Full Text
PHYSICAL CHEMISTRY
D. S. TSIKLIS, A. I. KULIKOVA, and L. I. SHENDEREI*
VOLUMES OF GASEOUS SOLUTIONS OF WATER IN ETHYLENE AT HIGH PRESSURES AND TEMPERATURES
(Presented by Academician A. N. Frumkin, May 18, 1960)
Using the constant-volume piezometer method, the volumes of gaseous solutions of water in compressed ethylene were measured at temperatures from 200 to 300° and pressures up to 100–150 atm. Into apparatus 1 (Fig. 1) of known volume, definite amounts of water and ethylene were introduced through valve 3 (the composition of the solution was chosen from data on phase equilibria in this system obtained earlier (¹)); the apparatus was heated, the gaseous solution was mixed with electromagnetic stirrer 2, the pressure was measured, and part of the solution was discharged through membrane valve 4 into evacuated, calibrated flasks 13, condensing the water en route in ampoule 11. After discharging a sample, the solution was again stirred, the pressure was measured, and part of the solution was again discharged. This was repeated until the entire loaded mixture had been discharged. A balance was then drawn up, the average composition of the mixture was determined, and, knowing the dependence of the molar volume of a solution of this composition on pressure, the molar volume on the saturation line was found.
Membrane valve 6, mounted in block 5, served to connect the pressure-measuring system 7. This system consists of a membrane, which serves as the zero instrument,** and lamp 8, which lights when the membrane closes an electric circuit. By creating oil pressure with press 9 in the space above the membrane, it is adjusted so that lamp 8 lights and goes out when the pressure changes by fractions of an atmosphere. At this moment the oil pressure (which is equal to the pressure in the apparatus) is measured with standard pressure gauges 10 of class 0.35. When a sample is discharged, water and ethylene are condensed in ampoule 11 at the temperature of liquid nitrogen. The ampoule is then heated to the temperature of a mixture of solid carbon dioxide and acetone, and the evaporating ethylene is pumped off by mercury pump 12 into evacuated flasks of up to 15 l capacity.
The volume of the column was determined by calibration with a gas of known compressibility. The change in the column volume with temperature was calculated from the equation for the volume expansion of stainless steel (³). The experimental data obtained are given in Table 1.
Figure 2 shows the volumes of solutions of water in ethylene on the saturation line, found by extrapolation.
Experimental data
The thermodynamic properties of a substance are most conveniently calculated from \(pvT\) data if these data are expressed by an equation of state. We attempted to represent the volumetric behavior of the investigated solutions by an equation—
* V. I. Alisova took part in carrying out the experiments.
** The instrument was constructed by us on the principle of a fully supported membrane, previously used in a membrane valve (²).
state in virial form * (4). Equation (1)
\[ pv = RT \left(1 + B(T)/v + C(T)/v^2\right), \tag{1} \]
where \(p\) is pressure, \(v\) is molar volume, \(R\) is the gas constant, and \(B(T)\) and \(C(T)\) are the second and third virial coefficients; in order to find these
Fig. 1. Apparatus for determining the volumes of gas solutions
coefficients, it was transformed into the equation of a straight line:
\[ \left(\frac{pv}{RT} - 1\right)v = B + C/v . \tag{2} \]
If the experimental data are represented by equation (1), then the values of the left-hand side of equation (2), calculated from the experimental data and plotted against \(1/v\), should fall on a straight line, which cuts off on the ordinate axis \(B_p\), and the tangent of whose angle of inclination to the abscissa axis is equal to \(C_p\). (\(B_p\) and \(C_p\) are the second and third virial coefficients of the gas solution of the given concentration.)
Fig. 2. Volumes of gas solutions of water in ethylene on the saturation line
The calculations we carried out showed that the values of the left-hand side of equation (2)—\(\Delta\)—lay well on a straight line, and we were able to calculate the values of \(B_p\) and \(C_p\) for the solutions we studied.
In order to be able to calculate the volumes of a solution of any concentration, and not only of the one investigated, it is necessary to know the concentration dependence of the second and third virial coefficients, which is given by equations (3) and (4)
\[ B_p = B_{11}N_1^2 + 2B_{12}N_1N_2 + B_{22}N_2^2; \tag{3} \]
\[ C_p = C_{111}N_1^3 + 3C_{112}N_1^2N_2 + 3C_{122}N_1N_2^2 + C_{222}N_2^3, \tag{4} \]
* This idea and the method of calculation were proposed by I. R. Krichevskii.
where \(B_{11}, B_{22}, C_{111}\), and \(C_{222}\) are the second and third virial coefficients of pure water and ethylene, while \(B_{12}, C_{112}\), and \(C_{122}\) are the second and third virial coefficients accounting for pair and triple interactions. Knowing \(B_{12}, C_{112}, C_{122}\), one can calculate \(B_p\) and \(C_p\), and therefore the molar volumes of solutions of water in ethylene of any composition.
Table 1
Molar volumes (liter/mole) of solutions of water in ethylene. \(N_2\)—mole fraction of ethylene in the solution
| Temperature | \(N_2\) | \(P\), ata | \(v\) |
|---|---|---|---|
| 200° | 0.287 | 1.97 | 17.85 |
| 200° | 0.287 | 4.70 | 7.86 |
| 200° | 0.287 | 8.16 | 4.43 |
| 200° | 0.287 | 11.7 | 2.94 |
| 200° | 0.287 | 15.9 | 2.14 |
| 200° | 0.500 | 1.77 | 29.3 |
| 200° | 0.500 | 5.16 | 7.39 |
| 200° | 0.500 | 9.13 | 4.05 |
| 200° | 0.500 | 14.07 | 2.45 |
| 200° | 0.500 | 23.75 | 1.45 |
| 200° | 0.773 | 3.70 | 10.26 |
| 200° | 0.773 | 14.45 | 2.55 |
| 200° | 0.773 | 27.1 | 1.38 |
| 200° | 0.773 | 39.85 | 0.914 |
| 200° | 0.773 | 53.80 | 0.662 |
| 200° | 0.90 | 8.8 | 4.32 |
| 200° | 0.90 | 32.6 | 1.112 |
| 200° | 0.90 | 58.6 | 0.594 |
| 200° | 0.90 | 84.3 | 0.403 |
| 200° | 0.90 | 98.3 | 0.340 |
| 250° | 0.237 | 2.3 | 18.45 |
| 250° | 0.237 | 10.1 | 3.81 |
| 250° | 0.237 | 19.3 | 2.04 |
| 250° | 0.237 | 30.2 | 1.27 |
| 250° | 0.237 | 42.2 | 0.889 |
| 250° | 0.546 | 6.3 | 6.63 |
| 250° | 0.546 | 24.6 | 1.684 |
| 250° | 0.546 | 42.6 | 0.974 |
| 250° | 0.546 | 59.6 | 0.674 |
| 250° | 0.546 | 76.0 | 0.508 |
| 250° | 0.760 | 51.0 | 0.823 |
| 250° | 0.760 | 67.8 | 0.616 |
| 250° | 0.760 | 83.8 | 0.489 |
| 250° | 0.760 | 101.2 | 0.398 |
| 250° | 0.760 | 115.7 | 0.345 |
| 250° | 0.760 | 128.8 | 0.306 |
| 250° | 0.925 | 7.8 | 5.247 |
| 250° | 0.925 | 43.6 | 0.925 |
| 250° | 0.925 | 74.1 | 0.549 |
| 250° | 0.925 | 100.2 | 0.399 |
| 250° | 0.925 | 126.8 | 0.314 |
| 300° | 0.212 | 6.4 | 7.152 |
| 300° | 0.212 | 20.4 | 2.224 |
| 300° | 0.212 | 40.9 | 1.055 |
| 300° | 0.212 | 70.4 | 0.592 |
| 300° | 0.212 | 88.1 | 0.451 |
| 300° | 0.385 | 4.7 | 9.63 |
| 300° | 0.385 | 21.8 | 2.023 |
| 300° | 0.385 | 35.5 | 1.242 |
| 300° | 0.385 | 52.2 | 0.827 |
| 300° | 0.385 | 68.0 | 0.621 |
| 300° | 0.385 | 83.7 | 0.496 |
| 300° | 0.385 | 90.5 | 0.457 |
| 300° | 0.385 | 98.8 | 0.419 |
| 300° | 0.551 | 5.8 | 7.59 |
| 300° | 0.551 | 25.2 | 1.801 |
| 300° | 0.551 | 50.4 | 0.879 |
| 300° | 0.551 | 74.4 | 0.578 |
| 300° | 0.551 | 107.5 | 0.394 |
| 300° | 0.551 | 128.3 | 0.325 |
To calculate \(B_{12}\), the values of the right-hand side of equation (5) were plotted against \(N_1N_2\), and, drawing a straight line by the method of least squares, the tangent of the angle of inclination of this straight line was calculated
\[ [2B_{12}N_1N_2 = (B_p - B_{11}N_1^2 - B_{22}N_2^2). \tag{5} \]
Table 2
Values of the second (cm\(^3\)/mole) and third (cm\(^6\)/mole\(^2\)) virial coefficients of equations (3) and (4)
| Temp., °C | \(B_{11}\) | \(B_{12}\) | \(B_{22}\) | \(C_{111}\cdot 10^3\) | \(C_{112}\cdot 10^3\) | \(C_{122}\cdot 10^3\) | \(C_{222}\cdot 10^3\) |
|---|---|---|---|---|---|---|---|
| 200 | −213 | −488 | −71 | +0.50 | +263 | −43 | +60 |
| 250 | −154 | −61 | −18 | −0.18 | −123 | +72 | −18 |
| 300 | −117 | −58 | −39 | +0.82 | +24 | +2.2 | +7.4 |
Next, using equation (3), the values of \(B_p\) were again calculated. They agreed satisfactorily with those calculated from equation (2). Then, by the method of least squares, the slopes of the straight lines passing (in coordi-
in the coordinates \(\Delta - 1/v\) through the values of \(B_p\) calculated by equation (3) and the experimental values of \(\Delta\). The tangent of the angle of inclination of this straight line is equal to \(C_p\).
The obtained values of \(C_p\) were used to calculate \(C_{112}\) and \(C_{122}\). Transforming equation (4) into the equation of a straight line
\[ (C_p - C_{111}N_1^3 - C_{222}N_2^3)/N_1^2N_2 = 3C_{112} + 3C_{122}N_2/N_1, \tag{6} \]
we drew, by the method of least squares, a straight line through the points on the plot in the coordinates
\[ \frac{C_p - C_{111}N_1^3 - C_{222}N_2^3}{N_1^2N_2} \]
against \(N_2:N_1\). On the ordinate axis the straight line cuts off the value \(3C_{112}\), and the tangent of its angle of inclination is equal to \(3C_{122}\). Table 2 gives the values of all virial coefficients*, necessary for calculation by equation (1).
The cubic equation (1) was solved with respect to pressure, and, in order to check the accuracy of the calculations, we calculated not the volumes, which would have been very complicated, but the pressures from the volume values found experimentally, and compared the data obtained with the pressure values recorded in the experiment. The comparison data are given in Table 3.
Table 3
Pressures calculated by equation (1) and read from the manometer in the ethylene—water system at 300°
| \(N_2 = 0.212\) | \(N_2 = 0.212\) | \(N_2 = 0.212\) | \(N_2 = 0.385\) | \(N_2 = 0.385\) | \(N_2 = 0.385\) | \(N_2 = 0.551\) | \(N_2 = 0.551\) | \(N_2 = 0.551\) |
|---|---|---|---|---|---|---|---|---|
| \(v\), l/m | \(P\), ata exp. | \(P\), ata calc. | \(v\), l/m | \(P\), ata exp. | \(P\), ata calc. | \(v\), l/m | \(P\), ata exp. | \(P\), ata calc. |
| 2.224 | 20.4 | 20.3 | 9.63 | 4.7 | 4.8 | 7.49 | 5.8 | 6.23 |
| 1.055 | 40.9 | 41.1 | 2.023 | 21.8 | 22.41 | 1.801 | 25.2 | 25.27 |
| 0.592 | 70.4 | 69.7 | 1.242 | 35.5 | 35.75 | 0.879 | 50.4 | 50.37 |
| 0.451 | 88.1 | 89.1 | 0.827 | 52.5 | 52.39 | 0.578 | 74.4 | 75.10 |
| 0.621 | 68.0 | 68.26 | 0.394 | 107.5 | 108.7 | |||
| 0.496 | 83.7 | 83.90 | 0.325 | 128.3 | 132.1 | |||
| 0.457 | 90.5 | 90.48 | ||||||
| 0.419 | 98.8 | 98.00 |
As can be seen from Table 3, the difference between the calculated and experimental pressure values is, as a rule, small. Such good agreement shows that equation (1) describes the volumetric behavior of solutions of water in ethylene at pressures up to 150 atm and temperatures of 200—300°.
The authors express their gratitude to I. R. Krichevsky for his interest in the work and valuable advice.
State Scientific-Research and Design Institute
of the Nitrogen Industry
and Products of Organic Synthesis
Received
18 V 1960
CITED LITERATURE
- D. S. Tsiklis, E. V. Mushkina, L. I. Shenderey, Inzh.-fiz. zhurn., 1, No. 8, 3 (1958).
- D. S. Tsiklis, Technique of Physicochemical Investigations at High Pressures, 1958; see also D. White, Rev. Scient. Instrum., 29, 648 (1958).
- H. Landolt, R. Börnstein, Physikalisch-Chemische Tabellen, 1936.
- I. R. Krichevsky, Phase Equilibria in Solutions at High Pressures, 1952.
- R. York, E. White, Am. Inst. Chem. Eng. J., A 40, No. 2, 227 (1944).
- M. P. Vukalovich, I. I. Novikov, Thermodynamic Properties of Water and Water Vapor, Moscow, 1955.
* The coefficients of pure water and ethylene were calculated from data in (5, 6).