00:01
So we can start this question by writing the ideal gas law, pv equals n -r -t, and also using the fact that n is equal to the mass of something divided by its molecular weight, m -w.
00:15
Then we can rearrange this equation so that it's pv equals mass times r -t over molecular weight.
00:28
And then we can solve for molecular weight such that it equals mass times r t over molecular or over pv and we know that mass over volume is equal to density so we can rewrite this as r t d for density over p for pressure and so we have all of these values.
01:03
Our r values 0 .082 -057 -liter atmospheres per mole kelvin times our temperature, which is 298 kelvin, times our density, which is 0 .670 grams per liter.
01:28
And then divide all of that by the pressure, 0 .993 -4 atmospheres.
01:38
And that gives us a molecular weight of 16 .49 grams per mole.
01:49
And so now that we have this molecular weight, we can find the mole fraction of helium and argon.
01:59
And so to do this, we use the equation for mole fractions.
02:03
So the mole fraction of helium times the molar mass of helium plus the mole fraction of argon times the molar mass of argon equals the molecular weight or 16 .49 grams per mole as we just found it to be.
02:25
So now we can do a little bit of algebra in order to find just the mole fraction.
02:31
Of helium.
02:35
And so again, we have mole fraction of helium times the molar mass of helium.
02:42
However, since we only have two gases, we know that the mole fraction of argon is equal to one minus the mole fraction of helium...