[gramentz]

I've looked at other posts about mole fractions but haven't found one like this question. Here's the problem:

A gas mixture has an average molecular weight of 134.62 g/mol. It is composed of two gases with MW's of 450.34 and 38.27 g/mol respectively. What is the mole fraction of the first gas?

My attempt:

450.34 / 134.62 = moles of gas A (3.342 mol)
38.27 / 134. 62 = moles of gas B (0.2842 mol)

moles of gas A/ moles of gases A+B
3.342 / 3.6262= .9216 of gas A

I've got to be missing a step. I am getting thrown off by the average molecular weight for some reason.

[ARGOS++]

Dear gramentz;

Yes! – you are missing something.

Use 1.00 mol of the gas with the average Molecular Weight (MW) and analyse it.
That results in two equations with two unknown:
Here the first equation:   x mol   +   y mol   =  1.00 mol.

Are you able to spend the second equation in x and y and with the MW’s given?

Good Luck!

[gramentz]

AHA, now it makes sense.


x + y = 1
450.34 x + 38.27 y = 134.62

x= -y + 1
450.34 (-y +1) + 38.27 y = 134.62
-450.34 y + 450.34 + 38.27 y = 134.62
-412.07 y+ 450.34 = 134.62
-412.07 y = -315.72
y = .76618
1- y = x
x = .2338

[ARGOS++]

Dear gramentz;

Congratulation!  -  Exact!

Good Luck!
                    ARGOS⁺⁺

[gramentz]

Thanks a lot, I appreciate it 

[ARGOS++]

Dear gramentz;

You 're welcome!   ─   Soon again.

Good Luck!
                    ARGOS⁺⁺

[pbesra]

Mi=Molecular weight of i component.
Mavg=Average Molecular weight of system.
Yi=mole fraction of i component.

then,
Mavg=Σ(Yi*Mi)   ;i= (1 to n )
and ΣYi=1 ; i= (1 to n)