Derive the following expression:M = \(\frac{mRT}{PV}\)

1.	Derive the following expression:M = \(\frac{mRT}{PV}\)
Answer» According to ideal gas equation, PV = nRT n = \(\frac{PV}{RT}\) Now, for a known mass ‘m’ of gas having molar mass ‘M’, number of moles ‘n’ is given as: n = \(\frac{m}{M}\) Therefore, \(\frac{m}{M}\) = \(\frac{PV}{RT}\) On rearranging the equation, we get M = \(\frac{mRT}{PV}\)

Answer»

According to ideal gas equation,

PV = nRT

n = \(\frac{PV}{RT}\)

Now, for a known mass ‘m’ of gas having molar mass ‘M’, number of moles ‘n’ is given as:

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

Therefore, \(\frac{m}{M}\) = \(\frac{PV}{RT}\)

On rearranging the equation, we get

M = \(\frac{mRT}{PV}\)

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