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AQA GCSE · Question 01.5 · Quantitative chemistry
The student calculated the concentration of sodium chloride in the salt solution. Table 1 shows the results.
The percentage by mass of sodium ions in sodium chloride is 39.3%.
Calculate the mean concentration of sodium ions in the salt solution.
The student calculated the concentration of sodium chloride in the salt solution. Table 1 shows the results.
The percentage by mass of sodium ions in sodium chloride is 39.3%.
Calculate the mean concentration of sodium ions in the salt solution.
How to approach this question
This is a multi-step calculation.
1. First, you need to calculate the mean concentration of sodium chloride. Look at the four trial results. Is there an anomalous result that should be excluded before calculating the mean? An anomaly is a result that does not fit the pattern of the others.
2. Calculate the mean of the remaining (concordant) results.
3. The question asks for the mean concentration of *sodium ions*, not sodium chloride. Use the percentage by mass given (39.3%) to find the concentration of just the sodium ions.
4. Convert the percentage to a decimal (divide by 100) and multiply it by the mean concentration of sodium chloride.
5. Give your final answer to an appropriate number of significant figures (usually 3 s.f. in chemistry calculations unless specified otherwise).
Full Answer
**Step 1: Identify and exclude the anomalous result.**
The results are 35.2, 34.6, 36.4, and 33.8.
The mean of all four is (35.2 + 34.6 + 36.4 + 33.8) / 4 = 35.0 g/dm³.
The result 36.4 is furthest from the mean, so it is the anomaly.
**Step 2: Calculate the mean concentration of sodium chloride from the concordant results.**
Mean = (35.2 + 34.6 + 33.8) / 3
Mean = 103.6 / 3
Mean = 34.533... g/dm³
**Step 3: Calculate the mean concentration of sodium ions.**
Concentration of Na⁺ = Mean concentration of NaCl × Percentage by mass of Na⁺
Concentration of Na⁺ = 34.533... g/dm³ × 39.3%
Concentration of Na⁺ = 34.533... × (39.3 / 100)
Concentration of Na⁺ = 34.533... × 0.393
Concentration of Na⁺ = 13.571... g/dm³
**Step 4: Round to an appropriate number of significant figures.**
The data is given to 3 significant figures, so the answer should be too.
Mean concentration = 13.6 g/dm³
This calculation requires careful data handling and percentage calculation.
1. **Identify Anomalies:** The results are 35.2, 34.6, 36.4, 33.8. To identify an anomaly, we look for the value that is furthest from the others. The range of the three lowest values is 35.2 - 33.8 = 1.4. The value 36.4 is 1.2 away from the next closest value (35.2). It is considered anomalous and should be excluded from the mean calculation to improve accuracy.
2. **Calculate Mean:** The mean of the concordant results is calculated: (35.2 + 34.6 + 33.8) / 3 = 103.6 / 3 = 34.533... g/dm³. This is the mean concentration of the entire sodium chloride compound.
3. **Calculate Percentage:** The question asks for the concentration of sodium ions only. We are told sodium ions make up 39.3% of the mass of sodium chloride. We need to find 39.3% of our calculated mean concentration.
39.3% of 34.533... = (39.3 / 100) * 34.533... = 0.393 * 34.533... = 13.571... g/dm³.
4. **Significant Figures:** The input data is given to 3 significant figures, so the final answer should also be rounded to 3 significant figures: 13.6 g/dm³.
Common mistakes
✗ Forgetting to exclude the anomalous result (36.4) before calculating the mean.
✗ Calculating the mean correctly but forgetting to calculate the concentration of sodium ions (the final step).
✗ Errors in percentage calculation (e.g., multiplying by 39.3 instead of 0.393).
✗ Rounding the answer to the wrong number of significant figures.
Practice the full AQA GCSE Chemistry Higher Tier Paper 2
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