Examples Based on the Mole, Avogadro’s Law and Avogadro’s Number.

We must think of the mole in three ways:

1. As the molecular mass in grams, e.g. for O2, 1 mole = 2x16 =32g.,
                    for CO2, 1 mole = 12+(2x16) = 44g.
                    and for H2SO4, 1 mole = (2x1) +32 + (4x16) = 98g.
2. As the amount that contains 6x1023 particles:
                    i.e. 1 mole, or 32g. of oxygen contains 6x1023 molecules.
3. If the substance is a gas, then 1 mole of it has a volume of 22.4 dm3 (22,400 cm3) at S.T.P.
                so 32g. of oxygen has a volume of 22.4 dm3 at S.T.P.

Worked Examples

(i)How many molecules are there in 64g. of oxygen?

    32g. (of oxygen) = 1 mole
So 64g. = 2 moles
1 mole contains 6 x 1023 molecules
So 2 moles contain 12 x 1023 molecules
    i.e. 1.2 x 1024 molecules. = Ans.

(ii) What is the volume in dm3 of 8.5g. of ammonia gas (NH3) at S.T.P?

17g. (of NH3) = 1 mole
so 8.5g. = 0.5 mole
so 0.5 mole has a volume of 22.4 / 2 = 11.2 dm3. = Ans.

(iii) How many molecules are there in 4.48 dm3 of sulphur dioxide?
            (The volume is measured at S.T.P.)

             22.4 dm3 = 1 mole
        so 4.48 dm3 = 4.48 / 22.4 mole
                           = 0.2 mole

    1 mole contains 6x1023 molecules
    so 0.2 mole contains 0.2 x 6 x 1023 molecules
                            = 1.2 x 1023 molecules = Ans.

(iv) What is the mass in grams at S.T.P. of 44,800 cm3 of CO2?

    22400 cm3 of CO2 at S.T.P. = 1 mole
so 44800 cm3 of CO2 at S.T.P. = 2 moles
    1 mole of CO2 = 44g.
so 2 moles of CO2 = 88g. = Ans.
(v) What is the relative molecular mass of a gas if 0.36g. of the gas has a volume of 500 cm3 at S.T.P?
Suggest what the gas might be.

At S.T.P. 500 cm3 of the gas weigh 0.36g.
        so 1 cm3 weighs 0.36 / 500
        so 22400 cm3 weigh 22400 x 0.36 / 500 = 16.128 g.

The gas is methane, CH4,whose Mr = 16.

Remember the three ways of looking at the mole:
 
 
1. 6 X 1023 Particles                                        2. Volume = 22.4 dm3 (if a gas!)
(Avogadro Number)
                     3. 1 mole contains the Atomic / Molecular Mass in grams