Using Dumas method, the following data on dimethyl ether at $25C$ were measured.

$\backslash$table$[[\frac{P}{T}$orr,$91\mathrm{.}74,188\mathrm{.}98,452\mathrm{.}8,639\mathrm{.}3,760\mathrm{.}0],[\frac{d}{g}{L}^{-1},0\mathrm{.}225,0\mathrm{.}456,1\mathrm{.}062,1\mathrm{.}468,1\mathrm{.}734]]$

$($a$)$ Deduce the relation between the pressure $(P)$ and density $($d$)$ of a perfect gas of molar mass M$.$

$($b$)$ Using the data of dimethyl ether, confirm that perfect behaviour is reached at low pressures and find the molar mass.

$($c$)$ Interpret the graph in terms of "ideal or real gas" behaviour.

$P=(\frac{RT}{M})d,41\mathrm{.}9\frac{g}{m}ol$

$97$