Start from the ideal gas law 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 = m/M_M#
This means that you can write
#PV = (m/M_M)RT#
Density is defined as mass per unit of volume
#rho = color(blue)(m/V)#
Therefore, if you rearrange the equation, you obtain
#PV = m/M_M * RT => P * M_M * V = mRT#
#P * M_M = color(blue)(m/V) * RT = rho * 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#.
