The density of an ideal gas a is 1.47 g/l at STP. Determine the density of a at 17°c and 700torr (mm).

Start from the idealgas laws equation, PV=nRT, where n is the number of moles.

The number of moles can be written as the ratio between the weight of the gas, i.e. its mass, and its molecular mass.

n=mMM

This means that you can write

PV=(mMM)RT

Density is defined as mass per unit of volume

ρ=V

Therefore, if you rearrange the equation, you obtain

PV=mMM⋅RT⇒P⋅MM⋅V=mRT

P⋅MM=mV⋅RT=ρ⋅RT

As a result,

MM=ρ⋅RTP=1.43gL⋅0.082atm⋅Lmol⋅K⋅(273.15+23)K0.789atm

MM=44 g/mol → rounded to two sig figs

The gas could be carbon dioxide, CO2.