Topic 2 of 9
Count atoms, nuclei and nucleons
The mole counts specified entities. Calculate the number of atoms or molecules first, then use their composition to count nuclei, protons, neutrons or electrons.
One mole contains 6.02 × 1023 entities. With amount of substance n, sample mass m, molar mass M and Avogadro constant NA:
N = nNA
NA = 6.02 × 1023 mol-1
Use matching mass units: g with g/mol, or kg with kg/mol. N counts the entity named by the molar mass. It is not automatically the count of every nucleus or nucleon within a molecule.
Separate relative mass from mass and molar mass
Relative atomic mass Ar is the mean atomic mass relative to one twelfth of the mass of a neutral carbon-12 atom. Relative molecular mass Mr is the corresponding ratio for a molecule. Both are dimensionless.
An individual atomic mass ma has a unit such as kg or u; molar mass M has a unit such as kg/mol or g/mol. The familiar numerical correspondence between relative mass and molar mass in g/mol is sufficient for the rounded supplied examples, but it does not give Ar or Mr a g/mol unit.
Worked argon sample
One nucleus per atom, forty nucleons per nucleus
A few times 10-4 mol should contain order 1020 entities. Now take 0.0200 g of pure neutral argon-40, with supplied M = 40.0 g/mol:
N = (5.00 × 10-4)(6.02 × 1023)
= 3.01 × 1020 atoms or nuclei
The same calculation uses 2.00 × 10-5 kg and 0.0400 kg/mol. Each argon-40 nucleus contains 18 protons and 22 neutrons:
| Entity | Calculation | Sample count |
|---|---|---|
| Protons | 18N | 5.418 × 1021 |
| Neutrons | 22N | 6.622 × 1021 |
| Electrons | 18N | 5.418 × 1021 |
| Nucleons | 40N | 1.204 × 1022 |
The electron count uses the stated neutrality. At three significant figures, the proton and neutron totals are 5.42 × 1021 and 6.62 × 1021. Use the supplied molar mass rather than treating mass number 40 as an exact molar-mass measurement.
This stable-isotope counting example is separate from the radioactive models later in the chapter.
A molecule can contain several nuclei
For H2O, supplied Ar(H) = 1.0 and Ar(O) = 16.0 give Mr = 2(1.0) + 16.0 = 18.0, without a unit. Using supplied M = 18.0 g/mol, a 1.80 g sample contains:
Nmolecules = 6.02 × 1022
Nnuclei = 3Nmolecules = 1.806 × 1023
There are three atomic nuclei in each molecule. The molecule count and nucleus count therefore differ even though they describe the same sample.