Effect of Pressure on Density

This is the average value of a between 0 and 80°C. Table D.l shows that at 20°C, a = 0.00112/°C, which is in reasonable but far from perfect agreement with the above result.  

When data are available in the form of Eq. D.6 they probably lead to better estimates of the effect of temperature change on density than does Eq. D.2. 

FIGURE D.3 Density-pressure plot for ethanol [1], low-pressure comer. 

Example D.4 Estimate the value of (jSiooo atm//3i atm)25 c for ethanol from the results in the previous example. 

From these examples and an examination of the tables and figures we can see the following  

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No real substances have constant density the density of every substance increases as the pressure increases. However, for most liquids at temperatures far below their critical temperatures, the effect of pressure on density is very small. For example, raising the pressure of water at 100 F from 1 to 1000 Ibf/ in causes the density to increase by 0.3 percent. In most engineering calculations, we can neglect such small changes in density. Then we take p outside the integral sign in Eq. 2.8 and find that the pressure is... 

There have been two approaches to modeling the effect of pressure on the viscosity of mixtures. Either the effect of pressure is implicitly included in the model (for example, as in the case of Cao et al. or in the TRAPP method, in which the effect of pressure on density directly affects the viscosity), or viscosities are first calculated at low pressure (from saturation to a few atmospheres) and then corrected... 

Ferry [l,p. 291] describes several equations that have been proposed to describe the combined effects of temperature and pressure like the WLF equation, these equations arise from assumptions regarding the dependence of free volume on pressure and temperature. The vertical shift factor b-j. can be easily generalized to account for the effect of pressure on density as shown by Eq. 4.78, but this effect is usually negligible. 

We see that, for a given pressure and temperature, the greater the molar mass of the gas, the greater its density. Equation 10 also shows that, at constant temperature, the density of a gas increases with pressure. When a gas is compressed, its density increases because the same number of molecules are confined in a smaller volume. Similarly, heating a gas that is free to expand at constant pressure increases the volume occupied by the gas and therefore reduces its density. The effect of temperature on density is the principle behind hot-air balloons the hot air inside the envelope of the balloon has a lower density than that of the surrounding cool air. Equation 10 is also the basis for using density measurements to determine the molar mass of a gas or vapor. 

A systematic study of the effect of pressure and density on the regiochemical course of the Diels-Alder reactions of methyl acrylate and 2-substituted 1,3-butadienes carried out in SC-CO2 was recently reported [87]. The reactions were compared with those carried out in a conventional medium such as toluene. Some results are illustrated in Table 6.15. 

Figure 6.5 Effect of pressure on the power density at hydrodynamic instability. (From Mathisen, 1967. Copyright 1967 by Office for Official Publications of the European Community, Luxembourg. Reprinted with permission.)... 

Marchaterre, J. F., 1956, The Effect of Pressure on Boiling Density in Multiple Rectangular Channels, USAEC Rep. ANL-5522, Argonne National Lab., Argonne, IL. (5)... 

Figure 25. The effect of pressure on radial density distribution in a riser.

The effect of pressure on chemical equilibria and rates of reactions can be described by the well-known equations resulting from the pressure dependence of the Gibbs enthalpy of reaction and activation, respectively, shown in Scheme 1. The volume of reaction (AV) corresponds to the difference between the partial molar volumes of reactants and products. Within the scope of transition state theory the volume of activation can be, accordingly, considered to be a measure of the partial molar volume of the transition state (TS) with respect to the partial molar volumes of the reactants. Volumes of reaction can be determined in three ways (a) from the pressure dependence of the equilibrium constant (from the plot of In K vs p) (b) from the measurement of partial molar volumes of all reactants and products derived from the densities, d, of the solution of each individual component measured at various concentrations, c, and extrapolation of the apparent molar volume 4>... 

Since the density of Pt decreases by only 0.009 g cm- from 0 to 1200 bars, the effect of pressure on the density of Pt can be neglected if weights below 1 g are used. Both f and V were found to be functions of pressure (36). Calibrations of the float at a given pressure indicate that the precision of the system is 10 ppm while the accuracies are about 20 ppm (116). We have used this system to measure the relative densities of D2O (117), seawater 0.16,118), and some major sea salts (36, 119). 

The effect of pressure on the ground-state electronic and structural properties of atoms and molecules have been widely studied through quantum confinement models [53,69,70] whereby an atom (molecule) is enclosed within, e.g., a spherical cage of radius R with infinitely hard walls. In this class of models, the ground-state energy evolution as a function of confinement radius renders the pressure exerted by the electronic density on the wall as —dEldV. For atoms confined within hard walls, as in this case, pressure may also be obtained through the Virial theorem [69] ... 

In the case of matter under high pressure, although its description corresponds more closely to the condensed phase, an atomistic view based on the orbital implementation of the KT renders useful information on the effects of pressure on stopping. We have shown here that this theory together with the TFDW density-functional method adapted to atomic confinement models allows for the estimate of pressure effects on stopping, as well as for stopping due to free-atoms. 

Table 3.5 Effect of Pressure on the In Situ Density of Seawater Having a Salinity of 35%o and Temperature of 0°C. ...

The paper of Gordon describes a model for diffusion-controlled reaction based on the "hole concept in liquids of Jost (Ref 1, p 459). in which the activation energy for diffusion is equated simply to pV. The marked effect of density, therefore, results from the strong dependence of pressure on density (p varying about as the density cubed) and the appearance of this factor in an exponential term. On this basis, Gordon derived an approximate expression for dependence of detonation velocity D on explosive density pQ. This equation is given on pp 833 and 836 of Gordon s paper. From this expression the critical diameter dc for composite explosives is related to an exponential function of density by ... 

Investigation at the Chemical Physics Institute of the Academy of Sciences has shown for large chge diameters of condensed expls, pressures of the order of 3.1C)5kg/cm2 arise in the detonation wave) 223 [Calcn of pressure from Van der Vaals equation of state p=RT/(v-b)] 224 (Assumption of Landau Stanyukovich that in the explosion products of Landau 8t Stanyukovich for a density in excess of 1 g/cm2 the main part of pressure is of elastic origin and depends only on the density of expln products, but not on the temp) 217 (Effect of pressure on thermal dissociation is discussed. In the case of condensed expls the pressure indirectly affects the molecular separation and alters the rate of chemical reaction. Experiments of Yu.N. Riabinin have shown that the reaction rate was diminished at a high pressure, up to 5.10 kg/cm2)... 

The effect of pressure on the measured bimolecular rate constant of the Diels-Alder reaction between maleic anhydride and isoprene was investigated in supercritical CO2 and subcritical propane. The reaction was carried out at 35°C in CO2 and 80°C in propane. The rate constants in supercritical CO2 agreed closely with the thermodynamic pressure effect predictions over the entire pressure range. The rate constants in the subcritical propane solvent significantly diverged from the thermodynamic pressure effect predictions and were found to deviate from this linear density dependence at the lower pressures studied. The results show solvent-solute and cosolvent-solute interaction (Reaves and Roberts, 1999). 

The density of cyclohexane has been measured from its melting point to the critical point.1 13Figure 40 12 presents the data of Reamer and Sage on the effect of pressure on the density or cyclohexane.1 Data on the other three compounds arc available up to the boiling... 

Figure 44-7 shows the effect of pressure on. the density of steam in metric units from 0°C to lOQtTC.3 392 Figure 44-8 is in metric units, and Figure 44-5 is in English units. 

At more "liquid-like" densities, the solvatochromic shifts in supercritical fluids approach those observed in the corresponding liquids. Figures 1 and 2 depict the pressure dependence of the wavelength of the absorption maximum of 2-nitroanisole in supercritical CO2, N2O, CC1F3 (Freon-13), and NH3. These measurements reflect the effect of pressure (fluid density) on the cybotatic region of these solvents. It is clear that the fluid density affects the cybotatic region, as evidenced by the shift in the absorption maximum with pressure and it is also evident that the magnitude of the shift is fluid dependent. 

Because of their rigid cell walls, large hydrostatic pressures can exist in plant cells, whereas hydrostatic pressures in animal cells generally are relatively small. Hydrostatic pressures are involved in plant support and also are important for the movement of water and solutes in the xylem and in the phloem. The effect of pressure on the chemical potential of water is expressed by the term VWP (see Eq. 2.4), where Vw is the partial molal volume of water and P is the hydrostatic pressure in the aqueous solution in excess of the ambient atmospheric pressure. The density of water is about 1000 kg m-3 (1 g cm-3) therefore, when 1 mol or 18.0 x 10-3 kg of water is added to water, the volume increases by 18.0 x 10-6 m3. Using the definition ofV,., as a partial derivative (see Eq. 2.6), we need to add only an infinitesimally small amount of water (dnw) and then observe the infinitesimal change in volume of the system (dV). We thus find that Vw for pure water is 18.0 x 10-6 m3 mol-1 (18.0 cm3 mol-1). Although Vw can be influenced by the solutes present, it is generally close to 18.0 x 10-6 m3 mol-1 for a dilute solution, a value that we will use for calculations in this book. 

The volume changes on mixing non-aqueous liquids, the densities of mixed liquids, of solutions of non-polar solutes in non-polar solvents, and the changes of total volume on the solution of solid salts in water, noticed at an early period and much investigated, can only be mentioned here some aspects of these will be dealt with later. Hyde found the densities of solutions of jp-nitrotoluene in carbon disulphide smaller than the density of either component, but the anomaly disappears if the p-nitrotoluene is supposed to be in the liquid state. Biron found that the volume change on mixing two liquids was Av=kx( —x where x , (1— ) are the mol fractions, and he investigated the effect of pressure on the value of Av. The apparent specific volume of alcohol in aqueous mixtures was determined by Brown, lo... 

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