Short Answer
Rule Statement
In the International System of Units (SI), the mole is the unit of amount of substance. Since the 2019 revision, it is defined by fixing the Avogadro constant to exactly 6.02214076 × 1023 mol−1. Therefore one mole contains exactly that many elementary entities. This is a definition, not a measurement. The exactness belongs to the definition and to the count when the entities are counted one by one. It does not transfer to laboratory quantities obtained by weighing, pipetting, or spectroscopy.
Key rule: exact numbers, including defined constants and direct counts, have no rounding uncertainty and do not limit significant figures. Measured numbers do. When you convert a measured mass to moles using molar mass, the result’s significant figures are governed by the measured mass and the uncertainty of the molar mass—not by the exact Avogadro constant.
Convention Comparison Table
| Quantity | Status | Sig-fig treatment | Example |
|---|---|---|---|
| Count of entities | Exact if individually counted | Infinite sig figs | 1000 argon atoms counted directly |
| Avogadro constant NA | Exact by SI definition | Infinite sig figs | 6.02214076×1023 mol−1 |
| Amount from exact count | Exact | No measurement uncertainty | n = N/NA for a counted number N |
| Mass on a balance | Measured | Limits result | 1.000 g carbon-12 |
| Molar mass from periodic table | Measured | Limits result; may have interval uncertainty | 12.011 g/mol for natural carbon |
| Volume in a flask or burette | Measured | Limits result | 25.00 mL solution |
| Amount from measured mass | Measured | Limits result | n = m/M |
Worked Examples
Example 1: Exact count to exact amount
Suppose you have exactly 12 carbon-12 atoms. Count = 12 (exact). NA is exact. Amount n = N/NA = 12 / 6.02214076×1023 = 1.992646…×10−23 mol. Because both inputs are exact, the result is exact as a defined quantity. If displayed in decimal, any rounding is only for presentation; it does not create measurement uncertainty.
Example 2: Measured mass to moles
You weigh 1.000 g of carbon-12 on a balance with 4 significant figures. Molar mass of carbon-12 is 11.9999999958(36) g/mol, effectively 12.000 g/mol to many figures. n = 1.000 g / 12.000 g/mol = 0.08333 mol (4 sig figs). The exact NA is not used yet. If you then convert to atoms: N = n × NA = 0.08333 × 6.02214076×1023 = 5.018×1022 atoms (4 sig figs). The limiting factor is the measured mass, not NA.
Example 3: Natural carbon
For natural carbon, molar mass is 12.011 g/mol (measured, with uncertainty). 1.000 g / 12.011 g/mol = 0.083257… = 0.08326 mol. Then N = 0.08326 × NA = 5.014×1022 atoms. Again, 4 sig figs.
Counter-Examples
Wrong: “NA = 6.022×1023, so it has 4 sig figs.” Correct: NA is exact; the value 6.022×1023 is a rounded textbook approximation. Using it may introduce rounding error, but the constant itself does not limit sig figs.
Wrong: “1 mol of water has a mass of exactly 18.015 g.” Correct: 1 mol is an exact amount only if it is exactly 1 mol by definition; the mass is calculated from the molar mass of water, which is measured (≈18.01528 g/mol with uncertainty). The mass is not exact.
Wrong: “Because the mole is exact, all stoichiometry is exact.” Correct: Stoichiometric coefficients are exact ratios, but real masses, volumes, and concentrations are measured and carry uncertainty.
Wrong: “Use NA to round the final answer.” Correct: NA is exact and never limits significant figures. Round according to the measured input with the fewest significant figures or, more rigorously, propagate uncertainty per GUM.
Standards Citation
The exact status of the mole is specified in the SI Brochure: BIPM, Le Système international d’unités (SI), 9th ed., 2019, Section 2.3.1. It states that the mole is defined by taking the fixed numerical value of the Avogadro constant to be 6.02214076×1023 when expressed in mol−1. NIST SP 330 (2019) reproduces this definition.
For significant figures and rounding, ASTM E29-22, Standard Practice for Using Significant Digits in Test Data to Determine Conformance with Specifications, provides industrial rules for rounding and reporting. ISO 80000-1:2009, Clause 6.4, gives general rounding conventions for quantities and units. The Guide to the Expression of Uncertainty in Measurement (JCGM 100:2008, GUM), Clause 1.2 and Clause 3.1.1, distinguishes exact quantities from measured quantities and requires uncertainty statements for the latter.
Common Mistakes
- Treating the Avogadro constant as a measured value with significant figures.
- Treating molar mass as exact because the mole is exact.
- Using 6.02×1023 as if it were the exact SI value.
- Letting exact conversion factors reduce the significant figures of a result.
- Confusing a count (discrete, exact if counted) with a measurement (continuous, uncertain).
- Rounding intermediate values, including NA, before the final calculation.
- Assuming “exact” means “no uncertainty in the real sample.”
Practice Problems
- How many significant figures should be reported for the number of molecules in 2.50 mol of CO₂? Assume 2.50 mol is a measured amount.
- You count exactly 1000 argon atoms. Express the amount in moles. How many significant figures are justified?
- A 0.2500 g sample of pure carbon-12 is measured. Calculate moles of carbon-12. Use M(¹²C) = 12.000 g/mol to five significant figures.
- Why does using NA = 6.022×1023 instead of the exact value not change the significant-figure count in a typical laboratory calculation?
Answers: 1. Three significant figures (limited by 2.50 mol). 2. n = 1000 / 6.02214076×1023 = 1.660539…×10−21 mol; exact count, so no measurement uncertainty—report as exact or with as many digits as needed. 3. 0.2500 / 12.000 = 0.02083 mol (4 sig figs). 4. Because NA is exact and does not limit sig figs; the rounded textbook value is a presentation approximation, and the measured input still controls the reported precision.
Quick Reference Table
| Quantity or constant | Exact? | Effect on sig figs |
|---|---|---|
| Avogadro constant NA | Yes, by SI definition | None; infinite sig figs |
| 1 mol | Yes, as a defined amount | None if used as exact definition |
| Count of entities | Yes, if individually counted | None; exact count |
| Mass on balance | No | Limits result |
| Molar mass from periodic table | No (mostly) | Limits result; may have interval uncertainty |
| Volume in flask or burette | No | Limits result |
| Amount from measured mass | No | Limits result |
Sources & Further Reading
- BIPM. The International System of Units (SI), 9th ed., 2019. Section 2.3.1.
- NIST. NIST Special Publication 330: The International System of Units (SI), 2019.
- JCGM 100:2008. Evaluation of measurement data — Guide to the expression of uncertainty in measurement (GUM).
- ISO 80000-1:2009. Quantities and units — Part 1: General, Clause 6.4.
- ASTM E29-22. Standard Practice for Using Significant Digits in Test Data to Determine Conformance with Specifications.
For more precision rules, see our related articles on Exact Numbers, Measurement Uncertainty, and Significant Figures.
FAQ
Is one mole exact?
Yes. One mole is defined as containing exactly 6.02214076×10^23 elementary entities. The definition is exact. A laboratory sample said to contain '1 mol' is exact only if that amount is established by definition or exact count; otherwise it is a measured amount with uncertainty.
Does Avogadro’s number have significant figures?
No. The Avogadro constant is exact in the SI. The familiar 6.022×10^23 is a rounded approximation for convenience. It should not be used to limit significant figures.
Why do textbooks use 6.02×10^23?
Because it is compact and sufficient for many introductory calculations. However, for precision work, use the exact value 6.02214076×10^23 mol−1 and let the measured inputs determine the reported significant figures.
Does the exact mole make molar mass exact?
No. Molar masses of real substances are generally measured or derived from measured atomic masses. They carry uncertainty. The exact mole does not make the molar mass of water, carbon, or any other substance exact.
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