Question

1. There are several models derived from first principles to describe gas diffusion under ideal conditions and all of them utilize very specific assumptions
2. 1. How do the values from both models calculated in part a, compare to the general gas-gas diffusion value of a generic gas molecule diffusing in a gas (the one value given in class)?
   2. How do the values from both models calculated in part a, compare to the Einstein-Boltzman general equation for diffusivity of an ideal gas molecule?

Answer 1

Diffusion coefficients of binary mixtures of dilute gases are comprehensively compiled, critically evaluated, and correlated by new semi‐empirical expressions. There are seventy‐four systems for which the data are sufficiently extensive, consistent and accurate to allow diffusion coefficients to be recommended with confidence. Deviation plots are given for most of these systems. Almost every gaseous diffusion coefficient which was experimentally determined and reported prior to 1970 can be obtained from the annotated bibliography and table of gas pairs.A detailed analysis of experimental methods is given, and intercomparison of their results helps establish reliability limits for the data, which depend strongly on temperature. Direct measurements are supplemented by calculations based on knowledge of intermolecular forces derived from independent sources—molecular beam scattering for high temperatures, and London dispersion constants for low temperatures. In addition, diffusion coefficients for several mixtures are obtained from experimental data on mixture viscosities and thermal diffusion factors. Combination of all these results gives diffusion coefficients over a very extensive temperature range, from very low temperatures to 10 000 K.All data are corrected for composition dependence and for quantum effects. New semi‐empirical equations are derived for making such corrections easily.

A diffusion is a process in physics. Some particles are dissolved in a glass of water. At first, the particles are all near one top corner of the glass. If the particles randomly move around ("diffuse") in the water, they eventually become distributed randomly and uniformly from an area of high concentration to an area of low concentration, and organized (diffusion continues, but with no net flux).

Diffusion from a microscopic and macroscopic point of view. Initially, there are solute molecules on the left side of a barrier (purple line) and none on the right. The barrier is removed, and the solute diffuses to fill the whole container. Top: A single molecule moves around randomly. Middle:With more molecules, there is a statistical trend that the solute fills the container more and more uniformly. Bottom: With an enormous number of solute molecules, all randomness is gone: The solute appears to move smoothly and deterministically from high-concentration areas to low-concentration areas. There is no microscopic force pushing molecules rightward, but there appears to be one in the bottom panel. This apparent force is called an entropic force.

Diffusion coefficient is the proportionality factor D in Fick's law(see Diffusion) by which the mass of a substance dM diffusing in time dt through the surface dF normal to the diffusion direction is proportional to the concentration gradient grad c of this substance: dM = −D grad c dF dt. Hence, physically, the diffusion coefficient implies that the mass of the substance diffuses through a unit surface in a unit time at a concentration gradient of unity. The dimension of D in the SI system is a square meter per second.

The diffusion coefficient is a physical constant dependent on molecule size and other properties of the diffusing substance as well as on temperature and pressure.

Diffusion coefficients of one substance into the other are commonly determined experimentally and presented in reference tables. Here, examples of self-diffusion and interdiffusion (binary diffusion) coefficients in a gaseous and liquid media are given in Tables 1, 2, and 3.

Table 1. Self-diffusion coefficient D_A of some gases at T = 273 K and p = 0.1 MPa

Table 2. Interdiffusion coefficient D_AB

Table 3. Diffusion coefficient of gases in liquids