The mole, Avogadro constant, molar mass, concentration, the ideal gas equation, empirical and molecular formulae, and percentage yield and atom economy.

What this dot point is asking

WJEC wants you to use the mole to relate mass, particles, gas volume and concentration, balance equations and work out reacting quantities, find empirical and molecular formulae, and calculate percentage yield and atom economy.

The answer

The mole and molar mass

The central relationship is $n = m / M$, where $n$ is moles, $m$ is mass and $M$ is molar mass. For particles, $N = n \times N_A$.

Concentration and gas volume

Empirical and molecular formulae

The empirical formula is the simplest whole-number ratio of atoms; the molecular formula is the actual number, a whole-number multiple of the empirical formula found by comparing the empirical mass with the relative molecular mass.

Yield and atom economy

Limiting reagents

When two reactants are mixed in amounts that are not in the exact stoichiometric ratio, one runs out first and limits the amount of product. To find the limiting reagent, calculate the moles of each reactant, divide by its coefficient in the balanced equation, and the smallest value identifies the limiting reagent. All product calculations must then be based on the limiting reagent, not the one in excess. Forgetting to check which reactant limits the reaction is one of the most common errors in quantitative questions.

The ideal gas equation in practice

The equation $pV = nRT$ links the four state variables of a gas. The most frequent mistake is mixing units, so convert before substituting: pressure to pascals (Pa), volume to cubic metres (m$^3$, dividing cm$^3$ by $10^6$), and temperature to kelvin (adding $273$ to degrees Celsius). Rearranged as $n = pV/RT$, it lets you find moles of a gas from its measured pressure, volume and temperature, which can then be combined with a mass to find a molar mass, a standard way to identify an unknown gas.

Examples in context

Titration in quality control. Concentration and mole calculations underpin acid-base titrations used to check the purity of pharmaceuticals and the acidity of foods. Atom economy in industry. Manufacturers favour addition reactions (atom economy near 100 percent) over substitution because waste by-products raise cost and environmental burden, a recurring theme in Unit 2's wider-impact content.

Try this

Q1. Calculate the number of moles in $9.80$ g of sulfuric acid ($M = 98.0$ g mol$^{-1}$). [1 mark]

• Cue. $n = 9.80 / 98.0 = 0.100$ mol.

Q2. Calculate the concentration when $0.250$ mol of solute is dissolved in $500$ cm$^3$ of solution. [1 mark]

• Cue. $c = 0.250 / 0.500 = 0.500$ mol dm$^{-3}$.

Q3. Calculate the atom economy for producing hydrogen from $\text{Zn} + \text{H}_2\text{SO}_4 \rightarrow \text{ZnSO}_4 + \text{H}_2$. [2 marks]

• Cue. $\dfrac{2.0}{2.0 + 161.5} \times 100 = 1.22$ percent (very low, because the zinc sulfate is the bulk by-product).

Q4. State how you identify the limiting reagent in a reaction. [1 mark]

• Cue. Divide the moles of each reactant by its coefficient; the smallest value is the limiting reagent.

Q5. State the units required for pressure, volume and temperature in $pV = nRT$. [1 mark]

• Cue. Pascals, cubic metres and kelvin.