Start from the ideal gas law equation, PV= nRTPV=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 = m/M_Mn=mMM
This means that you can write
PV = (m/M_M)RTPV=(mMM)RT
Density is defined as mass per unit of volume
rho = color(blue)(m/V)ρ=mV
Therefore, if you rearrange the equation, you obtain
PV = m/M_M * RT => P * M_M * V = mRTPV=mMM⋅RT⇒P⋅MM⋅V=mRT
P * M_M = color(blue)(m/V) * RT = rho * RTP⋅MM=mV⋅RT=ρ⋅RT
As a result,
M_M = (rho * RT)/P = (1.43 "g"/cancel("L") * 0.082(cancel("atm") * cancel("L"))/("mol" * cancel("K")) * (273.15 + 23)cancel("K"))/("0.789"cancel("atm")
M_M = "44 g/mol" -> rounded to two sig figs.
The gas could be carbon dioxide, CO_2.
