Orthobaric densities

To fit the orthobaric densities of caxbon monoxide by the empirical formula 

The densities qi of the liquid and Qg of the gas phase in mutual equilibrium at various temperatures measured by Mathias, Crommelin, Bijleveld, and Grigg (Proc. Acad. Sci. Amsterdam, 1932, 35, 551) are given in table 1. 

Several substances consisting of small non-polar molecules satisfy the relations in reduced form (Guggenheim, J. Chem. Ph -s. 1945, 13, 256) 

To calculate the heat of evaporation of liquid radon to estimate the density of liquid radon, its critical volume, and the Boyle temperature. 

The vapour pressure of liquid radon at temperatures extending up to the critical temperature was measured by Whjdlaw-Gray and Ramsay (J. Chem. Soc. 1909, 95, 1073). These measurements are recorded in table 1. The last entry relates to the critical temperature Tg and pressure p.  

---

Alejandre J, Tildesley D J and Chapela G A 1995 Molecular dynamics simulation of the orthobaric densities and surface tension of water J. Chem. Phys. 102 4574-83... 

The orthobaric density of incchylmtune has been reported from 0°C to the eritica] temperature.1,1111 The densities ct the other three compounds have been measured Usmii OX to 80X.1111,0144 The Lydersen technique an used to calculate the densities up to the critical point 1 When compared with I 3 experimental points, this method gave an average error ot fl.81 and a maximum error of 2 4X Figure 33-h shows the density of aqueous ethylcnediamine solutions over the 10-... 

Onsager and Fuoss viscosity equation, 125 order in liquids, 1 oriented molecules, 152, 155 0rsted s piezometer, 58 orthobaric density, 48, 327 Oseen correction for falling sphere equation, 87... 

Enthalpy of Formation Pohland (2) has studied the vaporization of SiBr from 260-426 K (0.8-755.5 mm Hg). This vapor pressure data (20 points) is corrected for vapor non-ideality by means of the equation AG /T -R In p - Bp/T. The Berthelot equation of state and critical constants T - 656 K and P 41.3 atm as suggested in the review article by Lapldus et al. (2) are used to calculate B. The recent study on orthobaric densities by Nisei son et al. ( ) reported T = 663 K. The use of this latter value does not signficantly affect the results. 

Johnson and Cubicciotti (6), in their study of the orthobaric densities of NbCl ... 

At its normal boiling point (77.15° C) the orthobaric densities of ethyl acetate are 0.828 (liquid) and 0.00323 (vapor) g. cc. . The rate of change of vapor pressure with temperature in the vicinity of the boiling point is 23.0 mm. deg.-h Calculate the heat of vaporization by (i) the Clapeyron equation, (ii) the Clapeyron-Clausius equation. 

ORTHOBARIC DENSITIES OF PHOSGENE ABOVE STANDARD PRESSURE [739]... 

We have applied the model over an extended range of external conditions from the triple point up to the critical point of water. Figure 2.24 compares the experimental " (steam tables) vapor pressures with the calculated ones. The two sets of values are practically identical. Figure 2.25 compares the corresponding values for the orthobaric densities of water. As observed, the density is well described over the full range. 

FIGURE 2.25 Orthobaric densities of water as calculated (line) by tbe cooperativity model. Symbols are experimental data. ... 

These observations are in agreement with the idea that the critical point is a single temperature and not a range of temperatures. It does appear, however, that the coexistence curve for gas and liquid has a very flat top. This is responsible for the rather large differences in critical densities which have been reported. Orthobaric densities for liquid and vapor (Table III) have been determined by Miller et al. (212) from 9° to 43°. In this work liquid sulfur hexafluoride was found to be a good solvent for nitrogen. 

An isochoric equation has been developed for computing thermodynamic functions of pure fluids. It has its origin on a given liquid-vapor coexistence boundary, and it is structured to be consistent with the known behavior of specific heats, especially about the critical point. The number of adjustable, least-squares coefficients has been minimized to avoid irregularities in the calculated P(p,T) surface by using selected, temperature-dependent functions which are qualitatively consistent with isochores and specific heats over the entire surface. Several nonlinear parameters appear in these functions. Approximately fourteen additional constants appear in auxiliary equations, namely the vapor-pressure and orthobaric-densities equations, which provide the boundary for the P(p,T) equation-of-state surface. 

Iteration for Coexisting Densities. Orthobaric densities near the critical point generally cannot be obtained accurately from isochoric PpT data by extrapolation to the vapor-pressure curve because the isochore curvatures become extremely large near the critical point. The present, nonanalytic equation of state, however, can be used to estimate these densities by a simple, iterative procedure. Assume that nonlinear parameters in the equation of state have been estimated in preliminary work. For data along a given experimental isochore (density), it is necessary merely to find the coexistence temperature, Ta(p), by trial (iteration) for a best, least-squares fit of these data. 

Cook, D. The Vapour Pressure and Orthobaric Density of Nitrous Oxide, ... 

Values of AHu, in g-cal/g-mole, were derived from orthobaric densities and the vapor pressure equations via the Clapeyron equation P ]. An approximate representation of the temperature dependence from the triple point to 32.7°K has recently been evaluated by least-squares ... 

Several techniques have been used to determine the orthobaric densities of the liquid and gas. The simplest method is that proposed by van Eck and recently used by the Reporter. A series of heavy-walled tubes are partially filled with varying but known amounts of the substance under investigation. Each is heated slowly in turn until the meniscus disappears out of either the top or bottom of the tube, i.e. the vapour phase completely condenses or the liquid gas completely evaporates. The temperature at which the tube becomes completely filled with vapour or liquid is noted. The volume of each tube is then found by weighing it in water and then cutting the tube open, emptying it and weighing the pieces in water. This method enables the densities of liquid and vapour to be calculated over a series of temperatures. This method is simple but time-consuming, and requires considerable experimental care. 

Adamson AW (1990) Physical chemistry of surfaces, 5th ed. Wiley, New York, p 101 ff Alejandro 1, Tddesley DJ, Chapela GA (1995) Molecular dynamics simulation of the orthobaric densities and surface tension of water. J Chem Phys 102 4574—4583 Allen HC, Gregson DE, Richmond DL (1999) Molecular structure and adsorption of dimethyl sulfoxide at the surface of aqueous solutions. J Phys Chem B 103 660-666 Aveyard R, Saleem SM (1976) Interfacial tensions at alkane-aqueous electrolyte interfaces. J Chem Soc, Faraday Trans 1(72) 1609-1617... 

Figure 7 Orthobaric densities for small alkenes. The filled circles are simulation results from present work, the filled triangles are from Spyriouni et al. (ref. 12), open symbols are experimental results (ref. 17), and the lines show an Ising fit to the simulation points. The error bars near the critical point are less than three times the size of the symbols. Error bars at lower temperatures are less than twice the size of the symbols...

The curves for Pr < 1 terminate at a curve representing orthobaric densities. The latter curve can itself be predicted using the Principle of Corresponding States equations for this purpose have been proposed by Guggenheim. ... 

Finally we want to note that using the orthobaric densities from PVT data and the D values from eq. (3.6),we find that the following relationship holds for thermodynamic states along the coexistence curve... 

Measured on the phase equilibrium line were the saturated vapor pressure p, orthobaric density of the liquid p, heat capacity of the saturated liquid C, and speed of sound in vapor w J.f in a wide interval of temperatures heat of vaporization 7 measured only at NBP (Table 29). The temperature dependence of saturated vapor pressure of Freon-22 was thoroughly investigated in the interval T from 203 K to the critical point (369.30 K) [3.17, 3.55, 3.56, 3.66]. The measurement results in [3.17, 3.66] were presented according to IPTS-48 and in [3.56] according to IPTS-68. It is important to note that in these works, function Ps(T) was investigated with highly pure samples. 

Table 42 shows that the saturation vapor pressure and orthobaric density of vapor and liquid have been measured repeatedly. We adopted experimental data of MEI [4.3] as reference values of p. These data were obtained statistically for a high-purity substance and with an error estimated by the authors at 0.1-0.2%. The results of comparison with the data of other researchers are shown in Fig. 34. 

The function < (p), which is the mean value of in a two-phase system of overall density p, and of orthobaric densities p and p, is a linear interpolation in p between and and so from (S.80)... 

We see that (7.14) is formally the same equation for the orthobaric densities as was obtained for the penetrable-sphere model in the mean-field approximation, namely (5.91), and is the analogue of (5.31) for the lattice-gas. Like (5.91), it has the solution... 

---