# Molar Volume Formula

What is Molar Volume?

The Molar Volume, represented by Vm, is the volume occupied by one mole of a substance which can be a chemical element or a chemical compound at Standard Temperature and Pressure (STP). It can be calculated by dividing Molar mass (M) by mass density (ρ). One mole of any gas at a particular temperature and pressure has fixed volume and known as its Molar gas volume.

The Molar volume is directly proportional to molar mass and inversely proportional to density. The formula of molar volume is expressed as

$V_{m}=Atomic\;weight\times\frac{Molar\;Mass}{Density}$

Where Vm is the volume of the substance.

The standard temperature used is 273 Kelvin or 0oC, and standard pressure is 1 atmospheres, i.e., 760 mm Hg. Experimentally, one mole of any gas occupies a volume of 22.4 liters at STP. The equation can be expressed as

1 mole of gas at STP = 22.4 liters of gas.

Example 1

The decomposition of NaClO3 produces NaCl and O2. Determine the volume of O2 if 42.6 g NaClO3 decomposes at STP? The density is given to be 0.213g/m3.

Solution

Parameters given are,

Density(ρ) = 0.215kg/m3

Molar mass = 42.5g/mol = 0.0425kg/mol

Atomic weight = 96

To substitute in the equation

Vm = Atomic weight x Molar mass / Density

= 96 x 0.0425 / 0.215

Therefore, Vm = 18.976 m3/mol

Example 2

Calculate the molar volume of Ice when the density = 0.9167 g/cm3, molar mass = 18g and atomic weight is 18.02g.

Solution

Parameters given are,

Density = 0.9167 g/cm3

Molar mass = 0.018kg

Atomic weight = 18.02g

Substitute in the formula for molar volume, we get

Vm = 18.02 x 0.018 / 0.0009167

= 353.83m3/mol