what is the density of methane gas at room temperature ?

Consider 1 mole of CH₄ at room temperature :
Molar Mass = (12.0 + 1.0×4) g = 16.0 g
Volume = 24 L

Density of CH₄ at room temperature = (16.0 g) / (24 L) = 0.667 g/L

if you start with these 2 equations
.. PV = nRT... .. .. ... ... .. .. .(ideal gas law)
.. .. n = mass / mw... .. . ....(definition of moles... mw is my abbrev for molecular weight)

substitute and rearrange
.. PV = (mass / mw) RT
.. (mass / V) = mw x P / (RT)

and we all know that density = mass / volume so that
.. density = mw x P / (RT)

solving
.. density = [16.04g/mol) x (__ atm)] / [(0.08206 Latm/molK) x (___ K)]

plug in your pressure and temp and calc away