Counting Atoms

Sources and simplifications

Every reference cited on this site, and every place a figure idealizes the real system.

References

  1. Bureau International des Poids et Mesures (2019). The International System of Units (SI), 9th edition. BIPM. standard Section 2.3.1, the mole; the molar mass of carbon 12 after the 2019 redefinition. (The mole and molar mass)
  2. Flowers, P., Theopold, K., Langley, R., Robinson, W. R. (2019). Chemistry 2e. OpenStax, Rice University. book §1.5 Measurement uncertainty, accuracy, and precision; §3.1 Formula mass and the mole concept; §4.1 Writing and balancing chemical equations; §4.3 Reaction stoichiometry; §4.4 Reaction yields. (The mole and molar mass)
  3. Furió, C., Azcona, R., Guisasola, J. (2002). The learning and teaching of the concepts 'amount of substance' and 'mole': a review of the literature. Chemistry Education Research and Practice 3(3), 277–292. doi:10.1039/B2RP90023H. paper (The mole and molar mass)
  4. Conférence Générale des Poids et Mesures (1971). Resolution 3 of the 14th CGPM (1971): SI unit of amount of substance (mole). BIPM. doi:10.59161/cgpm1971res3e. standard (The mole and molar mass)
  5. Azuma, Y., Barat, P., Bartl, G., et al. (2015). Improved measurement results for the Avogadro constant using a 28Si-enriched crystal. Metrologia 52(2), 360–375. doi:10.1088/0026-1394/52/2/360. paper (The mole and molar mass)
  6. Coursey, J. S., Schwab, D. J., Tsai, J. J., Dragoset, R. A. (2015). Atomic Weights and Isotopic Compositions with Relative Atomic Masses (NIST Standard Reference Database 144). National Institute of Standards and Technology. dataset Isotope masses from the 2020 Atomic Mass Evaluation; representative isotopic compositions. Retrieved 2026-11-10 for Cl, B, Br and Cu. (The mole and molar mass)
  7. Wang, M., Huang, W. J., Kondev, F. G., Audi, G., Naimi, S. (2021). The AME 2020 atomic mass evaluation (II). Tables, graphs and references. Chinese Physics C 45(3), 030003. doi:10.1088/1674-1137/abddaf. paper (The mole and molar mass)
  8. Commission on Isotopic Abundances and Atomic Weights (CIAAW), IUPAC (2024). Isotopic Compositions of the Elements 2024. CIAAW. dataset (The mole and molar mass)
  9. Commission on Isotopic Abundances and Atomic Weights (CIAAW), IUPAC (2024). Standard Atomic Weights. CIAAW. dataset The full table, with intervals for 14 elements. Retrieved 2026-11-10. (The mole and molar mass)
  10. Prohaska, T., Irrgeher, J., Benefield, J., et al. (2022). Standard atomic weights of the elements 2021 (IUPAC Technical Report). Pure and Applied Chemistry 94(5), 573–600. doi:10.1515/pac-2019-0603. paper (The mole and molar mass)
  11. Commission on Isotopic Abundances and Atomic Weights (CIAAW), IUPAC (2024). Abridged Standard Atomic Weights 2024. CIAAW. dataset Based on the Atomic Weights 2021 report, with the 2024 revisions for Gd, Lu and Zr. Retrieved 2026-11-10. (The mole and molar mass)
  12. National Center for Biotechnology Information (2026). PubChem compound records (computed molecular weights). National Library of Medicine. dataset Molecular weights of 35 compounds retrieved 2026-11-10 through the PUG REST interface for the cross-check described on the About page. (The mole and molar mass)
  13. Mohr, P. J., Newell, D. B., Taylor, B. N., Tiesinga, E. (NIST) (2024). CODATA 2022 recommended value: electron relative atomic mass. National Institute of Standards and Technology. dataset (The mole and molar mass)
  14. Lavoisier, A.-L. (1790). Elements of Chemistry, in a New Systematic Order (Traité élémentaire de chimie, 1789), translated by Robert Kerr. William Creech, Edinburgh; Project Gutenberg eBook 30775. book Part I, Chapter XIII, on the vinous fermentation. (Balancing equations)
  15. Yarroch, W. L. (1985). Student understanding of chemical equation balancing. Journal of Research in Science Teaching 22(5), 449–459. doi:10.1002/tea.3660220507. paper (Balancing equations)
  16. Nurrenbern, S. C., Pickering, M. (1987). Concept learning versus problem solving: Is there a difference?. Journal of Chemical Education 64(6), 508. doi:10.1021/ed064p508. paper (Balancing equations)
  17. Sanger, M. J. (2005). Evaluating students' conceptual understanding of balanced equations and stoichiometric ratios using a particulate drawing. Journal of Chemical Education 82(1), 131. doi:10.1021/ed082p131. paper (Balancing equations)
  18. Blakley, G. R. (1982). Chemical equation balancing: A general method which is quick, simple, and has unexpected applications. Journal of Chemical Education 59(9), 728. doi:10.1021/ed059p728. paper (Balancing equations)
  19. Herndon, W. C. (1997). On balancing chemical equations: past and present. Journal of Chemical Education 74(11), 1359. doi:10.1021/ed074p1359. paper (Balancing equations)
  20. Gauchon, L., Méheut, M. (2007). Learning about stoichiometry: from students' preconceptions to the concept of limiting reactant. Chemistry Education Research and Practice 8(4), 362–375. doi:10.1039/B7RP90012K. paper (Stoichiometry and the limiting reactant)
  21. IUPAC Compendium of Chemical Terminology (the Gold Book) (2019). extent of reaction, ξ. International Union of Pure and Applied Chemistry. doi:10.1351/goldbook.E02283. standard (Stoichiometry and the limiting reactant)
  22. Renny, J. S., Tomasevich, L. L., Tallmadge, E. H., Collum, D. B. (2013). Method of continuous variations: applications of Job plots to the study of molecular associations in organometallic chemistry. Angewandte Chemie International Edition 52(46), 11998–12013. doi:10.1002/anie.201304157. paper (Stoichiometry and the limiting reactant)
  23. LibreTexts (2023). 3.7: Limiting Reactants (Chemistry: The Central Science, Brown et al., LibreTexts map). LibreTexts. book 'a yield that appears to be greater than 100% ... usually happens when the product is impure or is wet with a solvent such as water.' Retrieved 2026-11-10. (Stoichiometry and the limiting reactant)
  24. US Environmental Protection Agency, Indoor Air Quality (2026). What is carbon monoxide?. US EPA. institutional CO 'results from incomplete oxidation of carbon in combustion'; gas ranges and unvented heaters as indoor sources. Retrieved 2026-11-10. (Stoichiometry and the limiting reactant)

Simplifications