Stoichiometry is the quantitative language of chemical reactions. Measured amounts (mass, solution volume and concentration, gas volume) become moles, and moles connect through the coefficients of a balanced chemical equation.
Stoichiometry and the mole concept
Chemical equations operate in particle counts, and the mole provides the bridge between laboratory measurements and microscopic entities. The central conversion is \( n = \dfrac{m}{M} \), where \(n\) is amount (mol), \(m\) is mass (g), and \(M\) is molar mass (g·mol\(^{-1}\)).
Coefficients in a balanced equation are mole ratios, not mass ratios. A coefficient “2” in front of a substance means \(2\) mol of that substance in the reaction stoichiometry.
Balanced equations and mole ratios
For a general reaction \[ a\,A + b\,B \rightarrow c\,C + d\,D, \] the stoichiometric relationships are \[ \frac{n_A}{a} = \frac{n_B}{b} = \frac{n_C}{c} = \frac{n_D}{d} \quad (\text{only for amounts that react or form according to the equation}). \]
Any conversion between substances uses a coefficient ratio, such as \[ n_C = n_A \cdot \frac{c}{a}. \]
Common conversion patterns
| Given quantity | Typical conversion to moles | Common target quantity | Typical conversion from moles |
|---|---|---|---|
| Mass \(m\) (g) | \( n = \dfrac{m}{M} \) | Mass \(m\) (g) | \( m = n\,M \) |
| Solution volume \(V\) (L) and molarity \(C\) (mol·L\(^{-1}\)) | \( n = C\,V \) | Required solution volume (L) | \( V = \dfrac{n}{C} \) |
| Gas volume \(V\) (L) at known \(T, P\) | \( n = \dfrac{P\,V}{R\,T} \) | Gas volume (L) | \( V = \dfrac{n\,R\,T}{P} \) |
| Particles (molecules, ions, atoms) | \( n = \dfrac{N}{N_A} \) | Particles | \( N = n\,N_A \) |
Limiting reactant and reaction extent
When more than one reactant amount is specified, only one typically runs out first. That reactant is the limiting reactant; it fixes the maximum amount of product possible under the given conditions (theoretical yield).
A compact limiting-reactant test uses “possible product moles” from each reactant. For product \(C\) in \(aA + bB \rightarrow cC\),
\(A\)-based prediction: \( n_C^{(A)} = n_A \cdot \dfrac{c}{a} \), \(B\)-based prediction: \( n_C^{(B)} = n_B \cdot \dfrac{c}{b} \).
The smaller predicted \(n_C\) identifies the limiting reactant and sets the reaction stoichiometry for all other amounts.
Theoretical yield and percent yield
Theoretical yield is the maximum product amount from stoichiometry (usually based on the limiting reactant). Actual yield is the experimentally obtained amount. Percent yield is \[ \%\text{yield} = \frac{\text{actual yield}}{\text{theoretical yield}} \times 100\%. \]
Stoichiometry visualization: the conversion pathway
Worked example within stoichiometry
Consider the synthesis of aluminum chloride: \[ 2\,\text{Al} + 3\,\text{Cl}_2 \rightarrow 2\,\text{AlCl}_3. \] A sample contains \(10.0\ \text{g}\) Al and chlorine is in large excess. The mass of \(\text{AlCl}_3\) predicted by stoichiometry follows directly from the 1:1 mole ratio between Al and \(\text{AlCl}_3\) in this balanced equation.
Numerical relationships
Moles of aluminum: \[ n(\text{Al}) = \frac{10.0\ \text{g}}{26.98\ \text{g·mol}^{-1}} = 0.3706\ \text{mol}. \]
Mole ratio from coefficients: \( \dfrac{2\ \text{mol AlCl}_3}{2\ \text{mol Al}} = 1\). \[ n(\text{AlCl}_3) = 0.3706\ \text{mol}. \]
Molar mass \(M(\text{AlCl}_3) = 26.98 + 3(35.45) = 133.33\ \text{g·mol}^{-1}\). \[ m(\text{AlCl}_3) = n\,M = (0.3706)(133.33) = 49.4\ \text{g}. \]
Accuracy notes and common pitfalls
- Mole ratio focus: coefficients define stoichiometry; subscripts in formulas define molar mass.
- Limiting reactant logic: the limiting reactant is the one that produces the smaller predicted amount of product.
- Units consistency: grams, liters, and atmospheres or pascals require a single coherent unit system inside \(PV = nRT\).
- Significant figures: the final reported amount typically matches the least precise measured input.
- Yield language: theoretical yield follows stoichiometry; actual yield is experimental; percent yield compares the two.
Stoichiometry remains valid across contexts (solids, solutions, gases) because the balanced equation fixes mole ratios. Differences across contexts appear only in the measurement-to-mole conversion.