Often, we have a multi-component mixture of gases and do not want to deal with the diffusion coefficients for every pair of gases. We would like to define a pseudo-binary diffusion coefficient for...

Often, we have a multi-component mixture of gases and do not want to deal with the diffusion coefficients for every pair of gases. We would like to define a pseudo-binary diffusion coefficient for each species relative to the mixture.

a. Show how using Fick’s Law in the form:

and the Stefan-Maxwell relations, equation (2.74), we can define such a coefficient based on individual binary diffusion coefficients for each pair of gases. Dim is the pseudo-binary diffusion coefficient.

b. Show in the limit where x x 1 2 ≈ ≈ 0 that:

c. Use your result to calculate the pseudo-binary diffusion coefficient for each species in the system H2O, He, N2.

d. Can your results be extended to higher order mixtures?