The mole concept - avogadro's law and molar volume
Francine Taylor-Campbell, Contributor

Members of Oberlin High School choir, winner of TVJ's 'All Together Sing' 2005, don the Jamaican national colours as they rock the audience in TVJ's studios, on November 17, 2006. - Colin Hamilton/Freelance Photographer

Avogadro's Law states that equal volumes of all gases measured at the same temperature and pressure contain equal numbers of molecules. The temperatures and pressures usually used are standard temperature and pressure (STP), which is 0ºC and 1 atmosphere pressure and room temperature (RTP) which is 20ºC and 1 atmosphere pressure.

1dm³ of any gas at STP contains the same number of molecules as 1dm3 of any other gas at STP.

22.4dm³ of any gas contains L molecules (6.0*1023) at STP. This is one mole of the gas and is called the molar volume.

At RTP the molar volume is 24dm³.

Calculations on molar volume

1(a) What is the volume of 8g of oxygen at (i)RTP (ii) STP

1 mole of oxygen (O2 ) = 2*16 = 32g 32g = 24dm³ at RTP and 22.4dm³ at STP Thus 8g = 24/4 dm³ at RTP and 22.4/4 dm³ at STP Volume of 8g of O2 at RTP = 6dm³ and at STP = 5.6dm³

(b) Calculate the mass of 4.8dm³ of (i) N2 (ii) CO2 at RTP.

(i) 1 mole of N2 = 28g
24dm³ at RTP = 28g
4.8dm³ = (28*4.8)/24 = 5.6g

(ii) 4.8dm³ of CO2 at RTP = (44*4.8)/24 = 8.8g

2. This question is concerned with the mole and its application.

Define the following:

(i) Avogadro's law
(ii) The mole
(iii) The relative molar mass (6 marks)

Determine:

(i) The number of moles of carbon in 18g of carbon (Relative atomic mass: C = 12)

(ii) The number of atoms in 18g of carbon

(iii) The number of molecules in 4.9g of sulphuric acid (RMM of sulphuric acid = 98) (3 mks)

(c) At room temperature and atmospheric pressure (r.t.p.), 1.6g of methane occupy a volume of 2.4dm³. Calculate the relative molar mass of methane. (ONE mole of any gas at r.t.p. has a volume of 24dm³ ) (2 marks)

ANSWERS

2. (a) (i) Avogadro's law states that equal volumes of gases measured at the same temperature and pressure contain equal number of molecules.

(ii) The mole is the amount of substance that contains avogadro's number of particles, that is 6.0*1023 particles.

(iii) The relative molar mass is the mass of one mole of a substance compared with the mass of one atom of carbon-12.

(b) (i) Number of moles of carbon = 1.5 mol (1 mol of carbon has a mass of 12g. Therefore # mol in 18g = 18g/12 gmol-1 = 1.5 mol).

(ii) 18g of carbon = 1.5 mol.

Now 1 mol has 6.0*1023 atoms, thus 1.5 mol has 1.5 x 6.0*1023 atoms = 9*1023 atoms.

(iii) # mol in 4.9g of sulphuric acid (H2SO4 ) = 4.9/98 = 0.05 mol.

Number of molecules of H2SO4 = 0.05 x 6.0*1023 = 3*1022 molecules.

(c) 1 mole CH4 has volume of 24dm³ at r.t.p.

Volume of gas = 2.4 dm³ thus # mol = 2.4/24 = 0.1 mol CH4,01 mol CH4 has a mass of 1.6g.

Molar mass or mass of 1 mol = 1.6/0.1 == 16g/mol

Francine Taylor-Campbell is an independent contributor.