Avogadro's law and molar volume
Francine Taylor-Campbell, Contributor

REVIEW OF FACTS

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 00C and 1 atmosphere pressure and room temperature (RTP) which is 200C and 1 atmosphere pressure.

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

22.4 dm3 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 24 dm3.

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 22.4 dm3 at STP

Thus 8g = 24/4 dm3 at RTP and 22.4/4 dm3 at STP

Volume of 8g of O2 at RTP = 6 dm3 and at STP = 5.6 dm3

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

(i) 1 mole of N2 = 28g

24 dm3 at RTP = 28g

4.8 dm3 = (28 * 4.8)/24 = 5.6g

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

(c) Calculate the volumes of the following at RTP

(i) 35.5g of Cl2

(ii) 1.7g NH3

(iii) 4g H2

d) Calculate the mass of 2.8 dm3 of each of the following gases at STP

(i) NO2

(ii) HBr

(iii) C2H6.

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

Define the following:

Avogadro's law

The mole

The relative molar mass

(6 mks)

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 24 dm3)

(2 mks)

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) 18 g 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

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. Send questions and comments to kerry-ann.hepburn@gleanerjm.com