Question

Estimate the value of the gas-phase diffusion coefficient for the following pairs using the Hirshfelder equation: a. Sulfur dioxide and nitrogen (N2) at 298 K and 1.5 x 105 Pa b. Hydrogen (H2) and air at 325 K and 2.0 x 105 Pa

Answer 1

a.
`D_(A-B)=0.0838(cm^2)/(s)`

b.
`D_(A-B) =0.460(cm^2)/(s)`

Step-by-step explanation:

Hello!

In this case, since the Hirschfelder's equation is:

`D_(A-B)=0.0018583\sqrt{T^3((1)/(M_A) +(1)/(M_B) )}(1)/(p\sigma ^2_(A-B)\Omega _(D,A-B))`

Whereas M is the molar mass and sigma is related to the size of the molecule and omega the collision integral depending on the dimensionless temperature and are parameters related to the Chapman-Enskog theory and the Lenard-Jones parameters which have been tabulated for sulfur dioxide, nitrogen, hydrogen and air. Thus, we proceed as follows:

a. In this case, we have that sigma for sulfur dioxide is 4.026 and that of nitrogen is 3.667, and the parameter e/K is 363 K and 99.8 K respectively.

It means that the pairs are:

`\sigma _(A-B)=(1)/(2) (4.026+3.667)=3.8465`

`e_(A-B)/K=√(363*99.8)=190.33`

For which:

`\Omega _(D,A-B)=1.180`

Based on Bird's E2 table.

Now, by plugging in the data, we obtain the following diffusion coefficient:

`D_(A-B)=0.0018583\sqrt{(298K)^3((1)/(64) +(1)/(28) )}(1)/(1.48atm*3.8465^2*1.180)=0.0838(cm^2)/(s)`

b. In this case, we have that sigma for hydrogen is 2.915 and that of air is 3.617, and the parameter e/K is 30.8 K and 97.0 K respectively.

It means that the pairs are:

`\sigma _(A-B)=(1)/(2) (2.915+3.617)=3.266`

`e_(A-B)/K=√(30.8*97.0)=54.66`

For which:

`\Omega _(D,A-B) =0.8202`

Based on Bird's E2 table.

Now, by plugging in the data, we obtain the following diffusion coefficient:

`D_(A-B)=0.0018583\sqrt{(325K)^3((1)/(2.02) +(1)/(28.96) )}(1)/(1.97atm*3.266^2*0.8202)=0.460(cm^2)/(s)`

Best regards!