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From Avogadro’s hypothesis, the ratio of molar
masses of two gaseous compounds is the same as the ratio of their densities, provided
that those densities are measured at the same temperature and pressure.
Can someone explain why?
From ideal gas equation we have pV =nRT
m/V = density
m/V = pM/RT
let d1 and d2 be the densities of two gases then the ratio d1/d2 is M1/M2 provided p and T remains constant
Will you accept that the molar masses of two gases will occupy same volume at same temperature and pressure?
Then the density of the gas depends only on mass(volume constant). Same volume of a solid has higher density than a liquid of same volume, because the it has generally more mass.
So, the gas of higher molar mass will have more mass distributed in the same volume than the gas of lower molar mass. Thus, these two quantities seem directly proportional(if you double the mass, the density doubles).
So, their ratios must also be same.
The answer has already been given, but this is just a theoretical explanation