Chemistry • Year 11 • Module 2 • Lesson 5

Mole Calculations — Consolidation

Build HSC Band 5–6 technique on multi-step mole problems, formula derivation, and evaluating experimental data in extended-response format. Show all working.

Master · Extended Response

1. Data + scenario: identifying an unknown hydrocarbon gas from mass spectrometry and combustion data

9 marks   Band 5–6

Scenario. A chemist collects a 3.71 L sample of unknown hydrocarbon gas X at SATP (25 °C, 100 kPa). The sample has a mass of 4.42 g and contains only carbon and hydrogen. Combustion analysis gives a carbon-to-hydrogen mass ratio of 6:1 (C:H). Use this data to identify gas X. (C = 12.011, H = 1.008)

Q1. Show all working in each step below to identify gas X.

  • Step 1: Use the gas volume data to find the number of moles of X. State the molar volume value you are using and why.
  • Step 2: Use moles and mass to calculate the molar mass of X.
  • Step 3: Convert the C:H mass ratio to a mole ratio using the 4-step empirical formula method, and determine the empirical formula.
  • Step 4: Calculate the multiplier n and derive the molecular formula.
  • Step 5: Name compound X and confirm your answer is chemically reasonable.
Step 1: SATP → Vm = 24.8. Step 2: MM = m ÷ n. Step 3: assume 100 g → 85.7 g C, 14.3 g H; find mole ratio → simplify. Step 4: n = MM(compound) ÷ MM(EF).

2. Experimental design — verifying the molar volume of oxygen at SATP

8 marks   Band 5–6

Research question. A student wants to verify experimentally that the molar volume of oxygen gas at SATP is 24.8 L mol−1. They will collect oxygen gas over water by the decomposition of hydrogen peroxide: 2H2O2(aq) → 2H2O(l) + O2(g), catalysed by MnO2(s).

Equipment available: digital balance (0.01 g), gas syringe (calibrated to 0.1 mL), 3% H2O2 solution (10 mL per trial), MnO2 catalyst, thermometer, barometer. Room temperature is 24 °C.

Q2. Design the investigation using the format below:

  • State a testable hypothesis including the predicted value of Vm.
  • Identify the independent variable, dependent variable, and at least two controlled variables.
  • Describe the procedure in at least five numbered steps, including how you will calculate Vm from the data.
  • Explain what result would falsify the predicted Vm value, including an acceptable range of error.
  • State two sources of uncertainty and one improvement to reduce each.
Hypothesis: Vm(O2) ≈ 24.8 L mol−1 at SATP. IV = mass of H2O2; DV = volume of O2 produced. Calculation: n(O2) = n(H2O2) ÷ 2; Vm = V(O2) ÷ n(O2). Source of error: water vapour in collected gas; room temperature differs from SATP.
Answers — Do not peek before attempting

Q1 — Sample Band 6 response (9 marks), annotated

Step 1 — Moles from gas volume: Conditions are SATP (25 °C, 100 kPa) → Vm = 24.8 L mol−1 [1 mark for correct Vm selection with reason]. n = V ÷ Vm = 3.71 ÷ 24.8 = 0.14960 mol [1 mark correct calculation; carry full precision].

Step 2 — Molar mass: MM = m ÷ n = 4.42 ÷ 0.14960 = 29.5 g mol−1 [1 mark for correct formula and answer]. Accept 29.5–29.6 g mol−1 depending on rounding point.

Step 3 — Empirical formula: C:H mass ratio = 6:1 → in 100 g: 85.71 g C, 14.29 g H [state assumption: treat ratio as %; 1 mark]. n(C) = 85.71 ÷ 12.011 = 7.136 mol. n(H) = 14.29 ÷ 1.008 = 14.177 mol. Ratio H:C = 14.177 ÷ 7.136 = 1.987 ≈ 2 [1 mark for correct mole ratio calculation and simplification]. Empirical formula: CH2.

Step 4 — Molecular formula: MM(CH2) = 12.011 + 2(1.008) = 14.027 g mol−1. n(multiplier) = 29.5 ÷ 14.027 = 2.10 ≈ 2 [1 mark; accept rounding to nearest whole number]. Molecular formula: CH2 × 2 = C2H4 [1 mark for applying multiplier to all subscripts].

Step 5 — Name and reasonableness: C2H4 is ethene (ethylene) [1 mark]. Reasonableness check: molecular formula obeys the CnH2n pattern for alkenes; MM = 28.054 g mol−1, consistent with calculated 29.5 g mol−1 within experimental uncertainty from sig figs [1 mark for explicit check; accept methane/ethane/propene if working is consistent]. Deduct marks if intermediate values were rounded prematurely.

Marking criteria summary (9 marks): 1 = correct Vm with justification; 1 = n from gas volume; 1 = MM from mass and moles; 1 = correct assumption for EF derivation (treat C:H as % or 100 g); 1 = correct mole ratio and simplification; 1 = correct empirical formula CH2; 1 = correct multiplier; 1 = correct molecular formula C2H4; 1 = name and reasonableness check.

Q2 — Sample Band 6 response (8 marks), annotated

Hypothesis: If the molar volume of O2 at SATP is 24.8 L mol−1, then measuring the volume of O2 produced from a known mass of H2O2 and calculating Vm = V ÷ n should yield a result within 5% of 24.8 L mol−1. IV = mass (amount) of H2O2 used; DV = volume of O2 collected in the gas syringe. Controlled variables: temperature of solution (24 °C, close to SATP); volume of H2O2 solution (10.0 mL per trial); mass of MnO2 catalyst (0.10 g per trial). [2 marks: 1 for hypothesis with predicted value; 1 for IV, DV, and two controlled variables]

Procedure: (1) Measure 10.00 g of 3% H2O2 solution (density ≈ 1.00 g mL−1; note exact mass on balance). Calculate n(H2O2): 3% by mass → mass H2O2 = 0.03 × 10.00 = 0.300 g; MM(H2O2) = 34.015 g mol−1; n(H2O2) = 0.300 ÷ 34.015 = 8.82 × 10−3 mol. (2) Add 0.10 g MnO2 to a conical flask fitted with a sealed stopper and tubing connected to a pre-zeroed gas syringe. (3) Inject H2O2 solution via a syringe port; start timing and allow reaction to complete (≈ 2–3 min). (4) Record final volume of O2 in gas syringe. Record room temperature and pressure. (5) Calculate: n(O2) = n(H2O2) ÷ 2 (from stoichiometry); Vm( ) = V(O2) ÷ n(O2). Repeat three times and average Vm. [2 marks: 1 for ≥4 logical steps with apparatus; 1 for calculation pathway shown]

Falsification: If the calculated Vm differs from 24.8 L mol−1 by more than 5% (i.e. <23.6 or >26.0 L mol−1) and the discrepancy is reproducible across three trials, the hypothesis is falsified — the measured molar volume under these conditions does not match the SATP standard. [1 mark for testable falsification criterion with stated range]

Sources of uncertainty and improvements: (1) Water vapour in collected gas inflates measured volume (O2 is collected over air, not water, but syringe may contain water vapour). Improvement: dry the gas syringe or apply a water-vapour correction using the vapour pressure of water at 24 °C. (2) Incomplete reaction if H2O2 solution concentration is not exactly 3%. Improvement: titrate a sample of the H2O2 solution to confirm its exact concentration before each trial. [2 marks: 1 per correctly explained source + improvement pair]

Marking criteria (8 marks): 1 = testable hypothesis with predicted Vm value; 1 = IV, DV, and ≥2 controlled variables identified; 1 = ≥4 logical procedure steps with apparatus; 1 = calculation pathway (n from H2O2 mass, stoichiometry, then Vm); 1 = falsification criterion with specific numerical range; 1 = one source of uncertainty with improvement; 1 = second source with improvement; 1 = appropriate use of precise chemical terminology (molar volume, SATP, stoichiometry, independent/dependent variable) throughout.

HSCScience • Chemistry • Year 11 • Module 2 • Lesson 5 • Worksheet 3 (Master)