# What is the molar form of the ideal gas law?

Jun 5, 2014

The molar mass form of the ideal gas equation can be written as

$P V = \left(\frac{m}{M}\right) R T$ … or P = (ρ/M) RT, as described below.

where

P is the pressure the gas exerts on the walls of the container that confines it.
V is the volume of that container.
R is the ideal gas constant, 8.314 Joules per mole-Kelvin.
T is the temperature of the gas.
m is the mass of the gas.
M is the mass of the gas per mole.

The molar mass form of the ideal gas equation can be derived by substituting n (the amount of gas inside the container measured in moles) into the more common form of the ideal gas equation

$P V = n R T$

where n = m/M. All other variables are the same as described above.

Divide both sides of the molar mass form of the ideal gas equation PV = (m/M) RT by V and we obtain

$P \frac{V}{V} = \left(\frac{m}{M V}\right) R T$

or

P = (ρ/M) RT

which is the other way to write the molar mass form of the ideal gas equation (as mentioned above), where ρ is the density of the gas, ρ = m/V. The symbol ρ might look like the letter "p" (as in Paul), but it is not. ρ is actually a greek letter pronounced "rho".