Question

Derive the relation M = dRT/p from gas law

Answer 1

We know that the number of moles of the substance is related to the molar mass and the equation is as follows :

n = $\frac{w}{M}$

where w is mass of substance in grams.

We know that ideal gas equation is:

PV = nRT

Now substituting the value of number of moles of the substance which is related to the molar mass in the ideal gas equation we  get the following equation:

PV = $\frac{w}{MRT}$

P = $\frac{wRT}{MV}$

Since we know that density is mass/volume = w/v

Substituting the value of density in the above equation we get

P = $\frac{dRT}{M}$

So the molar mass M is given as:

M = $\frac{dRT}{P}$.