Chemistry • Year 11 • Module 2 • Lesson 1
The Mole Concept
Build HSC Band 5–6 extended-response technique by evaluating real mole data, appraising a media claim, and reasoning about NA in historical and contemporary contexts.
1. Data + scenario: Loschmidt’s 1865 measurement of Avogadro’s number (Band 5–6)
8 marks Band 5–6
Scenario. In 1865, Austrian physicist Josef Loschmidt became the first person to estimate the number of molecules in a given volume of gas. He used measurements of the mean free path of gas molecules and the ratio of molecular volume to gas volume to estimate what we now call Avogadro's number. His estimate was approximately 4.0 × 1023 mol−1. The currently accepted value (since 2019) is NA = 6.02214076 × 1023 mol−1, fixed exactly as a defining constant of the SI. The table below compares values of NA from key historical measurements.
| Year | Scientist / Method | Value of NA (mol−1) | Relative error vs accepted value |
|---|---|---|---|
| 1865 | Loschmidt — mean free path | 4.0 × 1023 | ∼−34% |
| 1908 | Perrin — Brownian motion | 6.5 × 1023 | ∼+8% |
| 1917 | Millikan — oil drop (combined) | 6.064 × 1023 | ∼−0.3% |
| 1974 | X-ray crystallography (silicon) | 6.0220 × 1023 | <0.01% |
| 2019 | BIPM redefinition — fixed constant | 6.02214076 × 1023 | 0 (exact) |
Illustrative data. Values rounded for clarity. BIPM = Bureau International des Poids et Mesures. Relative error = (measured − accepted) / accepted × 100.
Q1. Analyse and evaluate the historical data above on the measurement of Avogadro's number. In your response you must:
- Describe the trend in accuracy of NA measurements over time, using at least three specific values from the table as evidence.
- A sample of helium contains 2.500 mol of atoms. Calculate the number of helium atoms using the 2019 accepted value of NA, and then recalculate using Loschmidt’s 1865 estimate (4.0 × 1023 mol−1). Compare the two answers and explain the practical significance of the difference for particle-count calculations.
- Evaluate whether the 2019 redefinition of the mole (fixing NA as an exact constant) has any practical effect on standard Year 11 mole calculations. Justify your answer with at least one calculation example.
- Identify one advantage of defining NA as a fixed constant rather than tying it to a physical artefact such as a carbon-12 sample.
- State one limitation of using X-ray crystallography (1974 method) to determine NA.
2. Source critique — evaluate a media claim about Avogadro’s number (Band 5–6)
7 marks Band 5–6
“Avogadro’s number is simply 6.022 × 1023. This means that if you have one gram of any substance, it will always contain exactly Avogadro’s number of atoms. This is why the mole is so useful — it makes every gram of every element contain the same number of atoms, which is what connects chemistry to the real world.”
— Year 11 student blog post, 2024. Name withheld.
Q2. The claim above contains a significant scientific error. In your response you must:
- Identify the specific scientific flaw in the claim and explain why it is incorrect, with precise reference to the definitions of the mole and Avogadro's number.
- A sample of carbon contains 0.0833 mol of atoms, and a sample of iron contains 0.0179 mol of atoms — each obtained from exactly 1 gram of the respective element using information beyond this lesson. Using N = n × NA, calculate N for each sample. Show all working. Use your results as evidence that equal masses of different elements do NOT contain equal numbers of atoms, and explain why neither answer equals NA.
- Write a corrected version of the claim that accurately describes the relationship between the mole, Avogadro's number, and mass.
- Describe one simple experiment a Year 11 student could perform to demonstrate that equal masses of different elements contain different numbers of atoms.
Q1 — Sample Band 6 response (8 marks), annotated
Trend in accuracy [1]: The accuracy of NA measurements improved dramatically over time. Loschmidt (1865) obtained 4.0 × 1023, approximately 34% below the accepted value. Perrin (1908) improved this to 6.5 × 1023 (+8%), demonstrating a significant gain using Brownian motion. Millikan’s combined estimate (1917) reached 6.064 × 1023, within 0.3% of the accepted value. By 1974, X-ray crystallography gave 6.0220 × 1023, accurate to better than 0.01%. In 2019, NA was fixed exactly at 6.02214076 × 1023 mol−1, removing measurement uncertainty entirely. The overall trend is a monotonic increase in precision over approximately 150 years.
Calculation — accepted value [1]: n = 2.500 mol; NA = 6.022 × 1023 mol−1. N = 2.500 × 6.022 × 1023 = 1.506 × 1024 atoms.
Calculation — Loschmidt (1865) [1]: N = 2.500 × 4.0 × 1023 = 1.0 × 1024 atoms. This is ~33% fewer than the accepted-value answer. Practical significance: using Loschmidt’s estimate would cause particle-count calculations to underestimate by about one-third, which would lead to incorrect predictions of how many entities are reacting — a fundamental error in any stoichiometric context.
Effect of 2019 redefinition [1]: The 2019 redefinition has no practical effect on Year 11 calculations. The value of NA changed by less than 1 part in 108 (from the pre-2019 measured value). For example, n = 9.033 × 1023 ÷ 6.022 × 1023 = 1.500 mol is identical to 4 significant figures before and after the redefinition. Any Year 11 calculation rounded to 3–4 significant figures is unaffected.
Advantage of fixed constant [1]: Defining NA as an exact numerical constant means the mole is reproducible anywhere in the universe without reference to a physical artefact (such as a carbon-12 sample that could be contaminated, destroyed, or whose mass could drift due to isotopic impurities). This makes the SI system more stable and self-consistent.
Limitation of X-ray crystallography [1]: X-ray crystallography requires a pure, defect-free crystal (e.g. silicon). Real crystals contain lattice defects and impurities that alter the unit cell volume, introducing systematic error. Also, the technique relies on knowing the molar mass and crystal structure precisely — errors in either propagate into the NA estimate.
Marking criteria (8 marks): 1 = trend described quantitatively with at least 3 data points; 1 = correct N for 2.500 mol He using accepted NA (N = 1.506 × 1024); 1 = correct N using Loschmidt value (N = 1.0 × 1024) with correct comparison; 1 = valid practical significance of difference stated; 1 = evaluates 2019 redefinition as having no practical effect on Year 11 calculations with example; 1 = names one genuine advantage of fixed constant; 1 = states one valid limitation of crystallography method; 1 = uses precise chemical terminology throughout (NA, mol−1, mole, significant figures, systematic error).
Q2 — Sample Band 6 response (7 marks), annotated
Flaw [1]: The claim that “every gram of every substance contains exactly NA atoms” is incorrect. One mole of any substance contains NA = 6.022 × 1023 entities, but one gram is NOT the same as one mole (except for hydrogen-1). The number of moles in one gram depends on the substance. The claim conflates mass (grams) with amount (moles); they are different quantities linked by molar mass, which varies between elements.
Calculation — carbon [1]: Given n(C) = 0.0833 mol (from 1 g of C, provided). N(C) = n × NA = 0.0833 × 6.022 × 1023 = 5.01 × 1022 atoms.
Calculation — iron [1]: Given n(Fe) = 0.0179 mol (from 1 g of Fe, provided). N(Fe) = n × NA = 0.0179 × 6.022 × 1023 = 1.08 × 1022 atoms.
Evidence from calculations [1]: 1.000 g of C contains 5.01 × 1022 atoms; 1.000 g of Fe contains only 1.08 × 1022 atoms. Neither equals NA = 6.022 × 1023. The carbon sample has approximately 4.6 times as many atoms as the iron sample for the same 1-gram mass, demonstrating that equal masses of different elements do NOT contain equal numbers of atoms. NA entities are only present when n = 1 mol exactly.
Corrected claim [1]: Avogadro’s number NA = 6.022 × 1023 is the number of entities in exactly one mole of any substance. One gram of a substance is NOT one mole (unless the substance has a molar mass of 1 g/mol). Therefore the number of atoms in a 1-gram sample differs between elements: the carbon sample (n = 0.0833 mol) contains far more atoms than the iron sample (n = 0.0179 mol), even though both have the same mass. The mole — not the gram — is the quantity that always contains NA entities.
Demonstration experiment [1]: Any valid qualitative or quantitative experiment that distinguishes atom count from mass — for example, noting that 1 g of neon contains a different number of atoms than 1 g of argon (both noble gases, so only the mole concept distinguishes them). Alternatively, accept: dissolving 1 g of two different metals in acid and measuring gas volume (different volumes indicate different atom counts despite equal masses). Credit any experiment linked explicitly to comparing n or N for equal masses of different substances.
Marking criteria (7 marks): 1 = correctly identifies the flaw (1 gram ≠ 1 mole; NA entities are per mole, not per gram); 1 = correct calculation for C with working shown (N = 5.01 × 1022); 1 = correct calculation for Fe with working shown (N = 1.08 × 1022); 1 = explicit comparison showing neither equals NA and C has more atoms than Fe per gram; 1 = corrected claim accurately describes the mole (1 mol = NA entities; 1 gram ≠ 1 mol for most substances); 1 = valid demonstration experiment described with a logical link to atom count vs mass; 1 = precise language throughout (mole, amount of substance, NA).