# Understanding the relation between pressure, ideal gas and, volume

I was given the following formula which is used for ideal gasses: $$pV = nRT$$

where:

• p:pressure
• V: volume
• n: number of moles
• R: gasconstant
• T: temperature

now when speaking about vaporpressure curves like this one: You can change the formula like so: $$pV = NkT = nRT = \frac{m}{M}RT$$

where:

• V: vapor volume
• m: mass of the vapor
• M: molar mass of the particles
• N: number of particles which are in vapor state
• n: amount of moles

Based on the previous formula you can calculate the pressure like this: $$\rho(T) = \frac{pM}{RT}$$

Now I would like to know where the volume is in this final formula to calculate the pressure?

Is this formula still applicable: $p = \frac{nRT}{V}$ ? (If not, in which cases is it?) This formula seems much easier to me.

• Please define $\rho$ – pentane Jan 22 '16 at 13:43

## 1 Answer

The answer you are looking for is that \begin{equation} \rho \propto 1/V \end{equation} and \begin{equation} m/\rho = 1/V \end{equation} with this knowledge you should be able to see how your final equation relates to \begin{equation} pV = nRT \end{equation}