Chemistry • Year 11 • Module 2 • Lesson 17
Back Calculations & Unknown Concentrations
Build HSC Band 5–6 extended-response technique on multi-step back calculations, experimental design for quantitative analysis, and evaluating sources of error in back-titration experiments.
1. Multi-step calculation — standardising a NaOH solution using oxalic acid dihydrate (Band 4–5)
8 marks Band 4–5
Scenario. A Year 11 student at a Sydney school is standardising a sodium hydroxide (NaOH) solution that will be used for back-calculation experiments throughout the term. She uses oxalic acid dihydrate (H2C2O4·2H2O, Mr = 126.07 g/mol) as the primary standard. She dissolves 0.945 g in distilled water and makes it up to 250.0 mL in a volumetric flask. She pipettes 25.00 mL aliquots into a conical flask and titrates with NaOH(aq) from the burette. The balanced equation is:
H2C2O4 + 2NaOH → Na2C2O4 + 2H2O
Her titration results are: Rough = 26.1 mL; T1 = 28.3 mL; T2 = 28.5 mL; T3 = 28.2 mL.
Q1. Use the data above to determine c(NaOH). In your response you must:
- (a) Identify the concordant titres and calculate the average titre. Justify your selection.
- (b) Calculate n(H2C2O4) in the full 250.0 mL solution, then determine n(H2C2O4) in each 25.00 mL aliquot.
- (c) Apply the mole ratio to find n(NaOH) at the equivalence point.
- (d) Calculate c(NaOH). Identify which volume you used and explain why.
- (e) State one property of oxalic acid dihydrate that makes it suitable as a primary standard, and one property that makes it slightly less ideal than some other primary standards.
2. Experimental design — determining the concentration of vinegar (Band 5–6)
7 marks Band 5–6
Research question. A food-science student wants to determine the concentration of acetic acid (ethanoic acid, CH3COOH) in a bottle of white vinegar bought from a Woolworths supermarket. The label claims the vinegar is “5% acidity”. Design a back-calculation titration to verify this claim and express the result as a molar concentration in mol/L.
Available equipment and reagents: standard laboratory glassware (burette, pipette, conical flask, volumetric flask); primary standard Na2CO3 (anhydrous, Mr = 105.99 g/mol); phenolphthalein indicator; distilled water; the bottle of vinegar. The reaction of acetic acid with NaOH is: CH3COOH + NaOH → CH3COONa + H2O.
Q2. Design the investigation in the format below.
- State your hypothesis, including the expected molar concentration of acetic acid (note: “5% acidity” means 5 g acetic acid per 100 mL; Mr(CH3COOH) = 60.05 g/mol).
- Outline a two-stage procedure: Stage 1 — prepare and standardise the NaOH solution using Na2CO3 (Na2CO3 + 2HCl → 2NaCl + H2O + CO2; note: the NaOH is standardised by first standardising HCl, then using it to standardise NaOH, or directly with an oxalate). Stage 2 — titrate vinegar with the standardised NaOH.
- Identify the independent variable, dependent variable, and two controlled variables.
- Explain what result would falsify your hypothesis.
- State two limitations and one way to improve reliability.
Q1 — Sample Band 5 response (8 marks), annotated
(a) Concordant titres and average: Discard rough (26.1 mL — always discarded). T1 = 28.3, T2 = 28.5, T3 = 28.2 mL. Range = 28.5 − 28.2 = 0.3 mL. Strictly, T1 and T3 are within 0.10 mL (28.3 − 28.2 = 0.1 mL) and T2 is 0.2 mL from T1 and 0.3 mL from T3. For strict concordance, use T1 and T3 only: average = (28.3 + 28.2) ÷ 2 = 28.25 mL. Alternatively, if using ≤0.20 mL as the HSC criterion, all three are concordant: average = (28.3 + 28.5 + 28.2) ÷ 3 = 28.33 mL. Accept either approach with justification [1 for identifying which titres are concordant AND averaging only those].
(b) n(H2C2O4) total and in aliquot:
n(total) = 0.945 ÷ 126.07 = 7.496 × 10−3 mol [1].
c = 7.496 × 10−3 ÷ 0.2500 = 0.02998 mol/L.
n(aliquot) = 0.02998 × 0.02500 = 7.496 × 10−4 mol [1].
(c) n(NaOH): Ratio H2C2O4:NaOH = 1:2, so n(NaOH) = 7.496 × 10−4 × 2 = 1.499 × 10−3 mol [1].
(d) c(NaOH) using average titre:
Using average titre 28.25 mL: c(NaOH) = 1.499 × 10−3 ÷ 0.02825 = 0.0531 mol/L [1].
The titre volume (average concordant titre from the burette) is used because NaOH is the unknown being standardised; it is in the burette and its titre volume is what produces n(NaOH) via n = c × V in the reverse direction — wait: in this experiment, the primary standard (H2C2O4) is in the flask and NaOH is in the burette. Therefore n(NaOH) = c(NaOH) × V(titre), and the flask volume is used for the primary standard calculation. c(NaOH) = n(NaOH) ÷ V(titre) [1 for using V(titre) for NaOH and explaining why].
(e) Primary standard suitability: Suitable property: high molar mass (126.07 g/mol) means a larger mass must be weighed for the same number of moles, reducing the relative percentage error in weighing [1]. Slightly less ideal: oxalic acid dihydrate can slowly lose some water of crystallisation if stored improperly or heated during drying, causing uncertainty in the true mass of H2C2O4. Accept: moderately toxic; or mildly hygroscopic in some conditions [1].
Marking criteria summary (8 marks): 1 = correct identification of concordant titres AND correct average; 1 = n(total) correct; 1 = n(aliquot) correct; 1 = n(NaOH) via 1:2 ratio; 1 = c(NaOH) using correct volume; 1 = explanation of which volume is used and why; 1 = valid suitable property of primary standard; 1 = valid limitation/less ideal property.
Q2 — Sample Band 6 response (7 marks), annotated
Hypothesis: If the vinegar label is accurate, c(CH3COOH) ≈ 0.833 mol/L [from 5 g / 60.05 g/mol ÷ 0.100 L]. Independent variable: the sample being analysed (standardised NaOH for Stage 1; vinegar for Stage 2). Dependent variable: the average concordant titre of each stage. Controlled variables: pipette volume (25.00 mL each stage), indicator (phenolphthalein, 3 drops), temperature (room temperature, 20–25 °C) [1 — hypothesis with expected c(CH3COOH), IV, DV].
Stage 1 — Standardise NaOH: (1) Weigh accurately ~0.530 g of anhydrous Na2CO3 on an analytical balance. Dissolve in distilled water and make up to 100.0 mL in a volumetric flask. (2) Pipette 25.00 mL aliquots of Na2CO3(aq) into a conical flask; add 3 drops of phenolphthalein. (3) Fill burette with the NaOH solution to be standardised. Titrate until the pink colour persists for 30 s. Record titre. (4) Repeat to obtain at least two concordant titres (within 0.10 mL). Discard rough. Average concordant titres. Use Na2CO3 + 2NaOH equation — wait: Na2CO3 reacts with HCl not NaOH; for direct standardisation of NaOH against Na2CO3 use Na2CO3(aq) in the burette against HCl — but the question specifies Na2CO3 to standardise NaOH. A correct approach: Na2CO3 can be used to standardise HCl first (Na2CO3 + 2HCl → 2NaCl + H2O + CO2), then use standardised HCl to standardise NaOH. OR use Na2CO3 directly with NaOH not possible (both bases). Award marks for any valid standardisation pathway using Na2CO3 as primary standard leading to c(NaOH) [1 — clear two-step or direct standardisation procedure with at least 4 numbered steps].
Stage 2 — Titrate vinegar: (5) Rinse and fill the burette with the standardised NaOH. Pipette 25.00 mL of vinegar into a conical flask; add phenolphthalein indicator. Titrate until pink endpoint. Record titre. Repeat to concordance. Calculate c(CH3COOH): n(NaOH) = c(NaOH) × V(titre, L); ratio 1:1; c(CH3COOH) = n(NaOH) ÷ V(flask = 0.02500 L) [1 — vinegar in flask, NaOH in burette, correct volume used for each].
Falsification: If c(CH3COOH) differs from 0.833 mol/L by more than the expected measurement uncertainty (e.g. >2%), the hypothesis is falsified and the label claim of 5% acidity is inaccurate [1].
Limitations: (1) Vinegar contains other weak acids (malic acid, tartaric acid trace) that may also react with NaOH and produce a titre slightly larger than expected, overestimating c(CH3COOH) [1]. (2) The phenolphthalein endpoint is observed visually; personal colour-perception differences mean the endpoint may be taken slightly early or late, introducing random error in each titre [1].
Improvement: Repeat the vinegar titration at least three times per aliquot and average concordant titres; alternatively use a pH meter to detect the exact pH 8.3 endpoint (phenolphthalein colour-change mid-range) to remove visual subjectivity [1].
Marking criteria (7 marks): 1 = hypothesis with expected c and IV/DV; 1 = Stage 1 valid standardisation with Na2CO3, at least 4 steps; 1 = Stage 2 correct titration setup (NaOH burette, vinegar flask) and correct volume used for c(CH3COOH); 1 = falsification condition stated; 1 = first valid limitation; 1 = second valid limitation; 1 = improvement that specifically addresses one of the limitations.