Mole and the Avogadro constant $N_A$

• The mole is the SI unit of amount of substance; one mole contains the number of elementary entities specified by the Avogadro constant.

• An elementary entity may be an atom, molecule, ion, electron, another particle or a specified group of particles.

• The Avogadro constant $N_A$ has units $\mathrm{mol^{-1}}$ and its value is supplied in the data booklet.

• Convert amount $n$ into number of entities $N$ using $N=nN_A$.

• Convert number of entities back into amount using $n=\frac{N}{N_A}$.

One mole represents an extremely large number of entities. The scale comparison helps visualize why the mole is useful for connecting microscopic particles with measurable macroscopic quantities. Source

Molar mass $M$: mass, moles and particles

• Molar mass $M$ is the mass of one mole of a substance and has units $\mathrm{g,mol^{-1}}$.

• Convert mass $m$ to amount $n$ using $n=\frac{m}{M}$.

• Rearrange when required: $m=nM$ and $M=\frac{m}{n}$.

• For mass-to-particle questions, first calculate moles using $n=\frac{m}{M}$, then calculate entities using $N=nN_A$.

• Always identify the requested elementary entity before giving the final particle number.

Finding an empirical formula

• Convert the mass of each element into a relative mole amount using $\text{amount}\propto\frac{\text{mass}}{A_r}$.

• For percentage-composition data, treat the percentages as proportional masses and calculate $\text{amount}\propto\frac{\text{percentage by mass}}{A_r}$.

• Divide every resulting amount by the smallest value to obtain the simplest ratio.

• If ratios are close to simple fractions rather than integers, multiply all values by the same small integer and apply sensible approximation.

• For combustion experiments, use measured mass changes to determine the relevant elemental masses before converting them into mole ratios.

• Write the final empirical formula using the resulting simplest whole-number ratio.

Molar concentration and concentration units

• Molar concentration is determined by the amount of solute and the volume of solution.

• Use $n=CV$, where $C$ is molar concentration and $V$ is solution volume.

• Rearrange as $C=\frac{n}{V}$ or $V=\frac{n}{C}$ when required.

• Square brackets represent molar concentration, for example $[\mathrm{X}]$.

• When concentration is in $\mathrm{mol,dm^{-3}}$, use volume in $\mathrm{dm^3}$; convert between $\mathrm{g,dm^{-3}}$ and $\mathrm{mol,dm^{-3}}$ using molar mass $M$.

Avogadro’s law and gas-volume ratios

• Avogadro’s law states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

• At fixed temperature and pressure, gas volume is directly proportional to amount: $V\propto n$.

• Therefore $\frac{V_1}{V_2}=\frac{n_1}{n_2}$ for gases measured under the same conditions.

• For reacting gases under identical conditions, use the required mole ratio to determine the corresponding gas-volume ratio.

• Check that the gases are compared at the same temperature and pressure before applying the relationship.

Relative masses $A_r$ and $M_r$

Empirical formula and molecular formula

Finding a molecular formula

• Begin with the known empirical formula and calculate its formula mass from the relevant $A_r$ values.

• Compare this value with the compound’s given molar mass.

• Calculate the integer multiplier $k=\frac{\text{given molar mass}}{\text{empirical-formula mass}}$.

• The multiplier $k$ should be a positive whole number.

• Multiply every subscript in the empirical formula by $k$ to obtain the molecular formula.

Standard solutions, serial dilution and calibration curves

• For a standard solution, choose volumetric glassware that measures or contains the required volume with appropriate precision.

• For dilution from a stock solution, transfer a measured aliquot with a volumetric pipette and make the solution up to the calibration mark in a volumetric flask.

• A serial dilution repeats a defined dilution step to produce solutions of progressively lower known concentration.

• For a calibration curve, prepare standards of known concentration and measure the relevant experimental response.

• Plot experimental response against known concentration, then use the response of an unknown sample to determine its concentration.

• Accurate volumetric measurements and consistent experimental conditions improve the reliability of the calculated concentration.

A volumetric pipette transfers a measured aliquot while the volumetric flask fixes the final solution volume. Correct transfer, filling to the calibration mark and thorough mixing are central to preparing solutions of known concentration. Source