3. The word ‘mole’ has been adopted to represent the Avogadro number of atoms of an element, that is, the relative atomic mass of an element. Thus, one mole of sodium weighs 23.0 g or one tenth of a mole of sodium weighs 2.3 g.

4. When applied to molecules, one mole of molecules is the relative molecular mass of that molecule, which is the summation of the individual relative atomic masses of the constituent atoms. For example, calcium carbonate contains calcium, carbon and oxygen in the ratio 1:1, 3 (i.e. CaCO₃). The accurate relative atomic masses are Ca = 40.1, C = 12.01, O = 16.00, thus the relative molecular mass is 40.1 + 12.01 + (3 × 16.00) = 100.11. For many purposes the relative atomic masses are rounded up to the nearest whole number except for chlorine and copper which are 35.5 and 63.5 respectively.

5. When applied to solutions, a 1 molar, (1 M), solution is one in which 1 mole of a solute is dissolved in a solvent in order that the volume of the solution is 1000 cm³ (1 dm³ or 1 litre). This means that if the concentration of the solution is known in moles per dm³, the number of moles in any volume of solution can be determined. For example, to find how many moles of sodium hydroxide, NaOH, are contained in 200 cm³ of a 2 M, (2 molar), solution:

    1000 cm³ of the solution contains 2 moles of NaOH

    Thus, 1 cm³ of the solution contains $\frac{2}{1000}$ moles of NaOH and 200 cm³ of the solution contains $\frac{2}{1000}$ × 200 moles of NaOH. That is, the number of moles of sodium hydroxide is 0.4.

    In order to find the mass of sodium hydroxide required to make 200 cm³ of 2 M solution:

    200 cm³ of a 2 M solution requires $\frac{2}{1000}$ × 200 moles.

    0.4 moles of NaOH has a mass found by the equation:

    mass of NaOH = number of moles × relative molecular of NaOH mass of NaOH

$\begin{array}{l}=0.4\times \text{(23+16+l)}\\ =0.4\times 40\\ =16g\end{array}$

    That is, the mass of sodium hydroxide required is 16 g.

6. When applied to gases, the molar volume of any gas is defined as occupying 22.4 dm³ at a temperature of 273 K and pressure 101.3 kPa (atmospheric pressure). Volumes of gases are easier to measure than masses. Using the molar volume definition, if the volume of a gas is known, the number of moles and hence the mass of the gas can be determined. For example, to find the number of moles of carbon dioxide gas which are contained in 100 cm³ of the gas measured at 273 K and 101.3 kPa. Use is made of the above definition that at 101.3 kPa and 273 K, 22400 cm³ of any gas is the volume of 1 mole of the gas.

    Thus, 22400 cm³ of CO₂ are equivalent to 1 mole of CO₂.

    and 1 cm³ of CO₂ is equivalent to $\frac{1}{22400}$ moles of CO₂.

    Thus, 100 cm³ of CO₂ are equivalent to$\frac{1}{2240}$ × 100 moles of CO₂

    = $\frac{1}{224}$ or 0.00446 moles of carbon dioxide.

    In order to find the mass of carbon dioxide gas occupying 100 cm³ at 273 K and 101.3 kPa, use is made of the fact that 100 cm³ of CO₂ is equivalent to 0.00446 moles.

    Mass of carbon dime = Number of moles of carbon dioxide

    × Relative molecular mass of carbon dioxide

$\begin{array}{l}=\text{0}\text{.00446}\times \text{ (12+2}\times \text{16)}\\ =\text{0}\text{.00466}\times \text{44}\\ =\text{0}\text{.196 g}\text{.}\end{array}$

    The mass of carbon dioxide is 0.196 g.

7. If the temperature and pressure of the gas are different from the values stated, the volume must be converted to these values using the gas laws (see Chapter 46).