3.5.1 Volumes of gases
Equal numbers of moles of any gas take up equal volumes
Molar volume
The volume occupied by one mole of any gas, equal to 24 dm324\ \text{dm}^324 dm3 at room temperature and pressure.
Amount of substance
A quantity measured in moles that represents how many particles of a substance are present.
- At the same temperature and pressure, equal numbers of moles of any gases occupy the same volume.
- At room temperature and pressure, one mole of any gas fills a molar volume of 24 dm324\ \text{dm}^324 dm3.
For gases, the volume depends only on the number of moles, not on which gas it is, so 24 dm324\ \text{dm}^324 dm3 works for oxygen, carbon dioxide or any other gas.
Volume of a gas comes straight from its moles
Mole
The amount of a substance, measured in mol, where one mole has a mass in grams numerically equal to its relative formula mass.
- The volume in dm3\text{dm}^3dm3 at room temperature and pressure is the moles multiplied by 242424, so V=n×24V = n \times 24V=n×24.
- Rearranged, the moles of gas are n=V24n = \dfrac{V}{24}n=24V.
0.5 mol0.5\ \text{mol}0.5 mol of carbon dioxide occupies 0.5×24=12 dm30.5 \times 24 = 12\ \text{dm}^30.5×24=12 dm3 at room temperature and pressure.
Using it with a balanced equation
Balanced equation
A chemical equation containing the same number of atoms of each element on both sides.
Coefficient
A large whole number placed before a chemical formula to show the relative number of particles or moles in a balanced equation.
- Change the mass of the reactant into moles using n=mMrn = \dfrac{m}{M_r}n=Mrm.
- Use the mole ratio in the equation to find the moles of gas produced.
- Multiply the moles of gas by 242424 to get its volume in dm3\text{dm}^3dm3.
- The molar volume of 24 dm324\ \text{dm}^324 dm3 is given in the exam, so use the value provided rather than trying to recall it.
- Keep the volume in dm3\text{dm}^3dm3 unless the question asks for cm3\text{cm}^3cm3, in which case multiply by 100010001000.
Worked example: gas released when a carbonate is heated
- Find the volume of carbon dioxide made when 5 g5\ \text{g}5 g of calcium carbonate decomposes in CaCO3→CaO+CO2\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2CaCO3→CaO+CO2.
- Moles of calcium carbonate =5100=0.05 mol= \dfrac{5}{100} = 0.05\ \text{mol}=1005=0.05 mol.
- The ratio is 1:11:11:1, so 0.05 mol0.05\ \text{mol}0.05 mol of carbon dioxide forms.
- Volume of carbon dioxide =0.05×24=1.2 dm3= 0.05 \times 24 = 1.2\ \text{dm}^3=0.05×24=1.2 dm3.
- What volume does one mole of any gas occupy at room temperature and pressure?
- Write the formula linking the volume of a gas to its number of moles.
- What volume does 2 mol2\ \text{mol}2 mol of hydrogen occupy at room temperature and pressure?
- How many moles of gas are there in 6 dm36\ \text{dm}^36 dm3 at room temperature and pressure?
