Derive the relation between density, molar mass and pressure.

1.	Derive the relation between density, molar mass and pressure.
Answer» Relation between density, molar mass and pressure: According to ideal gas equation, PV = nRT …..(1) On rearranging equation (1), we get \(\frac{n}{V}\) = \(\frac{P}{RT}\) ……….(2) Now, n = \(\frac{m}M\) On substituting the value of n, equation (2) becomes \(\frac{m}{MV}\) = \(\frac{P}{RT}\) \(\frac{d}M\) = \(\frac{P}{RT}\) ……….(3) where d = \(\frac{m}V\) = density of the gas On rearranging the equation, we get M = \(\frac{dRT}P\) ……(4) This equation can be used to calculate molar mass of a gas in terms of its density.

Answer»

Relation between density, molar mass and pressure:

According to ideal gas equation,

PV = nRT …..(1)

On rearranging equation (1), we get

\(\frac{n}{V}\) = \(\frac{P}{RT}\) ……….(2)

Now, n = \(\frac{m}M\)

On substituting the value of n, equation (2) becomes

\(\frac{m}{MV}\) = \(\frac{P}{RT}\)

\(\frac{d}M\) = \(\frac{P}{RT}\) ……….(3)

where d = \(\frac{m}V\) = density of the gas On rearranging the equation, we get

M = \(\frac{dRT}P\) ……(4)

This equation can be used to calculate molar mass of a gas in terms of its density.

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