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1. Stoichiometry

Stoichiometry is the accounting system of chemistry: it uses the mole ratios in a balanced equation to convert between amounts of reactants and products. Every calculation below runs through the same three-step map — grams to moles, moles to moles, moles back to grams.

The Mole and Molar Mass

One mole contains $6.022 \times 10^{23}$ particles (Avogadro's number). The molar mass $M$ of a substance converts between grams and moles: $$n = \frac{m}{M}$$

Example: How many moles are in 18.0 g of water? $$n = \frac{18.0\ \text{g}}{18.02\ \text{g/mol}} = 0.999\ \text{mol} \approx 1.00\ \text{mol}$$

Mole Ratios from Balanced Equations

For the reaction $2\,\text{H}_2 + \text{O}_2 \rightarrow 2\,\text{H}_2\text{O}$, the mole ratio $\frac{2\ \text{mol H}_2\text{O}}{2\ \text{mol H}_2}$ lets you convert a known amount of hydrogen into an amount of water.

Example: What mass of water forms from 8.0 g of $\text{H}_2$? $$8.0\ \text{g H}_2 \times \frac{1\ \text{mol}}{2.02\ \text{g}} \times \frac{2\ \text{mol H}_2\text{O}}{2\ \text{mol H}_2} \times \frac{18.02\ \text{g}}{1\ \text{mol}} = 71\ \text{g H}_2\text{O}$$

Limiting Reactant

When two reactant amounts are given, convert each to moles of product — the smaller result identifies the limiting reactant, which caps the yield.

Example: For $\text{N}_2 + 3\,\text{H}_2 \rightarrow 2\,\text{NH}_3$, 10.0 g $\text{N}_2$ needs $10.0 \times \frac{3(2.02)}{28.02} = 2.16$ g $\text{H}_2$. With only 1.5 g $\text{H}_2$ available, hydrogen limits, and the maximum ammonia is $$1.5\ \text{g H}_2 \times \frac{1\ \text{mol}}{2.02\ \text{g}} \times \frac{2\ \text{mol NH}_3}{3\ \text{mol H}_2} \times \frac{17.03\ \text{g}}{1\ \text{mol}} = 8.44\ \text{g NH}_3$$

Percent Yield

$$\text{Percent yield} = \frac{\text{actual yield}}{\text{theoretical yield}} \times 100\%$$ If the reaction above produced 6.90 g of ammonia, the percent yield is $\frac{6.90}{8.44} \times 100\% = 81.8\%$.

Practice Problems

How many moles are in 45.0 g of glucose, C₆H₁₂O₆? (M = 180.16 g/mol)
For 2 Al + 3 Cl₂ → 2 AlCl₃, what mass of AlCl₃ forms from 5.00 g of Al?
If 6.00 g of H₂ reacts with 40.0 g of O₂ to make water, which is limiting and what is the theoretical yield?
A reaction has a theoretical yield of 25.0 g but produces 18.5 g. Find the percent yield.