Question

A molar volume of gas has a density of $ 1.7824\;g{L^{ - 1}} $ at STP. What is the molecular mass of this gas?

Answer 1

Hint: To answer this question we have to know about the molecular mass. The total number of atoms present in the molecule is termed as molecular mass. Its unit is daltons, represented as $ Da $ or $ u $ . Different molecules have different molecular masses as they have different isotopes.

Complete answer:
The molecular mass of the molecule is the total of the mass of the atom present in the molecule based on the scale in which the atomic masses of hydrogen, carbon, nitrogen and oxygen are $ 1 $ , $ 12 $ , $ 14 $ and $ 16 $ respectively. Let us take an example of the molecular mass of carbon dioxide, which contains two atoms of oxygen and one atom of carbon, is $ 44\left( {32 + 12} \right) $ .
The molar volume of the Ideal gas in STP is $ 22.4L $ . As the density of the gas is $ 1.7824\;g{L^{ - 1}} $ at STP. So, at STP the molecular mass of the gas is:
 $ \Rightarrow 22.414\,Lmo{l^{ - 1}} \times 1.7824\;g{L^{ - 1}} $
 $ \Rightarrow 39.95\;g\;mo{l^{ - 1}} $
The molecular mass of the gas is $ 39.95\;g\,mo{l^{ - 1}} $ .

Additional Information:
The molar mass of the compound is termed as the quantity of atoms or molecules or compounds are present in one mole of substance. In other words, molar mass is the average of elements present in the compound which always vary in mass due to the presence of isotopes.

Note:
Molecular mass of the compound is the mass of one molecule. It differs because of isotopes. The unit of molecular mass is measured in amu which stands for atomic mass units. Whereas molar mass is the amount of molecules or atoms present in one mole of the substance. It's S.I. unit is $ gmo{l^{ - 1}} $ .