Number of Mole and Volume of Gas

Molar Volume of Gas

  1. Equal amount of gas occupies same volume of space.
  2. Molar volume of a gas is defined as the volume occupied by one mol the gas at certain condition
  3. At room temperature(25ºC) and pressure (1 atm), one mole of any gas occupies a volume of 24 dm³ (24 000 cm³ )
  4. At standard temperature(0ºC) and pressure (1 atm) one mole of any gas occupies a volume of 22.4 dm³ (22400cm³).
Number of mole of gasses Volume at s.t.p. (dm3)
1 mol of O2 gas  1 x 22.4 = 22.4
1 mol of H2 gas  1 x 22.4 = 22.4
2 mol of He gas  2 x 22.4 = 44.8
3.5 mol of N2 gas  3.5 x 22.4 = 78.4
Number of mole of gasses Volume at r.t.p. (dm3)
1 mol of O2  gas  1 x 24 = 24
1 mol of H2 gas  1 x 24 = 24
2 mol of He gas  2 x 24 = 48
3.5 mol of N2 gas  3.5 x 24 = 84
Example: What volume (at room temperature and pressure r.t.p.) would 2 moles of oxygen gas occupy? (Molar Gas Volume at r.t.p. = 24 dm³) Answer: Volume of gas = 2 x 24 = 48 dm³
Example: A sample of ozone gas has a volume of 960cm³ at room temperature and pressure. Find the number of mole of the ozone. [Molar volume at r.t.p. = 24.0dm³] Answer: Number of mole  = 960 cm3 / 24000 cm3 =0.04 mol

Volume of Gas, Mass of Substance and Number of Particles

Figure below shows the relationship between the number of mole of particles in a substance with the mass, number of particles and volume of gas.

Example

Find the number of particle in 1200cm³ of nitrogen gas at room temperature. (Molar Gas Volume at r.t.p. = 24 dm³)

Answer:

Number of mole of nitrogen gas
= 1200 cm3 / 24000 cm3
=0.05 mol

Number of nitrogen molecules = 0.05 mol × 6.02 × 1 023 = 3.01 × 1 022

 

Example

Example:

A gas jar containing 200cm³ of oxygen gas at s.t.p. Find the mass of the oxygen gas. [Relative atomic mass: Oxygen = 16; Molar volume of gas at s.t.p. = 22.4 dm³]

Answer:

Number of mole of oxygen gas, 
n = 200  cm3 / 22400  cm3
= 1 112  mol

Relative molecular mass of oxygen 
= 2×16 = 32
Mass of oxygen
= 1 112  × 32 gmol-1
=0.286g