Balancing equations and mole ratios
A balanced chemical equation is a recipe. Its coefficients give the mole ratios needed to predict how much product forms.
Conservation of mass
Atoms are neither created nor destroyed in chemical reactions, so every atom on the reactant side must appear on the product side. Balancing an equation means choosing coefficients so that each element's atom count matches. Subscripts in formulas must never be changed, since that would change the substances.
Balancing step by step
Balance \(\text{CH}_4 + \text{O}_2 \to \text{CO}_2 + \text{H}_2\text{O}\). Carbon: already 1 each. Hydrogen: 4 on the left, so put 2 in front of \(\text{H}_2\text{O}\). Oxygen: now 4 on the right (\(2 + 2\)), so 2 in front of \(\text{O}_2\). Result: \(\text{CH}_4 + 2\text{O}_2 \to \text{CO}_2 + 2\text{H}_2\text{O}\).
\text{CH}_4 + 2\text{O}_2 \to \text{CO}_2 + 2\text{H}_2\text{O}Tips for balancing
Start with the most complex molecule, balance elements that appear in only one reactant and one product first, leave free elements like \(\text{O}_2\) or \(\text{H}_2\) for last, and use fractions temporarily if needed, then multiply through. Check every element at the end.
Mole ratios
Coefficients give mole ratios. In \(\text{N}_2 + 3\text{H}_2 \to 2\text{NH}_3\), 1 mole of nitrogen reacts with 3 moles of hydrogen to give 2 moles of ammonia. These ratios are the bridge between amounts of different substances in a reaction.
Mass-to-mass calculations
Grams of A \(\to\) moles of A (divide by molar mass) \(\to\) moles of B (mole ratio) \(\to\) grams of B (multiply by molar mass). How much ammonia forms from 28.0 g of \(\text{N}_2\)? \(28.0/28.0 = 1.00\) mol \(\text{N}_2\), giving 2.00 mol \(\text{NH}_3\), or \(2.00 \times 17.0 = 34.0\) g.
Worked example: combustion of propane
\(\text{C}_3\text{H}_8 + 5\text{O}_2 \to 3\text{CO}_2 + 4\text{H}_2\text{O}\). Burning 44.0 g of propane (1.00 mol) produces 3.00 mol \(\text{CO}_2\), which is \(3.00 \times 44.0 = 132\) g of carbon dioxide: three times the mass of fuel burned, because oxygen from the air is added.
Reactions in solution
For solutions, moles = molarity \(\times\) volume. If 0.100 L of 0.500 M HCl reacts with NaOH in a 1 : 1 ratio, 0.0500 mol of NaOH is needed. Titrations use this to find unknown concentrations precisely.
Common mistakes
Changing subscripts to balance equations. Using mass ratios instead of mole ratios. Forgetting to convert back to grams at the end. Misreading coefficients as applying to only part of a formula.
Key takeaways
Balanced equations conserve atoms; only coefficients may change. Coefficients give mole ratios. The standard path is grams \(\to\) moles \(\to\) mole ratio \(\to\) moles \(\to\) grams. For solutions, moles equal molarity times volume.
Flashcard
Atoms are rearranged, not created or destroyed
Check your understanding
What coefficient balances: 2H2 + O2 -> ? H2O