Question

from dimensional analysis,derive the unit of 'M' in the equation PV=WRT/M where the symbol have their usual meaning​

Answer 1

Unit of M is gram/mole or gram-mole⁻¹

Explanation:

The ideal gas equation is

$PV=\frac{wRT}{M}$

$\implies M=\frac{wRT}{PV}$

Thus,

$\text{Unit of M} = \frac{\text{Unit of w}\times\text{Unit of R}\times \text{Unit of T}}{\text{Unit of P}\times\text{Unit of V}}$

$\text{Unit of M}=\frac{g\times (kg.m^2.K^{-1}.\text{mole}^{-1}.s^{-2})\times K}{kg.m.s^{-2}.m^{-2}\times m^3}$

$\implies \text{Unit of M}=\frac{g.m^2.\text{mole}^{-1}}{m^{2}}$

$\implies \text{Unit of M}=g.\text{mole}^{-1}$

Hope this answer is helpful.

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