Molar Volume of a Gas

The molar volume of a gas is equal to the volume occupied by the 1 mole of a gas at given conditions of temperature and pressure. The molar volume can be obtained by dividing the molar mass by the density of the gas at given temperature.
                              Molar volume = molar mass / density
The unit of molar volume is M³ / mole or dm³/mole

Introduction to molar volume of a gas :

The volume of an ideal gas can be obtained by the ideal gas equation
                                                                 PV = nRT
V/n = RT/P plug in the values of R = 8.31 joule / mole / Kelvin, let the temperature = 273 Kelvin and the pressure as 1 Pascal = 1.01*10⁵ N/m^2. These are the STP conditions.
V_MOLAR   = (8.31*273/1.01* 10 ⁵)=22.4 liters approximately.

So the molar volume of an ideal gas at ST P is equal to 22.4 liters

 The molar volume of a real gas can be obtained by using the vanderwaal’s equation:
                                                         (P+a/V²⁾ (V-b)  = nRT  
 The a and b are the constant and different for a gas specific.

By approximation and Avogadro’s’ law the volume of 1 mole of a gas at STP is 22.4 liter invariably with the nature and type of a gas. Then applying the gas equation we can find the volume of the gas at any temperature.

Molar Volume of a Gas Ilustration

Example: find the molar volume of CO2 at 2 atm pressure and 27 degree C.
 SOLUTION:
   The molar volume of CO2 at STP is 22.4 liters therefore applying the followings
   P₁=1 atm             P₂ =2 atm
     V₁= 22.4L           V₂=??
      T₁= 273 K          T₂= (27+273) = 300 K
APPLYING THE EQAUITON
      P1V1/T1 =P2V2/T2
      V2  =  P1T2V1/P2T1
       =  1*300*22.4 /(2*273) = 12.30 liters