The Mole Concept
Senior 2 · Chemistry
The Mole Concept
Lesson 5 of 5
22 min
The methane in Lake Kivu is measured not in kilograms but in cubic kilometres: an estimated 65 km³ of it lies dissolved in the deep water. Household biogas digesters in rural Rwanda are also sized by the volume of gas they produce each day. For gases, volume is far easier to measure than mass.
Remarkably, the volume of a gas depends only on how many moles of it there are, not on which gas it is. By the end of this lesson you will be able to use the molar gas volume to convert between the volume, moles and mass of a gas, and to calculate volumes of gases in reactions.
Equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules. The molecules of a gas are very far apart compared with their own size, so the space a gas takes up depends on how many molecules there are, not on how big or heavy they are.
It follows that one mole of any gas occupies the same volume at the same temperature and pressure. This volume is the molar gas volume, Vm.
Remember that 1 dm³ = 1000 cm³ = 1 litre. The key relationship is:
n = V ÷ Vm and V = n × Vm
What is the mass of 11.2 dm³ of oxygen at s.t.p.?
Solution. n = 11.2 ÷ 22.4 = 0.50 mol. M(O2) = 32 g/mol, so m = 0.50 × 32 = 16 g.
What volume does 8.0 g of methane occupy at s.t.p.?
Solution. n = 8.0 ÷ 16 = 0.50 mol. V = 0.50 × 22.4 = 11.2 dm³. Notice that 16 g of oxygen and 8 g of methane occupy the same volume, because both are 0.5 mol.
6.5 g of zinc reacts with excess dilute hydrochloric acid. What volume of hydrogen forms at r.t.p.?
Zn(s) + 2HCl(aq) → ZnCl2(aq) + H2(g)
Solution. n(Zn) = 6.5 ÷ 65 = 0.10 mol, so 0.10 mol of H2 forms. V = 0.10 × 24 = 2.4 dm³ = 2400 cm³.
Because equal volumes contain equal numbers of moles, gas volumes react in the same ratio as the coefficients (measured at the same temperature and pressure).
What volume of oxygen is needed to burn 10 dm³ of methane, and what volume of carbon dioxide forms?
CH4(g) + 2O2(g) → CO2(g) + 2H2O(l)
Solution. Ratio CH4 : O2 : CO2 = 1 : 2 : 1, so 10 dm³ of methane needs 20 dm³ of oxygen and forms 10 dm³ of carbon dioxide. (The water is a liquid, so its volume is not counted.)
How much energy is released by burning 1 m³ (1000 dm³) of methane, measured at s.t.p., if 1 mol releases 890 kJ?
Solution. n = 1000 ÷ 22.4 = 44.6 mol (that is 44.6 × 16 = 714 g). Energy = 44.6 × 890 = 39 700 kJ, about 39.7 MJ. On this basis the 65 km³ in Lake Kivu, if measured at s.t.p., would be about 2.9 × 1012 mol of methane (1 km³ = 1012 dm³).
1.00 dm³ of an unknown gas at s.t.p. has a mass of 1.25 g. Find its molar mass.
Solution. One mole occupies 22.4 dm³, so it has a mass of 1.25 × 22.4 = 28 g. M = 28 g/mol, which matches nitrogen, N2 (or carbon monoxide, CO).
Tip
Read the conditions. Use 22.4 dm³/mol at s.t.p. and 24 dm³/mol at r.t.p., whichever the question gives. Convert cm³ to dm³ first by dividing by 1000: 4800 cm³ is 4.8 dm³.
For gases reacting with gases, you do not need moles at all: the volumes are in the ratio of the coefficients.
Use Ar: H 1, C 12, N 14, O 16, Ca 40. Try each item before you read the solution.
What volume does 0.25 mol of carbon dioxide occupy at s.t.p.?
Solution: 0.25 × 22.4 = 5.6 dm³.
How many moles of gas are there in 480 cm³ at r.t.p.?
Solution: 480 cm³ = 0.480 dm³; 0.480 ÷ 24 = 0.020 mol.
What is the mass of 5.6 dm³ of ammonia, NH3, at s.t.p.?
Solution: n = 5.6 ÷ 22.4 = 0.25 mol; m = 0.25 × 17 = 4.25 g.
10 g of calcium carbonate reacts with excess hydrochloric acid. What volume of carbon dioxide forms at r.t.p.?
Solution: CaCO3(s) + 2HCl(aq) → CaCl2(aq) + H2O(l) + CO2(g). n(CaCO3) = 10 ÷ 100 = 0.10 mol, giving 0.10 mol of CO2; V = 0.10 × 24 = 2.4 dm³.
What volume of oxygen is needed to burn 5 dm³ of propane completely, at the same temperature and pressure?
Solution: C3H8(g) + 5O2(g) → 3CO2(g) + 4H2O(l). The ratio C3H8 : O2 is 1 : 5, so 5 × 5 = 25 dm³ of oxygen.
Summary
Sources and credits
This lesson adapts CC BY-SA material and is shared under CC BY-SA 4.0.
