270.1 219.5
−1.4 −1.3 2.7 0.7 −0.3 −1.7 1.7 −0.3 −0.5
0.8889 0.9072 0.9256 0.9627 0.9813 0.9860 0.9888 0.9906 0.9920
290.5 339.8 402.6 509.8 552.0 568.1 409.8 320.7 293.3
−6.5 −8.5 2.7 5.7 −4.3 −1.4 11.2 −16.8 4.2
0.7791 0.8130 0.8468 0.8808 0.8978 0.9318 0.9488 0.9659 0.9829
−381.0 −334.5 −243.0 −148.6 −62.9 74.9 140.6 201.4 181.8
12.4 −4.4 3.0 −12.7 7.8 0.8 −3.4 6.6 −4.5
1038
J. B. Ott et al. TABLE 1—continued
x
HmE J·mol−1
dHmE J·mol−1
0.0167 0.0667 0.1334 0.1834 0.2334 0.2834 0.3168 0.3668 0.4168
−7.7 −25.9 −42.4 −46.4 −54.9 −50.3 −53.0 −42.6 −32.2
1.0 1.5 −0.8 1.3 −3.7 1.5 −2.7 2.1 2.7
0.0340 0.0680 0.1019 0.1357 0.1695 0.2033 0.2539 0.2875 0.3379 0.3715
5.0 13.3 21.4 31.1 44.5 57.3 80.3 95.6 119.7 149.7
0.0 1.1 0.1 −0.9 0.5 0.0 0.3 −1.2 −4.8 4.9
x
HmE J·mol−1
dHmE J·mol−1
T=348.15 K, p=12.5 MPa 0.4501 −24.4 1.3 0.5001 −8.1 −0.1 0.5335 6.9 0.5 0.5835 27.6 −3.8 0.6168 48.8 −1.5 0.6501 68.1 −3.0 0.6834 96.1 2.0 0.7168 120.2 0.7 0.7668 168.1 4.6 T=348.15 K, p=15 MPa 0.4049 167.0 0.7 0.4551 201.5 1.0 0.4885 226.6 2.4 0.5385 258.8 −1.9 0.5717 285.1 −0.1 0.6049 305.7 −3.9 0.6547 344.8 −0.5 0.6878 369.6 1.0 0.7373 405.5 3.1 0.7703 420.8 −3.4
x
HmE J·mol−1
dHmE J·mol−1
0.8001 0.8334 0.8501 0.8834 0.9167 0.9500 0.9833
198.2 235.9 258.3 295.9 340.8 354.1 238.9
0.5 −0.4 1.0 −5.2 0.0 1.6 0.8
0.8197 0.8526 0.8854 0.9018 0.9346 0.9510 0.9673 0.9837
463.1 471.0 484.7 492.0 472.6 449.2 392.6 267.0
7.5 −3.4 −3.4 1.3 −3.2 1.7 3.4 −1.7
TABLE 2. Experimental excess molar volumes VmE for {xC2 H6+(1−x)CH3(CH2 )2OH}; dVmE is the deviation of the experimental results from equation (2) with the parameters given in table 4. At p=5 MPa for T=323.15 K and T=348.15 K, VmE and dVmE values are not included at high x nor for the two-phase region x
VmE dVmE cm3·mol−1 cm3·mol−1
0.0447 0.0899 0.1356 0.1818 0.2130 0.2443 0.2759 0.3077 0.3398 0.3721
−1.25 −2.09 −3.37 −4.36 −5.16 −5.72 −6.39 −6.94 −7.55 −8.39
−0.18 0.08 −0.09 0.01 −0.08 0.05 0.06 0.14 0.14 −0.13
0.0326 0.0652 0.0978 0.1305 0.1797 0.2125 0.2454 0.2949 0.3279 0.3776
−0.59 −0.98 −1.47 −1.90 −2.52 −2.92 −3.29 −3.76 −4.08 −4.53
−0.06 0.03 0.00 0.00 −0.01 −0.02 −0.01 0.04 0.04 0.03
x
VmE dVmE cm3·mol−1 cm3·mol−1
T=298.15 K, p=5 MPa 0.4047 −8.78 0.01 0.4375 −9.40 −0.12 0.4706 −9.68 0.03 0.5040 −10.11 −0.02 0.5376 −10.49 −0.08 0.5715 −10.75 −0.07 0.6056 −10.96 −0.10 0.6574 −10.84 0.14 0.6922 −10.81 0.14 0.7273 −10.73 0.06 T=298.15 K, p=10 MPa 0.4107 −4.86 −0.06 0.4439 −5.08 −0.07 0.4939 −5.27 −0.01 0.5272 −5.34 0.03 0.5774 −5.40 0.05 0.6109 −5.35 0.08 0.6444 −5.36 0.02 0.6948 −5.23 −0.06 0.7285 −5.09 −0.12 0.7622 −4.71 −0.02
x
VmE dVmE cm3·mol−1 cm3·mol−1
0.7627 −10.44 0.8164 −9.67 0.8525 −9.13 0.8889 −7.58 0.9256 −5.69 0.9441 −4.70 0.9627 −3.63 0.9813 −2.06 0.9860 −1.55 0.9888 −0.81
0.04 0.01 −0.31 0.02 0.20 0.08 −0.16 −0.16 −0.10 0.37
0.7960 0.8299 0.8638 0.8978 0.9318 0.9488 0.9659 0.9829 0.9872
0.04 0.03 0.00 0.13 −0.02 −0.11 −0.07 0.09 0.01
−4.30 −3.88 −3.39 −2.63 −2.02 −1.68 −1.16 −0.48 −0.43
1039
H E and V E for (ethane+propan-1-ol)
TABLE 2—continued x
VmE dVmE cm3·mol−1 cm3·mol−1
x
VmE dVmE cm3·mol−1 cm3·mol−1
x
VmE dVmE cm3·mol−1 cm3·mol−1
0.0167 0.0500 0.0834 0.1334 0.1667 0.2168 0.2501 0.2834 0.3334
−0.14 −0.71 −1.03 −1.61 −1.96 −2.39 −2.65 −2.99 −3.32
−0.10 0.05 −0.02 0.02 0.03 −0.02 −0.05 0.01 −0.05
T=298.15 K, p=12.5 MPa 0.3668 −3.68 0.09 0.4168 −3.89 0.01 0.4501 −4.04 0.01 0.4835 −4.11 −0.03 0.5335 −4.21 −0.05 0.5668 −4.28 0.00 0.6168 −4.29 0.05 0.6501 −4.14 −0.03 0.6834 −4.05 0.01
0.0340 0.0680 0.1019 0.1357 0.1695 0.2033 0.2539 0.2875 0.3379 0.3715
−0.50 −0.80 −1.26 −1.59 −1.91 −2.13 −2.56 −2.83 −3.13 −3.34
−0.02 0.09 −0.01 −0.02 −0.05 0.02 0.00 −0.03 0.01 0.00
T=298.15 K, p=15 MPa 0.4049 −3.50 0.02 0.4551 −3.67 0.06 0.4885 −3.82 0.01 0.5385 −3.91 −0.02 0.5717 −3.93 −0.04 0.6049 −3.90 −0.05 0.6547 −3.73 −0.02 0.6878 −3.54 0.02 0.7373 −3.27 0.01 0.7703 −3.02 0.03
— — — —
T=323.15 K, p=5 MPa 0.1664 −43.6 — 0.2130 −55.7 — 0.2443 −63.8 — 0.2918 −76.0 —
0.3398 −88.3 0.3721 −96.4 0.4047 −105.4 0.4541 −117.4
0.8130 0.8468 0.8706 0.8978 0.9148 0.9318 0.9488 0.9659 0.9829 0.9872
−9.79 −9.06 −8.32 −7.14 −6.18 −5.69 −4.18 −3.36 −1.99 −1.59
0.05 −0.12 −0.15 −0.04 0.14 −0.24 0.29 −0.02 −0.02 −0.03
0.7334 0.7668 0.8167 0.8501 0.8834 0.9334 0.9667 0.9833
−7.33 −6.80 −6.21 −5.42 −4.60 −2.95 −1.64 −0.82
0.08 −0.07 0.11 −0.01 0.01 −0.05 0.00 −0.05
0.0297 0.0597 0.0899 0.1356
−7.9 −15.8 −23.7 −35.9
0.0326 0.0652 0.0978 0.1305 0.1797 0.2125 0.2454 0.2949 0.3279 0.3776
−1.03 −1.86 −2.64 −3.58 −4.81 −5.39 −6.34 −7.45 −8.04 −8.93
−0.12 −0.06 0.04 −0.04 −0.02 0.18 −0.01 −0.06 0.01 0.03
T=323.15 K, p=10 MPa 0.4107 −9.51 0.00 0.4439 −10.04 −0.04 0.4939 −10.72 −0.08 0.5272 −10.98 0.00 0.5744 −11.40 −0.03 0.6109 −11.48 0.03 0.6444 −11.56 0.01 0.6948 −11.36 0.08 0.7285 −11.29 −0.10 0.7791 −10.32 0.20
0.0167 0.0500 0.0834 0.1334 0.1667 0.2168 0.2501 0.2834 0.3334
−0.42 −1.09 −1.72 −2.61 −3.24 −4.05 −4.61 −5.17 −5.82
0.05 0.02 −0.01 −0.04 0.02 −0.02 0.00 0.05 −0.01
T=323.15 K, p=12.5 MPa 0.3668 −6.24 −0.03 0.4168 −6.74 −0.10 0.4501 −7.18 0.03 0.4835 −7.58 0.16 0.5335 −7.71 0.01 0.5668 −7.76 −0.05 0.6168 −7.80 −0.05 0.6501 −7.79 0.01 0.6834 −7.56 −0.08
0.7334 0.7668 0.8167 0.8501 0.8834 0.9334 0.9667
−3.77 −3.54 −3.05 −2.74 −2.22 −1.44 −0.81
0.00 0.01 −0.03 0.04 −0.04 0.00 0.03
0.8197 0.8526 0.8854 0.9018 0.9346 0.9510 0.9673 0.9837
−2.56 −2.30 −1.94 −1.69 −1.19 −0.94 −0.65 −0.35
0.06 −0.02 −0.05 −0.01 0.01 −0.01 0.00 −0.01
— — — —
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J. B. Ott et al.
TABLE 2—continued x
0.0340 0.0680 0.1019 0.1357 0.1695 0.2033 0.2539 0.2875 0.3379 0.3715
VmE dVmE cm3·mol−1 cm3·mol−1
−0.78 −1.38 −1.88 −2.41 −2.92 −3.40 −4.01 −4.46 −5.01 −5.30
−0.04 −0.01 0.05 0.03 −0.01 −0.03 0.00 −0.04 −0.04 0.00
x
VmE dVmE cm3·mol−1 cm3·mol−1
T=323.15 K, p=15 MPa 0.4049 −5.52 0.07 0.4551 −5.83 0.11 0.4885 −6.14 −0.04 0.5385 −6.24 0.02 0.5717 −6.34 −0.05 0.6049 −6.34 −0.09 0.6547 −6.13 −0.03 0.6878 −5.83 0.09 0.7373 −5.54 0.00 0.7703 −5.19 0.02 T=348.15 K, p=5 MPa 0.1356 −48.1 0.1664 −58.6 0.2130 −75.1
0.0297 0.0597 0.0899
−10.7 −21.4 −32.0
0.0652 0.0978 0.1305 0.1797 0.2125 0.2454 0.2949 0.3279 0.3776
−4.08 −5.81 −8.07 −10.77 −12.83 −14.36 −17.27 −19.12 −21.58
−0.09 0.14 −0.16 0.04 −0.12 0.21 0.04 −0.07 −0.01
T=348.15 K, p=10 MPa 0.4107 −23.14 0.00 0.4439 −24.64 −0.01 0.4939 −26.58 0.07 0.5272 −27.93 −0.10 0.5774 −29.27 0.04 0.6109 −30.17 −0.10 0.6444 −30.38 0.22 0.6948 −31.21 −0.30 0.7285 −30.65 0.06
0.0167 0.0667 0.1334 0.1834 0.2334 0.2834 0.3168 0.3668 0.4168
−0.94 −2.61 −5.16 −7.11 −8.71 −10.42 −11.38 −12.91 −14.18
0.32 0.06 −0.01 0.06 −0.12 −0.06 −0.11 0.04 0.08
T=348.15 K, p=12.5 MPa 0.4501 −14.95 0.12 0.5001 −15.66 −0.11 0.5335 −16.32 0.01 0.5835 −16.91 −0.01 0.6168 −17.34 0.15 0.6501 −17.32 0.00 0.6834 −17.35 0.06 0.7168 −17.09 0.01 0.7668 −16.28 −0.04
0.0340 0.0680 0.1019 0.1357 0.1695 0.2033 0.2539 0.2875 0.3379 0.3715
−1.19 −2.09 −2.96 −3.88 −4.65 −5.45 −6.49 −7.15 −8.15 −8.55
−0.07 0.03 0.06 −0.02 0.00 −0.04 −0.01 0.01 −0.06 0.12
T=348.15 K, p=15 MPa 0.4049 −9.21 −0.02 0.4551 −9.89 −0.01 0.4885 −10.20 0.05 0.5385 −10.72 −0.05 0.5717 −10.91 −0.06 0.6049 −10.98 −0.03 0.6547 −10.88 0.01 0.6878 −10.65 0.07 0.7373 −10.14 0.08 0.7703 −9.76 −0.06
x
0.8197 0.8526 0.8854 0.9018 0.9182 0.9346 0.9510 0.9673 0.9837
VmE dVmE cm3·mol−1 cm3·mol−1
−4.60 −4.05 −3.45 −3.09 −2.68 −2.13 −1.79 −1.22 −0.80
−0.02 0.01 −0.02 −0.02 0.00 0.11 −0.03 0.01 −0.16
0.2443
−85.8
0.7791 0.8130 0.8468 0.8808 0.8978 0.9318 0.9488 0.9659
−29.68 −28.27 −26.11 −23.36 −22.26 −17.59 −13.14 −10.44
−0.01 0.08 0.28 0.21 −0.52 −0.55 0.83 −0.19
0.8001 0.8334 0.8501 0.8834 0.9167 0.9500 0.9833
−15.07 −14.26 −13.36 −11.47 −9.53 −6.25 −2.02
−0.37 0.04 −0.09 −0.08 0.41 0.21 −0.21
0.8197 0.8526 0.8854 0.9018 0.9346 0.9510 0.9673 0.9837
−8.58 −7.65 −6.47 −5.81 −4.10 −3.27 −2.19 −1.10
0.02 −0.02 −0.03 −0.07 0.05 −0.03 0.06 0.07
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H E and V E for (ethane+propan-1-ol)
TABLE 3. Parameters representing HmE of {xC2 H6+(1−x)CH3(CH2 )2OH} with equation (2). At p=5 MPa and T=323.15 K and T=348.15 K, (vapor+liquid) equilibrium is present and equation (2) and these parameters apply for 0QxQx1 , and x2QxQ1, where x1 and x2 are the (vapor+liquid) solubility bounds given in table 4. At all other (T,p), equation (2) applies over the entire range of composition. s is the standard deviation of HmE from equation (2) p/MPa
a0
a1
5.0 10.0 12.5 15.0
−1762.5 −471.0 −215.5 1.0
−1213.5 −859.0 −758.4 −641.8
5.0 a −14380 10.0 −832.9 12.5 −105.4 15.0 361.3 5.0 a 10.0 12.5 15.0 a
a2
a3
556.4 224.0 97.7 157.5
31530 −50030 −1019.8 270.1 −861.4 108.8 −688.6 −86.0
−3935 −13780 −2054.0 −1182.9 −32.1 −827.3 930.3 −587.4
30660 916.8 122.4 −225.0
a4
a5
T=298.15 K 549.2 −47.6 241.6 −61.4 195.3 −158.2 355.6 −210.2 T=323.15 K 2170 72770 175.7 60.5 321.4 −96.3 247.0 −12.0 T=348.15 K −15790 330.8 −271.2 184.4 165.1 199.2 275.0
a6
−769.1 −96.0 −48870 −248.1 −205.8
−1253.6 −718.0 −392.5
819.5
k
s
−0.99 −0.99 −0.99 −0.99
3.0 1.4 1.6 1.1
−0.98 −0.98 −0.98
7.9 4.2 2.8 1.5
0.50 −0.93 −0.93 −0.93
11.1 6.0 2.2 2.7
Values reported with four significant figures.
mixing due to phase equilibrium occurs, and reproducible results could not be obtained. Also, no attempt was made to fit to equation (1) the limited number of VmEs obtained at these (p,T ) conditions for values of x where only one phase was present. The HmE results are summarized in the three-dimensional plots of HmE against (p,x) and against (T,x) shown in figures 2(a) and 2(b). The results shown in figure 2(a) at p=5 MPa with T=323.15 K and T=348.15 K indicate that (vapor+liquid) equilibrium is present at these (p,T ) conditions, with the apparent HmE changing linearly over the region of x where phase separation occurs. At these (p,T ) conditions, large negative HmE s at low x can be explained as resulting from the condensation of TABLE 4. Parameters representing VmE of {xC2 H6+(1−x)CH3(CH2 )2OH} with equation (2); s is the standard deviation. The limited number of values at p=5 MPa with T=323.15 K and T=348.15 K (phase equilibrium is present over much of the composition range) were not fitted to equation (2) T/K
p/MPa
a0
a1
a2
a3
298.15 298.15 298.15 298.15 323.15 323.15 323.15 348.15 348.15 348.15
5.0 10.0 12.5 15.0 10.0 12.5 15.0 10.0 12.5 15.0
−40.20 −21.13 −16.77 −15.39 −42.83 −30.11 −24.61 −107.51 −63.09 −41.45
−4.57 7.47 4.93 3.76 −19.14 12.37 7.38 −11.18 34.26 32.92
1.04 −1.32 0.10 1.82 7.91 −2.78 0.31 13.17 −25.32 −14.76
4.33 1.50 0.66 −0.68 −5.00 3.25 1.61 −4.43 17.54 5.47
a4
−3.40 −3.27 −5.05 4.53 −5.58 −8.31
k
s
−0.65
0.13 0.06 0.04 0.03 0.11 0.06 0.06 0.26 0.16 0.05
−0.96 −0.79
−5.61
0.34
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J. B. Ott et al.
TABLE 5. Parameters for equation (3) representing HmE for {xC2 H6+(1−x)CH3(CH2 )2OH}. Equation (3) applies for x1QxQx2 (in the two-phase region), where x1 and x2 are the (vapor+liquid) solubility bounds; s is the standard deviation from equation (3) T/K
p/MPa
b0
b1
s
x1
x2
323.15 348.15
5.0 5.0
−3931 −2197
4129 2806
16.6 12.0
0.391 0.282
0.989 0.984
gaseous ethane into liquid propan-1-ol, while a major contributor to the positive HmE at high x is the vaporization of liquid propan-1-ol into the gaseous ethane. The results at p=5 MPa are not shown in figure 2(b) so that the HmE scale can be expanded. Figure 2(a) shows that, except at the highest pressure and temperature, HmE (x) is S shaped, changing from values of HmE Q0 at low x to values of HmE q0 at high x, with the crossover shifting to smaller x with increasing (p,T ). Figure 2(b) shows that the effect of pressure on HmE is most pronounced at T=348.15 K, where HmE (x) changes from the most negative results at p=10 MPa to the most positive results at p=15 MPa. (The results at p=5 MPa are excluded from the comparison.) In an earlier paper,(17) in which we reported HmE for (ethane+acetonitrile), we found a large change in HmE from negative to positive values as p increased over approximately the same pressure range, and attributed it to a change from gas-like to liquid-like behavior of the supercritical ethane. Figures 3(a) and 3(b) are three-dimensional plots of VmE against (p,x) and (T,x). As with the HmE plots, the results at p=5 MPa with T=323.15 K and T=348.15 K are excluded from figure 3(b) in order to expand the scale. Figure 3 shows that VmE W0 at all experimental pressures and temperatures.
FIGURE 2. (a) Three-dimensional plot of (x,p) against HmE for {xC2 H6+(1−x)CH3(CH2 )2OH}. The temperatures are as follows: w, 298.15 K; q, 323.15 K; r, 348.15 K. (b) Three-dimensional plot of (x,T ) against HmE for {xC2 H6+(1−x)CH3(CH2 )2CH2OH}. The pressures are as follows: w, 10 MPa; q, 12.5 MPa; r, 15 MPa.
H E and V E for (ethane+propan-1-ol)
1043
FIGURE 3. (a) Three-dimensional plot of (x,p) against VmE for {xC2 H6+(1−x)CH3(CH2 )2OH}. The temperatures are as follows: w, 298.15 K; q, 323.15 K; r, 348.15 K. (b) Three-dimensional plot of (x,T ) against VmE for {xC2 H6+(1−x)CH3(CH2 )2OH}. The pressures are as follows: w, 10 MPa; q, 12.5 MPa; r, 15 MPa.
The (1VmE/1T )p is large and increases with decreasing p as shown in figure 3(a). The (1VmE/1p)T is also large and increases with T as shown in figure 3(b). At p=5 MPa with T=323.15 K and T=348.15 K, =VmE = is especially large. A major contribution to this effect is the decrease in volume resulting from the condensation of supercritical ethane, present at a comparatively low pressure, into the liquid propan-1-ol during the mixing process. A similar, although somewhat smaller, effect is obtained at p=5 MPa and T=298.15 K, where the ethane is liquid, but behaves very much like a gas because the temperature is near the Tc of ethane. In earlier papers,(4, 18) we attributed the effect of pressure on HmE for systems containing liquid ethane at T=298.15 K to this gas-like behavior. The quantity (1HmE /1p)T can be calculated from VmE by means of equation (1). Figure 4 compares the results of this calculation at T=323.15 K and p=12.5 MPa with results obtained directly from HmE . Values of VmE(x) at p=12.5 MPa and T=(298.15, 323.15, and 348.15) K, obtained from equation (2) with the parameters given in table 4, were fitted to a quadratic equation in T. The equation was differentiated to give (1VmE/1T )p , which was used with VmE in equation (1) to calculate (1HmE /1p)T . The process was repeated at a series of values of x to generate the curve shown in figure 4. The quantity (1HmE /1p)T was derived from HmE in a similar manner by fitting HmE , obtained at T=323.15 K and p=(10, 12.5, and 15) MPa from equation (2) with the parameters given in table 3, to a quadratic equation in T, and differentiating. The results obtained from this calculation are shown in figure 4, and are lower than the values calculated from VmE . Analysis of the sources of error suggests that the results calculated from VmE are more accurate and, hence, that the major error is in the calculation of HmE . Also shown in figure 4 are the results of a calculation of (1HmE /1p)T from HmE that includes the fourth set of HmE values obtained at p=5 MPa. This calculation covers only the part of the composition range where phase equilibrium is not present. Agreement of the latter values with those calculated from VmE is much better
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J. B. Ott et al.
FIGURE 4. Comparison of (1HmE /1p)T at T=323.15 K and p=12.5 MPa calculated in different ways. ····W····W, Calculated from VmE results; — – —, calculated from HmE results at p=(10, 12.5, and 15) MPa; ——, calculated from HmE at (p=5, 10, 12.5, and 15) MPa. The latter calculation is limited to the region of low x where phase equilibrium is not present.
than with those in which only three pressures were used in the quadratic equation fit. The calculation demonstrates the difficulty in accurately calculating (1HmE /1p)T from HmE values at different pressures, especially when this pressure coefficient is large. Because of the nonlinear relation between HmE and p, adding HmE results at the extra pressure significantly increases the accuracy with which the pressure derivative can be obtained. The authors express appreciation to the Brigham Young University Chemistry Department for support of this project. The help of Bryant Marchant with the experimental measurements is also appreciated. REFERENCES 1. Younglove, B. A.; Ely, J. F. J. Phys. Chem. Ref. Data 1987, 16, 577. 2. Wilhoit, R. C.; Zwolinski, B. J. J. Phys. Chem. Ref. Data 1973, Supplement No. 1, 2, 38. 3. Sipowska, J. T.; Graham, R. C.; Neely, B. J.; Ott, J. B.; Izatt, R. M. J. Chem. Thermodynamics 1989, 21, 1085. 4. Ott, J. B.; Sipowska, J. T.; Owen, R. L.; Izatt, R. M. J. Chem. Thermodynamics 1990, 22, 683. 5. Sipowska, J. T.; Ott, J. B.; Woolley, A. T.; Izatt, R. M. J. Chem. Thermodynamics 1991, 23, 1013. 6. Sipowska, J. T.; Ott, J. B.; Neely, B. J.; Izatt, R. M. J. Chem. Thermodynamics 1991, 23, 551. 7. Sipowska, J. T.; Ott, J. B.; Woolley, A. T.; Marchant, B. G.; Gruszkiewicz, M. S. J. Chem. Thermodynamics 1993, 25, 999. 8. Ott, J. B.; Sipowska, J. T.; Woolley, A. T. J. Chem. Thermodynamics 1993, 25, 511. 9. Sipowska, J. T.; Ott, J. B.; Woolley, A. T.; Izatt, R. M. J. Chem. Thermodynamics 1990, 22, 1159. 10. Ott, J. B.; Sipowska, J. T.; Woolley, A. T.; Izatt, R. M. J. Chem. Thermodynamics 1992, 24, 75. 11. Sipowska, J. T.; Ott, J. B.; Woolley, A. T.; Izatt, R. M. J. Chem. Thermodynamics 1992, 24, 1087.
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12. Sipowska, J. T.; Lemon, L. R.; Ott, J. B.; Marchant, B. G.; Brown, P. R. J. Chem. Thermodynamics 1994, 26, 1275. 13. Lemon, L. R.; Sipowska, J. T.; Ott, J. B.; Marchant, B. G.; Brown, P. R. to be published. 14. Selected Values of Properties of Chemical Compounds. Thermodynamic Research Center Project: Texas A&M University, College Station, TX. 15. Ott, J. B.; Stouffer, C. E.; Cornett, G. V.; Woodfield, B. F.; Wirthlin, R. C.; Christensen J. J.; Deiters. U. K. J. Chem. Thermodynamics 1986, 18, 1. 16. Ott, J. B.; Sipowska, J. T.; Gruszkiewicz, M. S.; Woolley, A. T. J. Chem. Thermodynamics 1993, 25, 307. 17. Ott, J. B.; Neely, B. J.; Purdy, J. E.; Owen, R. L. Thermochim. Acta 1989, 154, 71. 18. Gruszkiewicz, M. S.; Sipowska, J. T.; Ott, J. B.; Brown, P. R.; Moore, J. D. J. Chem. Thermodynamics 1995, 27, 507–524.
Excess enthalpies and excess volumes for (ethane+propan-1-ol) at the temperatures (298.15, 323.15, and 348.15) K and at the pressures (5, 10, 12.5, and 15) MPa J. B. Ott, a L. R. Lemon, J. T. Sipowska, b and P. R. Brown Department of Chemistry, Brigham Young University, Provo, UT 84602 , U.S.A.
(Received 6 February 1995; in final form 31 March 1995) Excess molar enthalpies HmE and excess molar volumes VmE have been determined for {xC2 H6+(1−x)CH3(CH2 )2OH} at T=(298.15, 323.15, and 348.15) K and p=(5, 10, 12.5, and 15) MPa. The HmE s were measured with a high-temperature high-pressure flow calorimeter. The VmE s were measured simultaneously with a vibrating-tube densitometer inserted in the flow line of the calorimeter past the mixing chamber. (Vapor+liquid) equilibrium is present at p=5 MPa and T=(323.15 K and 348.15 K). The value of the pressure coefficient (1HmE /1p)T , which is large at all three temperatures, is calculated from VmE and (1VmE /1T )p . The results are in good agreement with the values obtained directly from the change in HmE with pressure. 7 1995 Academic Press Limited
1. Introduction In this paper, we report the excess enthalpies H E and excess volumes V E for (ethane+propan-1-ol). The measurements were made at pressures p=(5, 10, 12.5, and 15) MPa and temperatures T=(298.15, 323.15, and 348.15) K. The critical pressure pc and critical temperature Tc are 4.91 MPa and 305.50 K for ethane,(1) and 5.17 MPa and 536.71 K for propan-1-ol.(2) Figure 1 compares the (p,T ) conditions where experimental measurements were made with the (vapor+liquid) equilibrium lines for the two components. It is apparent that the propan-1-ol is a liquid at all the experimental temperatures, while the ethane is a liquid at the lowest temperature and a supercritical fluid at the two higher temperatures. We have not found (fluid+fluid) equilibria reported in the literature for this system and, hence, no critical locus is shown in figure 1, but at the two higher temperatures, (vapor+liquid) equilibrium is likely at p=5 MPa. This paper continues our study of (alkane+alkanol) mixtures. In previous papers, we reported HmE results for (ethane+methanol,(3) + ethanol,(4) and + butan-1-ol(5) ); a
Author to whom correspondence should be sent. Present address: Department of Chemistry, 566 MSB, University of Michigan-Flint, Flint, MI 48502-2186, U.S.A. b
0021–9614/95/091033+13 $12.00/0
7 1995 Academic Press Limited
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FIGURE 1. Q, (p,T ) conditions for measurements of HmE reported in this paper for {xC2 H6+(1−x)CH3(CH2 )2OH}. q, Critical points for ethane (A) and propan-1-ol (B). ——, The vapor pressures of the pure components.
(propane+methanol,(6, 7) + ethanol,(8) + propan-1-ol,(9) and + butan-1-ol(10) ); and (butane+methanol,(11) and + butan-1-ol(12) ). Results for VmE have been reported for (butane+ethanol,(13) and + butan-1-ol(12) ). For these two mixtures, we calculated the pressure coefficient (1HmE /1p)T from VmE and (1VmE/1T )p using the equation: (1HmE /1p)T=VmE −T(1VmE/1T )p ,
(1)
and obtained excellent agreement with results obtained directly from HmE . The effect of pressure on HmE of (butane+ethanol) and (butane+butan-1-ol) is small at the (p,T ) conditions where we made our measurements. We reported in earlier papers(3, 4) that (1HmE /1p)T is large for liquid (ethane+methanol,(3) and +ethanol(4) ) at T=298.15 K, which is 7.35 K below the critical temperature of ethane. Similarly, a large (1HmE /1p)T is expected for (ethane+propan-1-ol) at the same temperature. The pressure coefficient may also be large at T=323.15 K and T=348.15 K, where the ethane is a supercritical fluid. Both VmE and (1VmE/1T )p are small for the (alkane+alkanol) systems we have studied so far,(12, 13) but may become large when (1HmE /1p)T is large because of the relation given by equation (1).
2. Experimental Ethane (Matheson, mass fraction q0.99) and reagent-grade propan-1-ol (Mallinckrodt, mole fraction q0.99) were used without further purification. The propan-1-ol was stored over 0.3 nm molecular sieves to remove water. The densities at T=293.15 K and p=(5, 10, 12.5, and 15) MPa used to calculate the mole fractions
H E and V E for (ethane+propan-1-ol)
1035
x were respectively (358.8, 395.6, 407.2, and 416.0) kg·m−3 for ethane, and (807.3, 811.2, 813.2, and 815.2) kg·m−3 for propan-1-ol. The values for ethane were calculated from the modified BWR equation with 32 parameters given by Younglove and Ely.(1) The densities of the propan-1-ol were based on a density of 803.5 kg·m−3 ,(14) at ambient pressure and T=293.15 K, corrected to the pressures of the measurements using a value of 0.964 GPa−1 for the isothermal compressibility. The HmE measurements were made with the isothermal flow calorimeter that we have designated as calorimeter (1 and described earlier.(15) The VmE measurements were made with an Anton-Paar Model DMA 60 vibrating-tube densitometer with a Model DMA 512 measuring cell inserted into the flow line of the calorimeter between the exit tube and the back-pressure regulator. Details of the operation of this cell have been given previously.(16) Bath temperatures, controlled to 20.001 K, were monitored with a platinum resistance probe connected to a Hart Scientific Model 1006 thermometer calibrated with a Rosemount resistance thermometer (ITS-90). Pressures were measured with a Sensotec strain-gauge transducer connected to a Model 450D meter calibrated against a dead-weight gauge. Pressures and temperatures were measured with an accuracy better than 20.1 MPa and 20.02 K. We estimate the HmE s and VmEs to be accurate to 20.010·HmE and 20.015·VmE , if phase separation does not occur. The uncertainty in HmE increases to 20.02·HmE at the extremes of x and in the regions of x where phase equilibrium is present. When phase separation occurs, an HmE resulting from the mixing of two fluids is not measured. Rather, a value is obtained which is an average of HmE for the two mixtures in equilibrium, and this apparent HmE varies linearly with x.
3. Results and discussion Values of HmE and VmE for {xC2 H6+(1−x)CH3(CH2 )2OH} at each of the (p,T ) conditions are given in tables 1 and 2. To avoid round-off errors, the results are given to one more significant figure than is justified by the accuracy of the measurements. The results where phase separation is absent were fitted to the equation: n
XmE =x(1−x) s aj (1−2x) j/{1−k(1−2x)},
(2)
j=0
where XmE is either HmE /(J·mol−1 ) or VmE/(cm3·mol−1 ). The parameters aj , skewing parameter k, and the standard deviation s, are given in tables 3 and 4 for HmE and VmE . Deviations dHmE and dVmE of the experimental results from equation (2) are given in tables 1 and 2. The results of measurements of HmE at T=323.15 K and T=348.15 K in the composition range where phase equilibrium is present were fitted to the equation: HmE /(J·mol−1 )=b0+b1 x,
(3)
where b0 and b1 are parameters summarized in table 5. Values of VmE could not be obtained under these (p,T ) conditions; the measurement of VmE with the vibrating-tube densitometer is very sensitive to the changes in phase when incomplete
1036
J. B. Ott et al.
TABLE 1. Experimental excess molar enthalpies HmE for {xC2 H6+(1−x)CH3(CH2 )2OH}; dHmE is the deviation of the experimental results from equation (2) with the parameters given in table 3 or from equation (3) with the coefficients given in table 5 x
HmE J·mol−1
dHmE J·mol−1
0.0447 0.0899 0.1356 0.1818 0.2130 0.2443 0.2759 0.3077 0.3398 0.3721
−53.7 −109.1 −157.1 −204.8 −239.1 −268.2 −299.2 −330.5 −356.1 −375.5
2.6 −1.3 0.2 1.0 −1.3 0.8 −0.2 −2.9 −2.0 2.6
0.0326 0.0652 0.0978 0.1305 0.1797 0.2125 0.2454 0.2949 0.3279 0.3776
−15.6 −31.3 −45.2 −59.0 −80.3 −91.7 −99.5 −112.6 −118.1 −124.7
−0.4 −1.0 −0.2 0.3 −1.3 −0.9 1.7 1.4 2.0 1.0
0.0167 0.0500 0.0834 0.1334 0.1667 0.2168 0.2501 0.2834 0.3334
−12.0 −18.6 −32.3 −44.6 −56.9 −62.4 −69.1 −72.4 −74.5
−5.1 1.0 −1.2 1.4 −2.5 2.3 0.6 0.9 1.0
0.0340 0.0680 0.1019 0.1357 0.1695 0.2033 0.2539 0.2875 0.3379 0.3715
−7.1 −13.0 −16.8 −22.6 −25.1 −30.6 −30.4 −31.9 −32.7 −26.0
−0.2 −0.4 0.9 −0.5 0.8 −1.7 1.4 0.5 −2.0 1.7
0.0297 0.0597 0.0899 0.1356 0.1664 0.2130 0.2443 0.2918 0.3398 0.3721
−170.4 −340.0 −519.9 −772.1 −960.5 −1271.2 −1432.7 −1692.6 −1956.2 −2172.6
8.3 −0.5 −14.0 7.4 11.5 −14.4 3.3 −0.3 3.7 −2.1
x
HmE J·mol−1
dHmE J·mol−1
T=298.15 K, p=5 MPa 0.4047 −399.1 0.2 0.4375 −414.2 2.8 0.4706 −434.3 −3.0 0.5040 −438.3 3.3 0.5376 −446.7 1.4 0.5715 −449.2 1.3 0.6056 −448.0 0.8 0.6574 −446.8 −8.2 0.6922 −428.5 −2.1 0.7273 −412.6 −3.4 T=298.15 K, p=10 MPa 0.4107 −128.0 −1.3 0.4439 −125.5 −0.1 0.4939 −120.6 −1.7 0.5272 −113.6 −2.0 0.5774 −97.5 −1.4 0.6109 −82.1 0.8 0.6444 −67.9 −0.3 0.6948 −39.4 1.3 0.7285 −20.0 0.7 0.7622 25.1 1.9 T=298.15 K, p=12.5 MPa 0.3668 −76.2 −1.3 0.4168 −71.5 −0.9 0.4501 −67.1 −1.7 0.4835 −56.8 1.3 0.5335 −45.0 −1.2 0.5668 −31.7 0.2 0.6168 −11.6 −0.5 0.6501 5.2 0.5 0.6834 22.4 0.9 T=298.15 K, p=15 MPa 0.4049 −23.3 −0.3 0.4551 −12.5 0.0 0.4885 −4.4 −1.1 0.5385 14.8 1.0 0.5717 27.5 0.4 0.6049 41.9 0.0 0.6547 65.4 −0.6 0.6878 82.2 −0.5 0.7373 108.7 1.0 0.7703 122.2 −1.2 T=323.15 K, p=5 MPa 0.4047 −2211.4 48.2 0.4541 −2091.6 −36.0 0.4873 −1908.0 10.5 0.5376 −1710.1 0.7 0.5715 −1583.2 −12.4 0.6056 −1431.6 −1.6 0.6574 −1212.0 4.2 0.6922 −1087.9 −15.4 0.7273 −935.8 −8.3 0.7627 −793.7 −12.3
x
HmE J·mol−1
dHmE J·mol−1
0.7627 0.8164 0.8525 0.8889 0.9256 0.9441 0.9627 0.9813 0.9860 0.9888
−380.5 −332.6 −289.1 −230.3 −156.9 −107.2 −49.0 12.7 23.6 32.5
5.6 4.7 2.7 1.1 −5.2 −4.4 −1.4 2.5 0.5 3.1
0.7960 0.8299 0.8638 0.8978 0.9318 0.9488 0.9659 0.9829 0.9872
24.7 44.7 69.0 87.3 107.2 115.6 118.8 114.5 110.1
1.8 −1.0 0.6 −2.6 −1.6 −0.4 −1.1 0.8 2.8
0.7334 0.7668 0.8167 0.8501 0.8834 0.9334 0.9667
49.9 65.6 92.6 105.9 119.6 130.1 127.8
1.7 −0.5 0.6 −1.5 −0.5 −0.8 1.2
0.8197 0.8526 0.8854 0.9018 0.9346 0.9510 0.9673 0.9837
146.0 155.1 160.2 162.8 164.5 159.1 151.9 129.4
1.8 0.2 −1.8 −1.1 1.5 0.0 1.2 −1.3
0.8164 0.8525 0.8889 0.9256 0.9627 0.9819 0.9863 0.9890
−565.7 −410.6 −261.3 −104.3 53.7 127.6 153.5 165.5
−6.0 0.1 −1.0 4.5 9.3 3.9 11.7 0.0
1037
H E and V E for (ethane+propan-1-ol) TABLE 1—continued x
HmE J·mol−1
dHmE J·mol−1
0.0326 0.0652 0.0978 0.1305 0.1797 0.2125 0.2454 0.2949 0.3279 0.3776
−22.8 −45.4 −74.4 −89.4 −123.9 −145.4 −155.2 −177.9 −186.1 −200.2
2.5 3.6 −3.0 3.1 −2.0 −5.7 0.9 −0.7 2.6 1.4
0.0167 0.0500 0.0834 0.1334 0.1667 0.2168 0.2501 0.2834 0.3334
−6.7 −23.8 −26.5 −42.0 −47.0 −57.5 −60.3 −63.1 −59.3
0.1 −5.0 2.5 −0.1 1.9 −0.5 0.3 −0.6 2.7
0.0340 0.0680 0.1019 0.1357 0.1695 0.2033 0.2539 0.2875 0.3379 0.3715
−3.3 −7.0 −6.2 −5.6 −4.4 −0.5 4.8 8.6 22.5 33.8
−0.5 −2.1 0.0 0.8 0.9 2.3 0.9 −1.8 −0.8 −0.3
0.0297 0.0597 0.0899 0.1356 0.1664 0.2130 0.2443 0.2918 0.3398 0.3721 0.4047
−162.0 −309.6 −453.4 −698.9 −885.5 −1092.6 −1266.3 −1371.8 −1270.1 −1167.9 −1022.8
−3.6 −1.0 7.5 2.6 −17.8 18.8 −7.8 6.8 −26.2 −14.7 39.0
0.0652 0.0978 0.1305 0.1797 0.2125 0.2454 0.2949 0.3279 0.3776
−85.3 −135.4 −165.3 −226.3 −263.4 −313.4 −351.8 −397.7 −430.2
2.1 −6.5 4.0 2.1 3.4 −9.0 6.5 −5.8 7.4
x
HmE J·mol−1
dHmE J·mol−1
T=323.15 K, p=10 MPa 0.4107 −204.0 3.1 0.4439 −208.2 1.7 0.4939 −210.4 −1.6 0.5272 −208.3 −3.8 0.5744 −189.3 4.1 0.6109 −186.7 −6.0 0.6444 −165.0 0.9 0.6948 −141.7 −4.1 0.7285 −112.0 2.5 0.7791 −71.3 1.2 T=323.15 K, p=12.5 MPa 0.3668 −64.1 −4.8 0.4168 −48.4 2.7 0.4501 −46.5 −3.7 0.4835 −28.5 3.8 0.5335 −14.6 −2.0 0.5668 1.6 −1.5 0.6168 30.6 0.7 0.6501 52.5 2.9 0.6834 71.2 0.6 T=323.15 K, p=15 MPa 0.4049 46.8 0.3 0.4551 68.0 −0.1 0.4885 82.8 −1.6 0.5385 113.4 2.2 0.5717 130.6 0.2 0.6049 148.6 −1.7 0.6547 183.3 2.0 0.6878 201.4 −0.6 0.7373 235.0 2.6 0.7703 248.9 −2.6 T=348.15 K, p=5 MPa 0.4541 −919.0 4.2 0.4873 −831.6 −1.6 0.5376 −688.4 0.4 0.5715 −600.0 −6.2 0.6056 −500.7 −2.7 0.6574 −353.3 −0.6 0.6922 −257.0 −2.0 0.7273 −151.1 5.4 0.7627 −60.8 −3.7 0.8164 91.3 −2.3 0.8525 211.3 16.5 T=348.15 K, p=10 MPa 0.4107 −467.5 −3.7 0.4439 −487.9 −1.8 0.4939 −516.2 −5.0 0.5272 −513.3 8.3 0.5774 −527.8 −0.5 0.6109 −519.8 4.3 0.6444 −521.6 −7.0 0.6948 −488.4 −1.0 0.7285 −463.2 −4.7
x
HmE J·mol−1
dHmE J·mol−1
0.8130 0.8468 0.8706 0.8978 0.9148 0.9318 0.9488 0.9659 0.9829 0.9872
−28.6 −0.4 21.2 67.4 90.9 128.0 141.6 156.7 165.1 147.9
10.2 −0.2 −9.1 −1.0 −2.8 8.5 −2.4 −6.3 5.9 0.2
0.7334 0.7668 0.8167 0.8501 0.8834 0.9334 0.9667 0.9833
106.0 122.9 160.8 179.3 207.4 234.3 231.1 190.8
2.3 −3.6 −0.1 −4.4 2.0 3.1 2.8 −4.8
0.8197 0.8526 0.8854 0.9018 0.9182 0.9346 0.9510 0.9673 0.9837
275.6 289.4 302.9 303.2 302.3 297.7 292.1 270.1 219.5
−1.4 −1.3 2.7 0.7 −0.3 −1.7 1.7 −0.3 −0.5
0.8889 0.9072 0.9256 0.9627 0.9813 0.9860 0.9888 0.9906 0.9920
290.5 339.8 402.6 509.8 552.0 568.1 409.8 320.7 293.3
−6.5 −8.5 2.7 5.7 −4.3 −1.4 11.2 −16.8 4.2
0.7791 0.8130 0.8468 0.8808 0.8978 0.9318 0.9488 0.9659 0.9829
−381.0 −334.5 −243.0 −148.6 −62.9 74.9 140.6 201.4 181.8
12.4 −4.4 3.0 −12.7 7.8 0.8 −3.4 6.6 −4.5
1038
J. B. Ott et al. TABLE 1—continued
x
HmE J·mol−1
dHmE J·mol−1
0.0167 0.0667 0.1334 0.1834 0.2334 0.2834 0.3168 0.3668 0.4168
−7.7 −25.9 −42.4 −46.4 −54.9 −50.3 −53.0 −42.6 −32.2
1.0 1.5 −0.8 1.3 −3.7 1.5 −2.7 2.1 2.7
0.0340 0.0680 0.1019 0.1357 0.1695 0.2033 0.2539 0.2875 0.3379 0.3715
5.0 13.3 21.4 31.1 44.5 57.3 80.3 95.6 119.7 149.7
0.0 1.1 0.1 −0.9 0.5 0.0 0.3 −1.2 −4.8 4.9
x
HmE J·mol−1
dHmE J·mol−1
T=348.15 K, p=12.5 MPa 0.4501 −24.4 1.3 0.5001 −8.1 −0.1 0.5335 6.9 0.5 0.5835 27.6 −3.8 0.6168 48.8 −1.5 0.6501 68.1 −3.0 0.6834 96.1 2.0 0.7168 120.2 0.7 0.7668 168.1 4.6 T=348.15 K, p=15 MPa 0.4049 167.0 0.7 0.4551 201.5 1.0 0.4885 226.6 2.4 0.5385 258.8 −1.9 0.5717 285.1 −0.1 0.6049 305.7 −3.9 0.6547 344.8 −0.5 0.6878 369.6 1.0 0.7373 405.5 3.1 0.7703 420.8 −3.4
x
HmE J·mol−1
dHmE J·mol−1
0.8001 0.8334 0.8501 0.8834 0.9167 0.9500 0.9833
198.2 235.9 258.3 295.9 340.8 354.1 238.9
0.5 −0.4 1.0 −5.2 0.0 1.6 0.8
0.8197 0.8526 0.8854 0.9018 0.9346 0.9510 0.9673 0.9837
463.1 471.0 484.7 492.0 472.6 449.2 392.6 267.0
7.5 −3.4 −3.4 1.3 −3.2 1.7 3.4 −1.7
TABLE 2. Experimental excess molar volumes VmE for {xC2 H6+(1−x)CH3(CH2 )2OH}; dVmE is the deviation of the experimental results from equation (2) with the parameters given in table 4. At p=5 MPa for T=323.15 K and T=348.15 K, VmE and dVmE values are not included at high x nor for the two-phase region x
VmE dVmE cm3·mol−1 cm3·mol−1
0.0447 0.0899 0.1356 0.1818 0.2130 0.2443 0.2759 0.3077 0.3398 0.3721
−1.25 −2.09 −3.37 −4.36 −5.16 −5.72 −6.39 −6.94 −7.55 −8.39
−0.18 0.08 −0.09 0.01 −0.08 0.05 0.06 0.14 0.14 −0.13
0.0326 0.0652 0.0978 0.1305 0.1797 0.2125 0.2454 0.2949 0.3279 0.3776
−0.59 −0.98 −1.47 −1.90 −2.52 −2.92 −3.29 −3.76 −4.08 −4.53
−0.06 0.03 0.00 0.00 −0.01 −0.02 −0.01 0.04 0.04 0.03
x
VmE dVmE cm3·mol−1 cm3·mol−1
T=298.15 K, p=5 MPa 0.4047 −8.78 0.01 0.4375 −9.40 −0.12 0.4706 −9.68 0.03 0.5040 −10.11 −0.02 0.5376 −10.49 −0.08 0.5715 −10.75 −0.07 0.6056 −10.96 −0.10 0.6574 −10.84 0.14 0.6922 −10.81 0.14 0.7273 −10.73 0.06 T=298.15 K, p=10 MPa 0.4107 −4.86 −0.06 0.4439 −5.08 −0.07 0.4939 −5.27 −0.01 0.5272 −5.34 0.03 0.5774 −5.40 0.05 0.6109 −5.35 0.08 0.6444 −5.36 0.02 0.6948 −5.23 −0.06 0.7285 −5.09 −0.12 0.7622 −4.71 −0.02
x
VmE dVmE cm3·mol−1 cm3·mol−1
0.7627 −10.44 0.8164 −9.67 0.8525 −9.13 0.8889 −7.58 0.9256 −5.69 0.9441 −4.70 0.9627 −3.63 0.9813 −2.06 0.9860 −1.55 0.9888 −0.81
0.04 0.01 −0.31 0.02 0.20 0.08 −0.16 −0.16 −0.10 0.37
0.7960 0.8299 0.8638 0.8978 0.9318 0.9488 0.9659 0.9829 0.9872
0.04 0.03 0.00 0.13 −0.02 −0.11 −0.07 0.09 0.01
−4.30 −3.88 −3.39 −2.63 −2.02 −1.68 −1.16 −0.48 −0.43
1039
H E and V E for (ethane+propan-1-ol)
TABLE 2—continued x
VmE dVmE cm3·mol−1 cm3·mol−1
x
VmE dVmE cm3·mol−1 cm3·mol−1
x
VmE dVmE cm3·mol−1 cm3·mol−1
0.0167 0.0500 0.0834 0.1334 0.1667 0.2168 0.2501 0.2834 0.3334
−0.14 −0.71 −1.03 −1.61 −1.96 −2.39 −2.65 −2.99 −3.32
−0.10 0.05 −0.02 0.02 0.03 −0.02 −0.05 0.01 −0.05
T=298.15 K, p=12.5 MPa 0.3668 −3.68 0.09 0.4168 −3.89 0.01 0.4501 −4.04 0.01 0.4835 −4.11 −0.03 0.5335 −4.21 −0.05 0.5668 −4.28 0.00 0.6168 −4.29 0.05 0.6501 −4.14 −0.03 0.6834 −4.05 0.01
0.0340 0.0680 0.1019 0.1357 0.1695 0.2033 0.2539 0.2875 0.3379 0.3715
−0.50 −0.80 −1.26 −1.59 −1.91 −2.13 −2.56 −2.83 −3.13 −3.34
−0.02 0.09 −0.01 −0.02 −0.05 0.02 0.00 −0.03 0.01 0.00
T=298.15 K, p=15 MPa 0.4049 −3.50 0.02 0.4551 −3.67 0.06 0.4885 −3.82 0.01 0.5385 −3.91 −0.02 0.5717 −3.93 −0.04 0.6049 −3.90 −0.05 0.6547 −3.73 −0.02 0.6878 −3.54 0.02 0.7373 −3.27 0.01 0.7703 −3.02 0.03
— — — —
T=323.15 K, p=5 MPa 0.1664 −43.6 — 0.2130 −55.7 — 0.2443 −63.8 — 0.2918 −76.0 —
0.3398 −88.3 0.3721 −96.4 0.4047 −105.4 0.4541 −117.4
0.8130 0.8468 0.8706 0.8978 0.9148 0.9318 0.9488 0.9659 0.9829 0.9872
−9.79 −9.06 −8.32 −7.14 −6.18 −5.69 −4.18 −3.36 −1.99 −1.59
0.05 −0.12 −0.15 −0.04 0.14 −0.24 0.29 −0.02 −0.02 −0.03
0.7334 0.7668 0.8167 0.8501 0.8834 0.9334 0.9667 0.9833
−7.33 −6.80 −6.21 −5.42 −4.60 −2.95 −1.64 −0.82
0.08 −0.07 0.11 −0.01 0.01 −0.05 0.00 −0.05
0.0297 0.0597 0.0899 0.1356
−7.9 −15.8 −23.7 −35.9
0.0326 0.0652 0.0978 0.1305 0.1797 0.2125 0.2454 0.2949 0.3279 0.3776
−1.03 −1.86 −2.64 −3.58 −4.81 −5.39 −6.34 −7.45 −8.04 −8.93
−0.12 −0.06 0.04 −0.04 −0.02 0.18 −0.01 −0.06 0.01 0.03
T=323.15 K, p=10 MPa 0.4107 −9.51 0.00 0.4439 −10.04 −0.04 0.4939 −10.72 −0.08 0.5272 −10.98 0.00 0.5744 −11.40 −0.03 0.6109 −11.48 0.03 0.6444 −11.56 0.01 0.6948 −11.36 0.08 0.7285 −11.29 −0.10 0.7791 −10.32 0.20
0.0167 0.0500 0.0834 0.1334 0.1667 0.2168 0.2501 0.2834 0.3334
−0.42 −1.09 −1.72 −2.61 −3.24 −4.05 −4.61 −5.17 −5.82
0.05 0.02 −0.01 −0.04 0.02 −0.02 0.00 0.05 −0.01
T=323.15 K, p=12.5 MPa 0.3668 −6.24 −0.03 0.4168 −6.74 −0.10 0.4501 −7.18 0.03 0.4835 −7.58 0.16 0.5335 −7.71 0.01 0.5668 −7.76 −0.05 0.6168 −7.80 −0.05 0.6501 −7.79 0.01 0.6834 −7.56 −0.08
0.7334 0.7668 0.8167 0.8501 0.8834 0.9334 0.9667
−3.77 −3.54 −3.05 −2.74 −2.22 −1.44 −0.81
0.00 0.01 −0.03 0.04 −0.04 0.00 0.03
0.8197 0.8526 0.8854 0.9018 0.9346 0.9510 0.9673 0.9837
−2.56 −2.30 −1.94 −1.69 −1.19 −0.94 −0.65 −0.35
0.06 −0.02 −0.05 −0.01 0.01 −0.01 0.00 −0.01
— — — —
1040
J. B. Ott et al.
TABLE 2—continued x
0.0340 0.0680 0.1019 0.1357 0.1695 0.2033 0.2539 0.2875 0.3379 0.3715
VmE dVmE cm3·mol−1 cm3·mol−1
−0.78 −1.38 −1.88 −2.41 −2.92 −3.40 −4.01 −4.46 −5.01 −5.30
−0.04 −0.01 0.05 0.03 −0.01 −0.03 0.00 −0.04 −0.04 0.00
x
VmE dVmE cm3·mol−1 cm3·mol−1
T=323.15 K, p=15 MPa 0.4049 −5.52 0.07 0.4551 −5.83 0.11 0.4885 −6.14 −0.04 0.5385 −6.24 0.02 0.5717 −6.34 −0.05 0.6049 −6.34 −0.09 0.6547 −6.13 −0.03 0.6878 −5.83 0.09 0.7373 −5.54 0.00 0.7703 −5.19 0.02 T=348.15 K, p=5 MPa 0.1356 −48.1 0.1664 −58.6 0.2130 −75.1
0.0297 0.0597 0.0899
−10.7 −21.4 −32.0
0.0652 0.0978 0.1305 0.1797 0.2125 0.2454 0.2949 0.3279 0.3776
−4.08 −5.81 −8.07 −10.77 −12.83 −14.36 −17.27 −19.12 −21.58
−0.09 0.14 −0.16 0.04 −0.12 0.21 0.04 −0.07 −0.01
T=348.15 K, p=10 MPa 0.4107 −23.14 0.00 0.4439 −24.64 −0.01 0.4939 −26.58 0.07 0.5272 −27.93 −0.10 0.5774 −29.27 0.04 0.6109 −30.17 −0.10 0.6444 −30.38 0.22 0.6948 −31.21 −0.30 0.7285 −30.65 0.06
0.0167 0.0667 0.1334 0.1834 0.2334 0.2834 0.3168 0.3668 0.4168
−0.94 −2.61 −5.16 −7.11 −8.71 −10.42 −11.38 −12.91 −14.18
0.32 0.06 −0.01 0.06 −0.12 −0.06 −0.11 0.04 0.08
T=348.15 K, p=12.5 MPa 0.4501 −14.95 0.12 0.5001 −15.66 −0.11 0.5335 −16.32 0.01 0.5835 −16.91 −0.01 0.6168 −17.34 0.15 0.6501 −17.32 0.00 0.6834 −17.35 0.06 0.7168 −17.09 0.01 0.7668 −16.28 −0.04
0.0340 0.0680 0.1019 0.1357 0.1695 0.2033 0.2539 0.2875 0.3379 0.3715
−1.19 −2.09 −2.96 −3.88 −4.65 −5.45 −6.49 −7.15 −8.15 −8.55
−0.07 0.03 0.06 −0.02 0.00 −0.04 −0.01 0.01 −0.06 0.12
T=348.15 K, p=15 MPa 0.4049 −9.21 −0.02 0.4551 −9.89 −0.01 0.4885 −10.20 0.05 0.5385 −10.72 −0.05 0.5717 −10.91 −0.06 0.6049 −10.98 −0.03 0.6547 −10.88 0.01 0.6878 −10.65 0.07 0.7373 −10.14 0.08 0.7703 −9.76 −0.06
x
0.8197 0.8526 0.8854 0.9018 0.9182 0.9346 0.9510 0.9673 0.9837
VmE dVmE cm3·mol−1 cm3·mol−1
−4.60 −4.05 −3.45 −3.09 −2.68 −2.13 −1.79 −1.22 −0.80
−0.02 0.01 −0.02 −0.02 0.00 0.11 −0.03 0.01 −0.16
0.2443
−85.8
0.7791 0.8130 0.8468 0.8808 0.8978 0.9318 0.9488 0.9659
−29.68 −28.27 −26.11 −23.36 −22.26 −17.59 −13.14 −10.44
−0.01 0.08 0.28 0.21 −0.52 −0.55 0.83 −0.19
0.8001 0.8334 0.8501 0.8834 0.9167 0.9500 0.9833
−15.07 −14.26 −13.36 −11.47 −9.53 −6.25 −2.02
−0.37 0.04 −0.09 −0.08 0.41 0.21 −0.21
0.8197 0.8526 0.8854 0.9018 0.9346 0.9510 0.9673 0.9837
−8.58 −7.65 −6.47 −5.81 −4.10 −3.27 −2.19 −1.10
0.02 −0.02 −0.03 −0.07 0.05 −0.03 0.06 0.07
1041
H E and V E for (ethane+propan-1-ol)
TABLE 3. Parameters representing HmE of {xC2 H6+(1−x)CH3(CH2 )2OH} with equation (2). At p=5 MPa and T=323.15 K and T=348.15 K, (vapor+liquid) equilibrium is present and equation (2) and these parameters apply for 0QxQx1 , and x2QxQ1, where x1 and x2 are the (vapor+liquid) solubility bounds given in table 4. At all other (T,p), equation (2) applies over the entire range of composition. s is the standard deviation of HmE from equation (2) p/MPa
a0
a1
5.0 10.0 12.5 15.0
−1762.5 −471.0 −215.5 1.0
−1213.5 −859.0 −758.4 −641.8
5.0 a −14380 10.0 −832.9 12.5 −105.4 15.0 361.3 5.0 a 10.0 12.5 15.0 a
a2
a3
556.4 224.0 97.7 157.5
31530 −50030 −1019.8 270.1 −861.4 108.8 −688.6 −86.0
−3935 −13780 −2054.0 −1182.9 −32.1 −827.3 930.3 −587.4
30660 916.8 122.4 −225.0
a4
a5
T=298.15 K 549.2 −47.6 241.6 −61.4 195.3 −158.2 355.6 −210.2 T=323.15 K 2170 72770 175.7 60.5 321.4 −96.3 247.0 −12.0 T=348.15 K −15790 330.8 −271.2 184.4 165.1 199.2 275.0
a6
−769.1 −96.0 −48870 −248.1 −205.8
−1253.6 −718.0 −392.5
819.5
k
s
−0.99 −0.99 −0.99 −0.99
3.0 1.4 1.6 1.1
−0.98 −0.98 −0.98
7.9 4.2 2.8 1.5
0.50 −0.93 −0.93 −0.93
11.1 6.0 2.2 2.7
Values reported with four significant figures.
mixing due to phase equilibrium occurs, and reproducible results could not be obtained. Also, no attempt was made to fit to equation (1) the limited number of VmEs obtained at these (p,T ) conditions for values of x where only one phase was present. The HmE results are summarized in the three-dimensional plots of HmE against (p,x) and against (T,x) shown in figures 2(a) and 2(b). The results shown in figure 2(a) at p=5 MPa with T=323.15 K and T=348.15 K indicate that (vapor+liquid) equilibrium is present at these (p,T ) conditions, with the apparent HmE changing linearly over the region of x where phase separation occurs. At these (p,T ) conditions, large negative HmE s at low x can be explained as resulting from the condensation of TABLE 4. Parameters representing VmE of {xC2 H6+(1−x)CH3(CH2 )2OH} with equation (2); s is the standard deviation. The limited number of values at p=5 MPa with T=323.15 K and T=348.15 K (phase equilibrium is present over much of the composition range) were not fitted to equation (2) T/K
p/MPa
a0
a1
a2
a3
298.15 298.15 298.15 298.15 323.15 323.15 323.15 348.15 348.15 348.15
5.0 10.0 12.5 15.0 10.0 12.5 15.0 10.0 12.5 15.0
−40.20 −21.13 −16.77 −15.39 −42.83 −30.11 −24.61 −107.51 −63.09 −41.45
−4.57 7.47 4.93 3.76 −19.14 12.37 7.38 −11.18 34.26 32.92
1.04 −1.32 0.10 1.82 7.91 −2.78 0.31 13.17 −25.32 −14.76
4.33 1.50 0.66 −0.68 −5.00 3.25 1.61 −4.43 17.54 5.47
a4
−3.40 −3.27 −5.05 4.53 −5.58 −8.31
k
s
−0.65
0.13 0.06 0.04 0.03 0.11 0.06 0.06 0.26 0.16 0.05
−0.96 −0.79
−5.61
0.34
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J. B. Ott et al.
TABLE 5. Parameters for equation (3) representing HmE for {xC2 H6+(1−x)CH3(CH2 )2OH}. Equation (3) applies for x1QxQx2 (in the two-phase region), where x1 and x2 are the (vapor+liquid) solubility bounds; s is the standard deviation from equation (3) T/K
p/MPa
b0
b1
s
x1
x2
323.15 348.15
5.0 5.0
−3931 −2197
4129 2806
16.6 12.0
0.391 0.282
0.989 0.984
gaseous ethane into liquid propan-1-ol, while a major contributor to the positive HmE at high x is the vaporization of liquid propan-1-ol into the gaseous ethane. The results at p=5 MPa are not shown in figure 2(b) so that the HmE scale can be expanded. Figure 2(a) shows that, except at the highest pressure and temperature, HmE (x) is S shaped, changing from values of HmE Q0 at low x to values of HmE q0 at high x, with the crossover shifting to smaller x with increasing (p,T ). Figure 2(b) shows that the effect of pressure on HmE is most pronounced at T=348.15 K, where HmE (x) changes from the most negative results at p=10 MPa to the most positive results at p=15 MPa. (The results at p=5 MPa are excluded from the comparison.) In an earlier paper,(17) in which we reported HmE for (ethane+acetonitrile), we found a large change in HmE from negative to positive values as p increased over approximately the same pressure range, and attributed it to a change from gas-like to liquid-like behavior of the supercritical ethane. Figures 3(a) and 3(b) are three-dimensional plots of VmE against (p,x) and (T,x). As with the HmE plots, the results at p=5 MPa with T=323.15 K and T=348.15 K are excluded from figure 3(b) in order to expand the scale. Figure 3 shows that VmE W0 at all experimental pressures and temperatures.
FIGURE 2. (a) Three-dimensional plot of (x,p) against HmE for {xC2 H6+(1−x)CH3(CH2 )2OH}. The temperatures are as follows: w, 298.15 K; q, 323.15 K; r, 348.15 K. (b) Three-dimensional plot of (x,T ) against HmE for {xC2 H6+(1−x)CH3(CH2 )2CH2OH}. The pressures are as follows: w, 10 MPa; q, 12.5 MPa; r, 15 MPa.
H E and V E for (ethane+propan-1-ol)
1043
FIGURE 3. (a) Three-dimensional plot of (x,p) against VmE for {xC2 H6+(1−x)CH3(CH2 )2OH}. The temperatures are as follows: w, 298.15 K; q, 323.15 K; r, 348.15 K. (b) Three-dimensional plot of (x,T ) against VmE for {xC2 H6+(1−x)CH3(CH2 )2OH}. The pressures are as follows: w, 10 MPa; q, 12.5 MPa; r, 15 MPa.
The (1VmE/1T )p is large and increases with decreasing p as shown in figure 3(a). The (1VmE/1p)T is also large and increases with T as shown in figure 3(b). At p=5 MPa with T=323.15 K and T=348.15 K, =VmE = is especially large. A major contribution to this effect is the decrease in volume resulting from the condensation of supercritical ethane, present at a comparatively low pressure, into the liquid propan-1-ol during the mixing process. A similar, although somewhat smaller, effect is obtained at p=5 MPa and T=298.15 K, where the ethane is liquid, but behaves very much like a gas because the temperature is near the Tc of ethane. In earlier papers,(4, 18) we attributed the effect of pressure on HmE for systems containing liquid ethane at T=298.15 K to this gas-like behavior. The quantity (1HmE /1p)T can be calculated from VmE by means of equation (1). Figure 4 compares the results of this calculation at T=323.15 K and p=12.5 MPa with results obtained directly from HmE . Values of VmE(x) at p=12.5 MPa and T=(298.15, 323.15, and 348.15) K, obtained from equation (2) with the parameters given in table 4, were fitted to a quadratic equation in T. The equation was differentiated to give (1VmE/1T )p , which was used with VmE in equation (1) to calculate (1HmE /1p)T . The process was repeated at a series of values of x to generate the curve shown in figure 4. The quantity (1HmE /1p)T was derived from HmE in a similar manner by fitting HmE , obtained at T=323.15 K and p=(10, 12.5, and 15) MPa from equation (2) with the parameters given in table 3, to a quadratic equation in T, and differentiating. The results obtained from this calculation are shown in figure 4, and are lower than the values calculated from VmE . Analysis of the sources of error suggests that the results calculated from VmE are more accurate and, hence, that the major error is in the calculation of HmE . Also shown in figure 4 are the results of a calculation of (1HmE /1p)T from HmE that includes the fourth set of HmE values obtained at p=5 MPa. This calculation covers only the part of the composition range where phase equilibrium is not present. Agreement of the latter values with those calculated from VmE is much better
1044
J. B. Ott et al.
FIGURE 4. Comparison of (1HmE /1p)T at T=323.15 K and p=12.5 MPa calculated in different ways. ····W····W, Calculated from VmE results; — – —, calculated from HmE results at p=(10, 12.5, and 15) MPa; ——, calculated from HmE at (p=5, 10, 12.5, and 15) MPa. The latter calculation is limited to the region of low x where phase equilibrium is not present.
than with those in which only three pressures were used in the quadratic equation fit. The calculation demonstrates the difficulty in accurately calculating (1HmE /1p)T from HmE values at different pressures, especially when this pressure coefficient is large. Because of the nonlinear relation between HmE and p, adding HmE results at the extra pressure significantly increases the accuracy with which the pressure derivative can be obtained. The authors express appreciation to the Brigham Young University Chemistry Department for support of this project. The help of Bryant Marchant with the experimental measurements is also appreciated. REFERENCES 1. Younglove, B. A.; Ely, J. F. J. Phys. Chem. Ref. Data 1987, 16, 577. 2. Wilhoit, R. C.; Zwolinski, B. J. J. Phys. Chem. Ref. Data 1973, Supplement No. 1, 2, 38. 3. Sipowska, J. T.; Graham, R. C.; Neely, B. J.; Ott, J. B.; Izatt, R. M. J. Chem. Thermodynamics 1989, 21, 1085. 4. Ott, J. B.; Sipowska, J. T.; Owen, R. L.; Izatt, R. M. J. Chem. Thermodynamics 1990, 22, 683. 5. Sipowska, J. T.; Ott, J. B.; Woolley, A. T.; Izatt, R. M. J. Chem. Thermodynamics 1991, 23, 1013. 6. Sipowska, J. T.; Ott, J. B.; Neely, B. J.; Izatt, R. M. J. Chem. Thermodynamics 1991, 23, 551. 7. Sipowska, J. T.; Ott, J. B.; Woolley, A. T.; Marchant, B. G.; Gruszkiewicz, M. S. J. Chem. Thermodynamics 1993, 25, 999. 8. Ott, J. B.; Sipowska, J. T.; Woolley, A. T. J. Chem. Thermodynamics 1993, 25, 511. 9. Sipowska, J. T.; Ott, J. B.; Woolley, A. T.; Izatt, R. M. J. Chem. Thermodynamics 1990, 22, 1159. 10. Ott, J. B.; Sipowska, J. T.; Woolley, A. T.; Izatt, R. M. J. Chem. Thermodynamics 1992, 24, 75. 11. Sipowska, J. T.; Ott, J. B.; Woolley, A. T.; Izatt, R. M. J. Chem. Thermodynamics 1992, 24, 1087.
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12. Sipowska, J. T.; Lemon, L. R.; Ott, J. B.; Marchant, B. G.; Brown, P. R. J. Chem. Thermodynamics 1994, 26, 1275. 13. Lemon, L. R.; Sipowska, J. T.; Ott, J. B.; Marchant, B. G.; Brown, P. R. to be published. 14. Selected Values of Properties of Chemical Compounds. Thermodynamic Research Center Project: Texas A&M University, College Station, TX. 15. Ott, J. B.; Stouffer, C. E.; Cornett, G. V.; Woodfield, B. F.; Wirthlin, R. C.; Christensen J. J.; Deiters. U. K. J. Chem. Thermodynamics 1986, 18, 1. 16. Ott, J. B.; Sipowska, J. T.; Gruszkiewicz, M. S.; Woolley, A. T. J. Chem. Thermodynamics 1993, 25, 307. 17. Ott, J. B.; Neely, B. J.; Purdy, J. E.; Owen, R. L. Thermochim. Acta 1989, 154, 71. 18. Gruszkiewicz, M. S.; Sipowska, J. T.; Ott, J. B.; Brown, P. R.; Moore, J. D. J. Chem. Thermodynamics 1995, 27, 507–524.