Relative molecular mass of an unknown gas in a mixture A gaseous mixture contains oxygen and another unknown gas in the molar ratio of 4:1 diffuses through a porous plug into 245 seconds, under similar conditions same volume of oxygen takes 220 seconds to diffuse. What is the molecular mass of the unknown gas?


I used the Graham's law of diffusion to find the molecular mass of mixture.
i.e.
$$\frac{r_\text{mix}}{r_{\ce{O2}}}=\frac{220}{245}=\sqrt{\frac{M_{\ce{O2}}}{M_\text{mix}}}$$
$$M_\text{mix}=39.6$$

But what's next? How do I calculate the $M_\text{gas}$?
After getting relative molecular mass ie $39.6$,

$$\mathrm{M_{net} = \frac{(n_1\times M_1 + n_2\times M_2)}{(n_1 + n_2)}} \tag{i}$$

Given that the molar ratio of gases is $4:1$, the molar ratio of oxygen is $\mathrm{4x}$ and that of the unknown gas is $\mathrm x$. Plug $\mathrm{n_1 = 4x,\ n_2 = x,\ M_1= 32,\ M_2 = M,\ M_{net} = 39.6}$ in equation (i) and get $\mathrm M$.