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

Answer:

a. $D_{A-B}=0.0838\frac{cm^2}{s}$

b. $D_{A-B} =0.460\frac{cm^2}{s}$

Explanation:

Hello!

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

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

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:

$\sigma _{A-B}=\frac{1}{2} (4.026+3.667)=3.8465$

$e_{A-B}/K=\sqrt{363*99.8}=190.33$

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:

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

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:

$\sigma _{A-B}=\frac{1}{2} (2.915+3.617)=3.266$

$e_{A-B}/K=\sqrt{30.8*97.0}=54.66$

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:

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

Best regards!