Derive the relation between density of a gas and its molar mass.

1.	Derive the relation between density of a gas and its molar mass.
Answer» Relation between density of a gas and its molar mass: According to Avogadro’s law, V ∝ n Now, n = \(\frac{m}{M}\) (where, m is the mass of the gas and M is the molar mass of the gas) ∴ V ∝ \(\frac{m}{M}\) M ∝ \(\frac{m}{V}\) But, \(\frac{m}{V}\) = d (where, d is the density of the gas) ∴ d ∝ M Thus, density of a gas is directly proportional to its molar mass.

Answer»

Relation between density of a gas and its molar mass:

According to Avogadro’s law, V ∝ n

Now, n = \(\frac{m}{M}\) (where, m is the mass of the gas and M is the molar mass of the gas)

∴ V ∝ \(\frac{m}{M}\)

M ∝ \(\frac{m}{V}\)

But, \(\frac{m}{V}\) = d (where, d is the density of the gas)

∴ d ∝ M

Thus, density of a gas is directly proportional to its molar mass.

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