Calculations involving molar volume - Higher
The molar volumeThe volume occupied by one mole of any gas (24 dmÂł or 24000 cmÂł at room temperature and pressure). can be used in calculations involving the massThe amount of matter an object contains. Mass is measured in kilograms (kg) or grams (g). of solids, and volumes of gases, in reactions.
Calculating a volume from a mass
Worked example
4.6 g of sodium reacts completely with excess water:
2Na(s) + 2H2O(l) → 2NaOH(aq) + H2(g)
Calculate the volume of hydrogen produced. (Ar of Na = 23, molar volume = 24 dm3)
Step 1 - Calculate the amount of sodium in moles
Amount in mol = \(\frac{\textup{mass}}{{\textup{atomic mass}}}\)
Amount in mol = \(\frac{\textup{4.6}}{\textup{23}}\)
Amount of sodium = 0.20 mol
Step 2 - Find the amount of hydrogen in moles
From the balanced chemical equationA chemical equation written using the symbols and formulae of the reactants and products, so that the number of units of each element present is the same on both sides of the arrow., the mole ratioThe ratio of the amounts of two substances as shown in a balanced equation. Na:H2 is 2:1
Therefore 0.20 mol of Na produces \(\frac{\textup{0.20}}{\textup{2}}\) = 0.10 mol of H2
Step 3 - Calculate the volume of hydrogen
Volume = amount in mol Ă— molar volume
Volume = 0.10 Ă— 24
= 2.4 dm3
Question
Calcium carbonate decomposeIf a substance decomposes, it breaks down into simpler compounds or elements. to form calcium oxide and carbon dioxide when it is heated:
CaCO3(s) → CaO(s) + CO2(g)
Calculate the volume of carbon dioxide produced from completely decomposing 1.0 g of calcium carbonate. (Mr of CaCO3 = 100, molar volume = 24,000 cm3)
Amount of calcium carbonate = \(\frac{\textup{1.0}}{\textup{100}}\) = 0.010 mol
Amount of carbon dioxide = 0.010 mol (because the mole ratio is 1:1)
Volume of carbon dioxide = 0.010 Ă— 24,000
= 240 cm3
Calculating a mass from a volume
Worked example
Lithium hydroxide absorbs carbon dioxide from the air:
2LiOH(s) + CO2(g) → Li2CO3(s) + H2O(l)
Calculate the mass of lithium hydroxide needed to absorb 12 dm3 of carbon dioxide. (Mr of LiOH = 24, molar volume = 24 dm3)
Step 1 - Calculate the amount of carbon dioxide
Amount in mol = \(\frac{\textup{volume}}{\textup{molar~volume}}\)
Amount in mol = \(\frac{\textup{12}}{\textup{24}}\)
= 0.50 mol
Step 2 - Find the amount of lithium hydroxide
From the balanced equation, the mole ratio LiOH:CO2 is 2:1
Therefore 0.50 mol of CO2 is absorbed by (0.50 Ă— 2) = 1.0 mol of LiOH
Step 3 - Calculate the mass of lithium hydroxide
Mass in g = Mr Ă— amount in mol
Mass = 24 Ă— 1.0
= 24 g
Question
Sodium reacts with chlorine to produce sodium chloride:
2Na(s) + Cl2(g) → 2NaCl(s)
Calculate the mass of sodium chloride produced from 960 cm3 of chlorine and an excess of sodium. (Mr of NaCl = 58.5, molar volume = 24,000 cm3 )
Amount of chlorine = 960 cm3 Ă· 24,000 cm3/mol = 0.040 mol
Amount of sodium chloride = 0.080 mol (because the mole ratio is 1:2)
Mass of sodium chloride = 58.5 Ă— 0.080 = 4.68 g