Lesson 2 of 5
Particles, moles and mass
I can state the mole in terms of particle number, use the Avogadro constant and N = nN_A, and establish Nk = nR.Syllabus
Syllabus 9478, 12(d). State the mole in terms of particle number, use the Avogadro constant and N = nN_A, and establish Nk = nR.
Make a guess. You are not marked.
Which contains more molecules: 2.0 g of hydrogen gas (H2) or 32 g of oxygen gas (O2)?
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They contain the same number, because each is one mole.
H2 has molar mass 2.0 g/mol and O2 has 32 g/mol, so each sample is 1.0 mol. One mole of anything contains 6.02 x 1023 particles.
Specify what you are counting. For a molecular gas, the gas particles are molecules; counting every atom inside those molecules gives a different number.
Connect an amount to a particle count
N is the number of specified particles and is dimensionless. n is the amount of substance, measured in mol. One mole contains the Avogadro number of specified entities. Using the supplied rounded Avogadro constant:
N = nNA
The unit mol cancels with mol-1, leaving a count. Before a precise calculation, roughly half a mole already suggests order 1023 particles. A result of only a few hundred particles would be inconsistent with that amount.
Distinguish mass quantities
Relative atomic mass Ar compares the average mass of an atom with one twelfth of the mass of a carbon-12 atom. Relative molecular mass Mr compares the mass of a molecule with that same reference. Both are ratios and have no unit.
Molar mass M is mass divided by amount, in kg/mol. It is different from the mass m of one particle, in kg. A sample's mass is the mass of all its particles together.
Worked molecular count
A 0.0160 kg oxygen sample
Use the supplied values Ar(O) = 16.0, Mr(O2) = 32.0 and M(O2) = 0.0320 kg/mol. The relative masses are dimensionless; the molar mass has a unit.
| Quantity | Calculation and result |
|---|---|
| Amount of O2 | 0.0160 / 0.0320 = 0.500 mol of molecules |
| Molecule count | 0.500 × 6.02 × 1023 = 3.01 × 1023 |
| Atom count | 2 × 3.01 × 1023 = 6.02 × 1023 |
The molecular ideal-gas equation uses 3.01 × 1023 molecules as N. The two atoms in each O2 molecule are not two independent gas particles in this model.
Check your understanding
An oxygen sample has mass 0.0160 kg and supplied molar mass 0.0320 kg/mol. Using N_A = 6.02 x 1023 mol-1, what particle number N belongs in pV = NkT for this molecular gas?
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3.01 x 1023 oxygen molecules.
n = 0.0160/0.0320 = 0.500 mol of molecules, so N = nN_A = 3.01 x 1023 molecules. There are twice as many atoms, but they are not independent gas particles in this model.
Move between particle and mole equations
The Boltzmann constant k relates energy per particle to temperature. The molar gas constant R uses amount in moles instead. With supplied rounded values:
R = 8.31 J/(mol K)
R = NAk
Substitute N = nNA:
Thus pV = NkT and pV = nRT describe the same particle count. Use either N with k or n with R; pairing N with R counts the mole conversion twice. Small numerical differences from separately rounded constants are rounding effects.