Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

Density prediction using equations

For a series of reactions where the molecular weight of the branches (Mb) and the number of grafting sites per backbone chain (grafting site density,/) remain constant for each generation, the molecular weight of a generation G polymer can be predicted using equation (3). [Pg.216]

Because of the problem associated with Teller s theorem, discussed in Section 11, let us again examine the predictions of the central field model of molecules of Sections 9 and 10. From this model stemmed the energy relations (96)—(98). Equation (81) is again the complete expression for the sum of the eigenvalues in this simplest density description. Using equation (93), with the chemical potential equal to zero, as was demonstrated to be so for neutral molecules in the central field model, one can eliminate Fen + 2Fee by subtracting equations (81) and (93), to obtain... [Pg.123]

Where i0 is the exchange current density (Am 2), a is the transfer coefficient and r) is the overpotential (V) (0o-Eo) predicted using equation 5. [Pg.101]

The Hirshfeld functions give an excellent fit to the density, as illustrated for tetrafluoroterephthalonitrile in chapter 5 (see Fig. 5.12). But, because they are less localized than the spherical harmonic functions, net atomic charges are less well defined. A comparison of the two formalisms has been made in the refinement of pyridinium dicyanomethylide (Baert et al. 1982). While both models fit the data equally well, the Hirshfeld model leads to a much larger value of the molecular dipole moment obtained by summation over the atomic functions using the equations described in chapter 7. The multipole results appear in better agreement with other experimental and theoretical values, which suggests that the latter are preferable when electrostatic properties are to be evaluated directly from the least-squares results. When the evaluation is based on the density predicted by the model, both formalisms should perform well. [Pg.71]

The temperature independence of the CH frequency shifts is also reflected in the nearly constant attractive force parameters (see Table I). In fact, the frequency shifts predicted using the average attractive force parameter, Ca = 0.973, reproduce the experimental results to within 3% throughout the experimental density and temperature range. It thus appears that the attractive force parameter may reasonably be treated as a temperature and density independent constant. This behavior is reminiscent of that found for attractive force parameters derived from high pressure liquid equation of state studies using a perturbed hard sphere fluid model (37). [Pg.30]

Most fluidisation processes are operated at high temperatures and pressures. It is important, therefore, to be able to predict changes in fluidisation with the operating conditions. Using Equations (35) and (36), the effect of temperature and pressure can be determined. With increasing temperature, gas viscosity increases while gas density decreases. For small particles, the fluid-particle interaction is dominated by the viscous effects. Equation (35) shows that varies with 1 jp, and wmf should therefore decrease with temperature. For large particles, the inertial effects dominate Equation (36) predicts that wn,r will vary with (1 /p/)0 5, should therefore increase with temperature. [Pg.220]

However, the methods for calculating the density of a supercritical fluid are rather conventional. An equation of state or a corresponding state method can be used. They must be used with caution because the critical region is notorious as a region where the accuracy of density predictions is poor. [Pg.221]

The modified Rackett equation, density = was used. See Spencer, C. R, and R. P. Danner, Improved Equation for Prediction of Saturated Liquid Density, /. Chem. Eng. Data 17, 236... [Pg.139]

These approximations can then be used in the osmotic equation of state to obtain the compressibility factor. Monte Carlo simulations using the above-discussed Monte Carlo techniques have been performed to assess the approximations inherent in the generalized Flory theory of hard-core chain systems. This theory does quite well in predicting the equations of state of hard-core chains at fluid densities. The question then arises, why does it do so well since the theory typically only incorporates information from a dimer fluid as a reference state ... [Pg.180]

Therefore. Equation (112) can be used to predict the true density of binary mixtures. After calculating predicted true densities (Equation (112)] and substituting Equations (110) and (111) into Equations (108) and (109). we can obtain dm and for the binary mixture based upon the corresponding values of n, d. and k of the constituent powders and the true densities. Upon obtaining the values of dm and Am itie tensile strength of binary tablets (aim) can be derived for a given relative density of the mixture (Om) using Equation (106), i.e.. [Pg.523]

Consider the flow of a single-phase SCF mixture, which can be observed above the mixture critical pressure P, as seen in Figure 2. Because processes of particle formation using SCFs are usually carried out in turbulent flow systems, we consider turbulent flows. In this section we assume isothermic conditions to distinguish the pure effects of fluid flow. Under typical supercritical conditions, the SCF mixture is a dense fluid, and the local fluid density is strongly dependent on local pressure and composition. To predict the effects of pressure on fluid density, the Peng-Robinson equation of state (EOS) (21) is often used (16,17,22) because of its accurate density predictions at high pressure and its relatively simple form... [Pg.103]

The values of the properties which will be fitted by using equations 2.9 and 2.10 will be selected from available and apparently reliable experimental data whenever there are sufficient amounts of such data. Some important properties of polymers, such as the van der Waals volume (Chapter 3) and the cohesive energy (Chapter 5), are not directly observable. They are inferred indirectly, and often with poor accuracy, from directly observable properties such as molar volume (or equivalently density) and solubility behavior. When experimental data are unavailable or unreliable, the values of the properties to be fitted will be estimated by using group contributions. The predictive power of such correlations developed as direct extensions and generalizations of group contribution techniques will then be demonstrated by using them... [Pg.86]

The two approaches presented in this section need not be mutually exclusive one can use a correlation for some properties and an equation of state for others. Because of the poor liquid density predictions of many cubic equations of state, it is common to use semiempirical correlations for liquid density (such as the Rackett equation [15]) while using an EOS for vapor-liquid equilibria. [Pg.7]


See other pages where Density prediction using equations is mentioned: [Pg.199]    [Pg.100]    [Pg.346]    [Pg.272]    [Pg.67]    [Pg.220]    [Pg.251]    [Pg.259]    [Pg.403]    [Pg.340]    [Pg.50]    [Pg.150]    [Pg.123]    [Pg.284]    [Pg.284]    [Pg.430]    [Pg.672]    [Pg.138]    [Pg.2839]    [Pg.482]    [Pg.483]    [Pg.2749]    [Pg.23]    [Pg.38]    [Pg.14]    [Pg.125]    [Pg.301]    [Pg.666]    [Pg.355]    [Pg.446]    [Pg.83]    [Pg.95]    [Pg.434]    [Pg.2838]    [Pg.166]   


SEARCH



Density equations

Density prediction

Useful Equations

© 2024 chempedia.info