The molecular weight of the unknown gas is 42.06 g.
The idea is that the density of the gas tells you the mass of this gas that occupies exactly 1 L under some unspecified pressure and temperature conditions.
In this case, you know that the density of the gas was 1.51g/L.
This means that 1.51 g/L of this gas occupies exactly 1 L under the pressure and temperature conditions used in the experiment.
You are also aware that the total volume of the flask is 2.00 L. At this point, you can use the density of the gas to calculate the mass of gas required to fill the given volume with the sample.
[tex]2.00 L . \frac{1.51g}{1L} =3.02g[/tex]
You must now determine the mass of exactly one mole in order to determine the molar mass of the gas. Since you are aware that this sample contains 0.0718 moles of gas and weighs 12.5 g, you can infer that one mole will weigh that much.
[tex]1 mol. gas .\frac{3.02g}{0.0718} =42.06g[/tex]
As a result, the gas's molar mass can be expressed as molar mass = 42.06 g/ mol.
This indicates that 42.06 g makes up 1 mole of this gas.
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