Deriving the ideal gas law in terms of density and molar mass

[AzzidReign]

Homework Statement

Using the equation P=m/V show that the equation PV=nRT can become P/p=(R/MW)T

P=pressure
p=density of air
n=number of moles of gas
R=gas constant
T=temperature
m=mass
V=volume
MW=mass of one mole of air

Homework Equations

P=m/V
PV=nRT
P/p=(R/MW)T

The Attempt at a Solution

I was reading that n=m/MW, is that right?
And where I'm stuck at is properly matching each letter from the first equation with the second one and how that can translate to the final equation.

 

[therealnihl]

Hmm, what is big M and W?

 

[AzzidReign]

Hmm, what is big M and W?

MW is the mass of one mole of air.

 

[Macch]

PV = nRT
PV = (m/MW)RT
PV/m = RT/MW

as V is the volume of air with mass m:

p = m/V

P/p = RT/MW

 

[Macch]

PV = nRT
PV = (m/MW)RT
PV/m = RT/MW

as V is the volume of air with mass m:

p = m/V

P/p = RT/MW

 

[AzzidReign]

PV = nRT
PV = (m/MW)RT
PV/m = RT/MW

as V is the volume of air with mass m:

p = m/V

P/p = RT/MW

So you said it's safe to basically put it as 1/p=V/m?
Which would allow you to plug it into the final equation?