Finding percentage of the gas in a binary gaseous mixture of the given density At STP, the density of a gas in a vessel is $0.9002$. If the gas is a mixture of argon and helium, what percentage of the gas is argon?


I am stuck on this. From what I can gather, the only influencing characters would be moles and grams. This idea is based of off of STP and given constants. 

I have a couple equations written down but I can’t seem to the flow going.

R, T, P are all known along with acccording densities. I also want to say $22.4$ is also a known at $V_\mathrm{tot}$ and therefore $n_\mathrm{tot} = 1$.

$$n(\ce{Ar}) + n(\ce{He}) = 1$$

$$\frac{n(\ce{Ar})}{n(\ce{Ar}) + n(\ce{He})}d(\ce{Ar}) + \frac{n(\ce{He})}{n(\ce{Ar}) + n(\ce{He})}d(\ce{He}) = d_\mathrm{tot}$$

$$d = PM/RT$$
Well, I can see all the relations you require knowledge of in the question itself!

Calculate the effective molecular mass from 

$$M = \frac{dRT}{P}$$ 

$R$ is known, $d$ given. $P$ and $T$ are available from the fact that it is at STP.

$M$ comes out to be ${20.176 u}$.

Effective molar mass is easily calculated below:

$$M_\mathrm{eq} = M_1x_1 + M_2x_2$$

where $x_i$ is the mole fraction of each gas. You can replace $x_2$ by $1-x_1$.

Plugging in the values and solving for $x_1$, argon mole fraction comes out to be $0.4493$.

I believe you can now calculate the demanded percentage, be it by mass or by moles.