Formulae, reacting amounts and reaction efficiency

What you’ll learn

• Determine empirical and molecular formulae from composition.
• Use mole ratios and identify a limiting reactant.
• Distinguish percentage yield from atom economy.

Understand the idea

An empirical formula is the simplest whole-number atom ratio. Divide each elemental mass by its relative atomic mass, then divide all the amounts by the smallest. A ratio such as $1:1.5$ must be multiplied throughout to obtain $2:3$; do not round 1.5 to an integer. Molecular formulae are whole-number multiples of the empirical formula.

A balanced equation specifies mole ratios, so convert reactant masses into moles before comparing them. The limiting reactant gives the smaller product amount when each reactant is used in the equation's ratio. Excess material does not increase the theoretical yield once another reactant is exhausted.

Percentage yield compares actual and theoretical product amounts. Atom economy measures what fraction of reactant mass is incorporated into the desired product in the balanced equation, even if the reaction proceeds perfectly. Count stoichiometric coefficients in its mass totals. A process can have high yield but poor atom economy if it inevitably produces substantial by-products.

Key formulae

$$n_i=\frac{m_i}{A_{r,i}}$$

$$\text{molecular multiplier}=\frac{M_r}{\text{empirical formula mass}}$$

$$\%\text{ yield}=\frac{\text{actual product amount}}{\text{theoretical product amount}}\times100$$

$$\%\text{ atom economy}=\frac{\text{coefficient}\times M_r\text{ of desired product}}{\sum(\text{coefficient}\times M_r)\text{ of reactants}}\times100$$

Worked example

A compound contains $2.40$ g carbon, $0.400$ g hydrogen and $3.20$ g oxygen. Its relative molecular mass is 60. Find its formula. Use $A_r$: C = 12, H = 1, O = 16.

1. Amounts are $2.40/12=0.200$, $0.400/1=0.400$ and $3.20/16=0.200$ mol.
2. Divide by $0.200$ to obtain the ratio $1:2:1$, giving empirical formula $\mathrm{CH_2O}$.
3. The empirical formula mass is $30$, so the molecular multiplier is $60/30=2$.

Answer: Molecular formula $\mathrm{C_2H_4O_2}$.