Mass Diffusivity (Dab) for binary gas mixtures at low pressure is a function of pressure and temperature, and nearly independent of composition for any gas-pair system. The equation 16.3-1 of Bird, Stewart, and Lightfoot is used to estimate mass diffusivity for gas-pairs at low pressures.

The following picture shows a binary system of gas A and gas B, where both gases are diffusing into each other:

Now, let's work through two examples that will deal with binary gas systems such as the one shown in the picture.

Example 1

This is the example 16.3-1 given in BS&L.

Estimate the mass diffusivity for the gas-pair system argon-oxygen at 293.2K and 1atm total pressure.

> restart;

Equation 16.3-1, the equation used for estimation:

> eq1:= p*Dab/(Pca*Pcb)^(1/3)/(Tca*Tcb)^(5/12)/(1/Ma + 1/Mb)^(1/2) = a*(T/sqrt(Tca*Tcb))^b;

For this system, we know the following, where gas A is argon and gas B is oxygen:

> p:= 1;T:= 293.2; Pca:= 49.0; Pcb:= 49.7; Tca:=151.2;Tcb:=154.4; Ma:=39.94; Mb:= 32;

Since this is a system of nonpolar gas-pairs, the constants a and b used in the equation are:

> a:=2.745e-4; b:=1.823;

Therefore, equation 16.3-1 from above can be solved for Dab to find the numerical answer for mass diffusivity:

> solve(eq1,Dab);

From this, we find that the mass diffusivity is 0.1899803852 cm^2/sec.

Example 2

Estimate the mass diffusivity for the system helium-chlorine at 300K and 1 atm total pressure.

> restart;

Using equation 16.3-1 from BS&L:

> eq1:= p*Dab/(Pca*Pcb)^(1/3)/(Tca*Tcb)^(5/12)/(1/Ma + 1/Mb)^(1/2) = a*(T/sqrt(Tca*Tcb))^b;

For this system, we know the following information, where gas A is helium and gas B is chlorine:

> p:=1;T:=300;Pca:=2.26;Pcb:=76.1;Tca:=5.26;Tcb:=417;Ma:=4.003;Mb:=70.91;

Since this is a system of nonpolar gas-pairs, the constants a and b used in the equation are:

> a:=2.745e-4; b:=1.823;

Here we solve equation 16.3-1 to find Dab:

> solve(eq1,Dab);

From this, we find the estimation of mass diffusivity is 0.5713896655 cm^2/sec for the specified system.