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gfd43tg

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## Homework Statement

A gas mixture contains 50% He and 50% O2 by volume at 500 K and 1 bar. The absolute

mass fluxes of each species along the transportation direction z are ##\hat J_{He} = -0.8 \frac {kg}{m^{2} s}## and ##\hat J_{O_{2}} = 0.8 \frac {kg}{m^{2} s}##. Determine the mass and molar average velocities. Also determine the mass and molar diffusion fluxes.

## Homework Equations

## The Attempt at a Solution

Hello, I am having considerable trouble solving this problem. The main reason I believe is because of all these definitions of terms and sorting them out. I will explain my thoughts. Firstly, I would like to mention that I will use the carat ''^" to denote mass quantities and ''~" for molar quantities.

So to begin, I figure I will calculate the mass concentration of oxygen, using the ideal gas law modified with the molar mass included,

## P_{O_{2}} V_{O_{2}}M_{O_{2}} = N_{O_{2}} M_{O_{2}}RT##

[tex] \hat C_{O_{2}} = \frac {P_{O_{2}}M_{O_{2}}}{RT} [/tex]

where ##P_{O_{2}} = y_{O_{2}}P = 0.5P##

So now I have the mass concentration of oxygen, and I divide the total mass flux given in the problem by the mass concentration to get the so called "average mass velocity".

[tex] \bar V_{O_{2}}^{mass} = \frac {\hat J_{O_{2}}}{\hat C_{O_{2}}} [/tex]

I calculate 2.08 meters/sec

Now, if I do the ''molar average velocity"

[tex] \tilde J_{O_{2}} = \frac { \hat J_{O_{2}}}{M_{O_{2}}}[/tex]

[tex] \tilde C_{O_{2}} = \frac {P_{O_{2}}}{RT}[/tex]

[tex] \bar V_{O_{2}}^{molar} = \frac {\tilde J_{O_{2}}}{\tilde C_{O_{2}}} [/tex]

Once again, I end up with 2.08 meters/sec.

So I do not know how to differentiate "average mass velocity'' from "average molar velocity". I thought velocity is velocity is velocity, period. I reckon this might have something to do with my partial pressure, one should be based on molar fraction, and the other on mass fraction, since I am using volume fraction right now. How can I go from a volume fraction to a mass fraction?

EDIT: I now know how to convert, I just use the ratio of the densities. I find that the mass fraction, ##\hat y_{O_{2}} = 0.889##. Now, I go back to my ideal gas law,

##P_{O_{2}}V_{O_{2}}M_{O_{2}} = N_{O_{2}}M_{O_{2}}RT##

But I am unsure of where I should make the substitution in with the mass fraction. I guess it would be ##P_{O_{2}} = \hat y_{O_{2}}P##?? If so, I find

$$ \hat C_{O_{2}} = \frac {\hat y_{O_{2}}PM_{O_{2}}}{RT} $$

and I calculate the mass concentration to be 0.684 kg/m^3

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