A gas in a vessel is under pressure of $\pu{1800kPa}$. The design temperature of the tank is $\pu{423K}$. The gas consists of (by volume) $20\ \%$ of $\ce{CH4}$ and $80\ \%$ $\ce{N2}$. Estimate the density (in $\pu{kg/m^3}$) of the gas.
I can't just use the ideal gas law to find out the density of the mixture as there are two components, right?
$$\rho=\frac{pM_\mathrm r}{RT}$$
From the ideal gas law, I can also predict that vol% equals mol%. But with this, am I supposed to find the average value of $M_\mathrm r$ and then substitute it into the equation above?