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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.
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