4.3.2.1 - Moles, masses and particle numbers

Amount of substance in moles (Higher)

Chemists need a practical way to count particles that are too small and numerous to count individually.

The amount of substance is measured in moles, with unit symbol $\mathrm{mol}$. One mole is a fixed number of specified particles, rather as a dozen is a fixed number of objects. A mole is vastly larger than a dozen: approximately $6.02\times10^{23}$ particles. Specify what is counted: atoms, molecules, ions, electrons or formula units can all be counted in moles.

One mole of carbon atoms contains the same number of atoms as one mole of carbon dioxide contains molecules. Their masses differ because each carbon dioxide molecule contains a carbon atom and two oxygen atoms. Equal amounts in moles mean equal numbers of the stated particles, not equal masses or equal numbers of all atoms inside those particles.

For carbon, the stated particle is an atom. For oxygen gas, $\ce{O2}$, it is usually a molecule. For sodium chloride, $\ce{NaCl}$, a formula unit represents one sodium ion for every chloride ion in the lattice; it is not a separate sodium chloride molecule. Amounts in moles can also describe the coefficients in chemical equations, allowing tiny particle ratios to predict measurable laboratory quantities.

Converting between mass and moles (Higher)

The mass of one mole in grams is numerically equal to the substance's relative formula mass.

$M_r$ itself is a relative number with no unit. Molar mass is mass per mole and has unit $\mathrm{g\,mol}^{-1}$. Water has $M_r=18$, so its molar mass is $18\,\mathrm{g\,mol}^{-1}$. Carbon has $A_r=12$, so 1 mol of carbon atoms has mass 12 g. A heavier particle gives a heavier mole because a mole always contains the same number of stated particles.

For 8.80 g carbon dioxide, using $A_r(\ce{C})=12$ and $A_r(\ce{O})=16$:

The mass is one fifth of the mass of one mole, so the amount is one fifth of a mole.

To find the mass of $0.150\,\mathrm{mol}$ sodium carbonate, $\ce{Na2CO3}$, use $A_r(\ce{Na})=23$, $A_r(\ce{C})=12$, $A_r(\ce{O})=16$:

Multiplying amount by mass per mole gives mass in grams. If a 9.60 g pure sample contains 0.240 mol, molar mass can instead be recovered:

Its corresponding relative formula mass is 40.0, without the molar-mass unit.

Convert kilograms to grams before using these molar masses. For example, $0.00880\,\mathrm{kg}=8.80\,\mathrm{g}$. Use the mass of the specified pure substance: an impure sample's total mass also includes material outside that substance's formula. Carry extra calculator digits through a calculation and round the final answer to a sensible number of significant figures or the number requested.

The Avogadro constant and particle numbers (Higher)

The Avogadro constant connects a measurable amount in moles to an actual number of particles.

Use the approximate value $N_A=6.02\times10^{23}\,\mathrm{mol}^{-1}$. In standard form, $6.02\times10^{23}$ means 6.02 multiplied by ten to the power 23. The exponent expresses scale; it is not an extra multiplier of 23.