Coefficients in Gases

it is a good assumption that the mean velocity of the molecules in the positive and negative directions is equal, or 

We will be estimating the velocity of a molecule from kinetic theory, not the x-component of this velocity. Thus, from the Pythagoras theorem, the velocity of a molecule, v, is given by 

If we calculate the secondary effects from statistical mechanics, and make Ax small, equation (3.6) becomes 

We have previously developed another equation for J, as well, that we will use here  

setting the right-hand side of the right-hand side of equation (3.7) equal to the left-hand side of equation (2.2), gives 

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Diffusion is one of the most important natural processes. The varying rate of diffusion yields an excellent characteristic of individual states of aggregation. While diffusion coefficients in gases are of the order of 10-1 cm2 s-1, those in solutions are of the order of 10 5cm2 s 1 and, in solids, of 10 10 cm2 s 1. 

The experimental results for dispersion coefficients in gases show that they can be satisfactorily represented as Peclet number expressed as a function of particle Reynolds number, and that similar correlations are obtained, irrespective of the gases used. However, it might be expected that the Schmidt number would be an important variable, but it is not possible to test this hypothesis with gases as the values of Schmidt number are all approximately the same and equal to about unity. 

Table 3.4 Experimental values of diffusion coefficients in gases at 1 atm (Cussler, 1997)...

It is a trivial matter to evaluate Boltzmann equation. This gives the rotational diffusion coefficient in gases as a function of pressure and temperature. 

So far, we have treated the diffusion coefficients which appeared above as parameters which would necessarily need to be determined by experiment. As a result of 150 years of effort, the experimental measurements of these coefficients are now extensive. Their general characteristics are shown in Table I (Cussler, 1997). In general, diffusion coefficients in gases and liquids can be accurately estimated, but those in solids and polymers can not. In gases, estimates based on kinetic theory are accurate to around 8%. In liquids, estimates based on the assumption that each solute is a sphere moving in a solvent continuum are accurate to around 20%, but can be supplemented by extensive data and empiricisms (Reid et al., 1997). 

Prediction of diffusion coefficients in gases, liquids, amorphous solids and plastic materials using an uniform model... 

In general, diffusion coefficients in gases can be often be predicted accurately. Predictions of diffusion coefficients in liquids are also possible using the Stokes-Einstein equation or its empirical parallels. On the contrary in solids and polymers, models allow coefficients to be correlated but predictions are rarely possible. 

The aim of this Chapter is the development of an uniform model for predicting diffusion coefficients in gases and condensed phases, including plastic materials. The starting point is a macroscopic system of identical particles (molecules or atoms) in the critical state. At and above the critical temperature, Tc, the system has a single phase which is, by definition, a gas or supercritical fluid. The critical temperature is a measure of the intensity of interactions between the particles of the system and consequently is a function of the mass and structure of a particle. The derivation of equations for self-diffusion coefficients begins with the gaseous state at pressures p below the critical pressure pc. A reference state of a hypothetical gas will be defined, for which the unit value D = 1 m2/s is obtained at p = 1 Pa and a reference temperature, Tr. Only two specific parameters, Tc, and the critical molar volume, VL, of the mono-... 

The rate of molecule-molecule collisions given by Zj = /2 N/V)Trd u estimates the upper bound of gas phase chemical reaction rates and calculates the distance a molecule travels between collisions as well as the diffusion coefficient in gases The Boltzmann distribution... 

Magnasco, V., Battezzati, M., Rapallo, A., and Costa, C. (2006) Keesom coefficients in gases. Chem. Phys. Lett., 428, 231-235. 

Diffusion coefficients in gases are usually about 1000 times larger than diffusion coefficients in liquids. 

Diffusion coefficients in binary liquid mixtures are of the order 10 m /s. Unlike the diffusion coefficients in ideal gas mixtures, those for liquid mixtures can be strong functions of concentration. We defer illustration of this fact until Chapter 4 where we also consider models for the correlation and prediction of binary diffusion coefficients in gases and liquids. 

This section provides some rypscaJ experimental values of imerdiflusion coefficients in gases, in solutions of nonelectrolytes, electrolytes, and macromolecules, in solids, and for gases in poroas solids. Thenreiical and empirical correlations for predicting diffusivities will also be discussed Tor use in (hose cases where estimates mast be mude because exparimantal data are unavailable. A critical discussion of predicting diffusivities in a fluid phase can be found in the bode by Reid ei al,10... 

The flow perturbation gas chromatographic methods used for the measurement of diffusion coefficients in gases are the stopped-flow and the reversed-flow techniques. 

A comparison of experimental values of binary diffusion coefficients in gases with the values estimated by Eqs. (3.1.78a) and (3.1.78) indicates that both equations are suitable (Table 3.1.10), but Eq. (3.1.78b) is slightly more successful. Equation (3.1.78a) should not be used for polar molecules like ethanol or water. 

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