4.5 Stoichiometry

Stoichiometry is the quantitative bookkeeping of chemical reactions—using a balanced equation’s coefficients as mole ratios to relate amounts of reactants and products. Because atoms are conserved (conservation of mass), you can calculate how many moles (or grams, liters, or molarity) of product form from a given reactant amount, or how much reactant is needed for a desired product. Key ideas: mole concept, molar mass, Avogadro’s number, limiting vs. excess reactant, theoretical and percent yield, and using mole ratios with the ideal gas law or solution molarity for gas/solution problems. Stoichiometry is tested in AP Unit 4 (LO 4.5.A) and appears on both multiple-choice and free-response questions that emphasize mathematical routines, so you’ll want fluency converting units and setting up mole-ratio conversion factors. For targeted review, see the Topic 4.5 study guide (https://library.fiveable.me/ap-chemistry/unit-4/stoichiometry/study-guide/GjwCuhOQRvWLb4rKjYD2) and practice sets (https://library.fiveable.me/practice/ap-chemistry).

Balancing equations is just making sure atoms are conserved so you can use the coefficients as mole ratios in stoichiometry. Quick method: write the unbalanced formulae, count atoms of each element on both sides, and adjust integer coefficients (start with elements that appear once, leave H and O for last). Recount and repeat until all elements match and coefficients are in lowest whole-number ratio. Those coefficients are your stoichiometric coefficients—they give mole ratios used to convert between moles (or mass, volume, molarity) of reactants and products. For problems, convert grams/volume to moles, use the balanced-equation mole ratio, then convert back to desired units; include checks for limiting reactant, theoretical yield, percent yield. This aligns with CED 4.5.A: coefficients give proportional information for calculations. Want more worked examples? See the Topic 4.5 study guide (https://library.fiveable.me/ap-chemistry/unit-4/stoichiometry/study-guide/GjwCuhOQRvWLb4rKjYD2) and practice problems (https://library.fiveable.me/practice/ap-chemistry).

Mole ratios come straight from the balanced equation—the coefficients tell you how many moles of each substance react or form. Treat those coefficients as conversion factors. Quick steps you’ll use on AP stoichiometry problems (Topic 4.5): 1. Balance the equation. Example: 2 H2 + O2 → 2 H2O gives H2:O2: H2O = 2:1:2. 2. Convert your given amount to moles (grams → mol by molar mass; molecules → mol by Avogadro’s number; volume → mol if gas with PV = nRT; or use M × V for solutions). 3. Use the mole ratio (from coefficients) to convert moles of the known substance to moles of the unknown. E.g., 3.00 mol H2 × (1 mol O2 / 2 mol H2) = 1.50 mol O2 needed. 4. Convert moles back to the requested unit (grams, liters, molecules). Mole ratios also tie into limiting reactant, theoretical yield, percent yield, and mix with ideal gas law or molarity in multi-step AP problems (CED 4.5.A.1–4.5.A.3). For more examples and practice, see the Topic 4.5 study guide (https://library.fiveable.me/ap-chemistry/unit-4/stoichiometry/study-guide/GjwCuhOQRvWLb4rKjYD2) and the AP practice question bank (https://library.fiveable.me/practice/ap-chemistry).

Theoretical yield is the maximum amount of product you can make from given reactants using the balanced equation and mole ratios—it assumes the reaction goes perfectly with the limiting reactant fully consumed. Actual (or experimental) yield is what you actually collect in the lab (usually less because of incomplete reactions, side reactions, losses, or measurement error). Percent yield links them: % yield = (actual yield / theoretical yield) × 100%. Example: if theoretical yield is 10.0 g but you isolate 7.5 g, percent yield = (7.5/10.0)×100 = 75%. On the AP, you’ll use the balanced equation, find the limiting reactant, calculate theoretical yield (moles → mass), then compare to experimental mass for percent yield (Topic 4.5 keywords: limiting reactant, theoretical yield, percent yield). For extra practice, check the Topic 4.5 study guide (https://library.fiveable.me/ap-chemistry/unit-4/stoichiometry/study-guide/GjwCuhOQRvWLb4rKjYD2) and more practice problems (https://library.fiveable.me/practice/ap-chemistry).

You always balance the equation first because stoichiometry is just bookkeeping of atoms and moles—atoms are conserved. A balanced equation gives stoichiometric coefficients that tell you exact mole ratios (conversion factors) between reactants and products, so you can convert moles of one substance into moles of another. If the equation isn’t balanced you’ll use the wrong ratios and get wrong answers for limiting reactant, theoretical yield, percent yield, or any mole-based calculation. On the AP exam you’ll be expected to use those coefficients for conversions and to justify amount changes (CED 4.5.A, EK 4.5.A.1–3). For practice, review the Topic 4.5 study guide (https://library.fiveable.me/ap-chemistry/unit-4/stoichiometry/study-guide/GjwCuhOQRvWLb4rKjYD2) and try problems from the Unit 4 page (https://library.fiveable.me/ap-chemistry/unit-4) or the AP practice set (https://library.fiveable.me/practice/ap-chemistry) to get fluent with mole ratios and limiting-reactant setups.

1) Always start with a balanced chemical equation—the stoichiometric coefficients give the mole ratios (CED 4.5.A.2). 2) Convert grams of your given substance to moles: moles = mass (g) ÷ molar mass (g·mol⁻¹). Use the periodic table to get molar mass. 3) Use the mole ratio from the balanced equation to convert moles of the given to moles of the target: moles_target = moles_given × (coef_target / coef_given). 4) Convert moles of the target to grams: mass_target (g) = moles_target × molar mass_target (g·mol⁻¹). Example template: mass A → nA = massA / M_A → nB = nA × (b/a) → massB = nB × M_B. AP tips: always show the balanced equation, include units and sig figs, and check for limiting reactant/theoretical or percent yield when multiple reactants are present (CED keywords). For a quick review, see the Topic 4.5 stoichiometry guide (https://library.fiveable.me/ap-chemistry/unit-4/stoichiometry/study-guide/GjwCuhOQRvWLb4rKjYD2) and practice lots of problems (https://library.fiveable.me/practice/ap-chemistry).

“Atoms must be conserved” means every atom you start with in the reactants still exists in the products—none are created or destroyed. In practice that’s why you must balance chemical equations: the number of each element’s atoms on the left equals the number on the right. Example: 2 H2 + O2 → 2 H2O has 4 H and 2 O on both sides. For AP Chem stoichiometry (CED 4.5.A.1–A.2) balanced equations give stoichiometric coefficients that are mole ratios—those ratios let you calculate product amounts from reactant amounts (and vice versa), find limiting reactants, theoretical yields, and percent yield. This conservation principle underpins mole-conversion factors, ideal-gas and molarity-linked stoichiometry too. Review examples and practice problems in the Topic 4.5 study guide (https://library.fiveable.me/ap-chemistry/unit-4/stoichiometry/study-guide/GjwCuhOQRvWLb4rKjYD2) and more practice at the unit page (https://library.fiveable.me/ap-chemistry/unit-4) or practice problem bank (https://library.fiveable.me/practice/ap-chemistry).

Start with a balanced equation and a clear question. Example: how many grams CO2 form from 16.0 g CH4 in the reaction CH4 + 2 O2 → CO2 + 2 H2O? Step 1—convert given mass to moles: mol CH4 = 16.0 g ÷ 16.04 g·mol⁻¹ = 0.998 mol (use molar mass; show units). Step 2—use the mole ratio (stoichiometric coefficients): from the balanced equation 1 mol CH4 → 1 mol CO2, so mol CO2 = 0.998 mol. Step 3—convert moles product to grams: mass CO2 = 0.998 mol × 44.01 g·mol⁻¹ = 43.9 g CO2 (report with correct sig figs). Notes tied to the CED: always start with a balanced equation, use mole ratios from coefficients (4.5.A.2), show unit conversions and the mole concept (4.5.A.1). For exam free-response, write each step, label units, and state limiting reactant/theoretical yield/percent yield when those are asked. Need more practice? Check the AP Chem Stoichiometry study guide (https://library.fiveable.me/ap-chemistry/unit-4/stoichiometry/study-guide/GjwCuhOQRvWLb4rKjYD2) and try problems at (https://library.fiveable.me/practice/ap-chemistry).

You find the limiting reagent by using the balanced equation and mole ratios. Steps: (1) Balance the reaction. (2) Convert the masses/volumes/concentrations of each reactant to moles. (3) Use the stoichiometric coefficients to compute how many moles of product (or of some other reactant) each reactant could make/consume. (4) The reactant that makes the fewest moles of product (or that runs out first) is the limiting reagent; the other(s) are in excess. Quick tip: you can also divide moles available by the coefficient for each reactant (moles available / stoichiometric coefficient). The smallest result identifies the limiting reagent. That’s exactly the mole-ratio reasoning in CED 4.5.A (use coefficients to relate amounts and calculate product/theoretical yield). Want practice? Work through the stoichiometry study guide on Fiveable (https://library.fiveable.me/ap-chemistry/unit-4/stoichiometry/study-guide/GjwCuhOQRvWLb4rKjYD2) and try problems from the AP unit page (https://library.fiveable.me/ap-chemistry/unit-4) or the practice set (https://library.fiveable.me/practice/ap-chemistry).

Think of coefficients as mole-conversion factors—they tell you the ratio of moles of each substance in a balanced equation. Quick recipe (use for gram → mole → mole ratio → gram, or for gases/solutions with PV=nRT or molarity): 1) Start with given amount (often grams, L gas, or molarity). 2) Convert to moles (grams ÷ molar mass; or for gas use n = PV/RT; or for solution use moles = M × L). 3) Use the balanced equation coefficients as a mole ratio to convert: moles of A × (coefficient of B / coefficient of A) = moles of B. 4) Convert moles of B to the desired units (grams, volume, etc.). Remember to check for limiting reactant if more than one reactant is given (compare moles needed vs available). For AP free-response, show each step, units, and the mole-ratio step clearly—graders expect that (CED 4.5.A.1–4.5.A.3). For extra practice and worked examples, see the Topic 4.5 study guide (https://library.fiveable.me/ap-chemistry/unit-4/stoichiometry/study-guide/GjwCuhOQRvWLb4rKjYD2), the Unit 4 overview (https://library.fiveable.me/ap-chemistry/unit-4), and practice problems (https://library.fiveable.me/practice/ap-chemistry).

Stoichiometry and the ideal gas law connect whenever one (or more) reactants or products is a gas. Use PV = nRT to convert measured gas conditions (P, V, T) into moles (n), then treat those moles like any other quantity in stoichiometric calculations—use the balanced equation and mole ratios to find limiting reactants, theoretical yield, or percent yield. For example, measure CO2 volume at STP → compute nCO2 with PV = nRT → use the reaction’s coefficients to find moles (and mass) of reactant consumed or product formed. You can also work backwards: from grams → moles → predict gas volume or partial pressure. AP CED explicitly expects you to combine stoichiometry with the ideal gas law for gas stoichiometry problems (Topic 4.5). Practice applying this flow—PV = nRT ↔ mole ratio ↔ molar mass—in both MC and free-response questions. For a focused review, see the Topic 4.5 study guide (https://library.fiveable.me/ap-chemistry/unit-4/stoichiometry/study-guide/GjwCuhOQRvWLb4rKjYD2) and try practice problems (https://library.fiveable.me/practice/ap-chemistry).

Molarity is just a way to express how many moles of a solute are in a given volume (M = mol/L), so it plugs straight into stoichiometry problems by giving you moles to use with mole ratios from a balanced equation. Typical steps: (1) convert volume of solution to moles using M × L; (2) use stoichiometric coefficients as mole-ratio conversion factors to find moles of product or other reactant; (3) convert those moles to grams, liters (via ideal gas law), or back to concentration as needed. That’s how titrations and solution stoichiometry are done on the exam: use molarity → moles → mole ratio → desired quantity (CED 4.5.A.2–4.5.A.3; keywords: mole ratio, molarity, solution stoichiometry, ideal gas law). For extra practice and worked examples check the Topic 4.5 study guide (https://library.fiveable.me/ap-chemistry/unit-4/stoichiometry/study-guide/GjwCuhOQRvWLb4rKjYD2), the Unit 4 overview (https://library.fiveable.me/ap-chemistry/unit-4), and lots of practice problems (https://library.fiveable.me/practice/ap-chemistry).

Short answer: your calculated stoichiometric “theoretical yield” is the maximum amount of product predicted by the balanced equation assuming complete reaction and pure reagents—real lab yields almost always fall below that. Common reasons your answers don’t match the theoretical yield: - math/setup errors: equation not balanced, wrong mole ratio, using grams instead of moles, or wrong molar mass (double-check units and sig figs). - limiting reagent mistakes: you must find the limiting reactant before calculating theoretical yield. - state/condition issues: gas or solution problems need PV = nRT or M = n/V conversions. - experimental losses: incomplete reaction, side reactions, impure reagents, product lost during transfer/filtration or drying → these lower actual yield. - reporting errors: percent yield = (actual yield/theoretical yield) × 100%; theoretical must be in the same units as actual. AP exam tip: show balanced equation, all conversions (g ↔ mol), identify limiting reagent, and box your percent yield—the College Board expects the full conversion chain (use CED stoichiometry keywords: mole ratio, limiting reactant, theoretical yield, percent yield). For a step-by-step checklist and practice problems, see the Topic 4.5 study guide (https://library.fiveable.me/ap-chemistry/unit-4/stoichiometry/study-guide/GjwCuhOQRvWLb4rKjYD2) and try more problems at (https://library.fiveable.me/practice/ap-chemistry).

If one reactant is in excess, it means another reactant is limiting—the limiting reactant determines how much product can form (the theoretical yield) because atoms are conserved and coefficients give mole ratios (CED 4.5.A). The excess reactant simply remains after the reaction goes to completion; you can calculate how much is left by: - Convert initial masses/volumes to moles. - Use the balanced equation’s mole ratio to find moles of limiting reactant consumed and moles of excess reactant required. - Subtract required moles from initial moles of the excess to get leftover moles (and convert to g if needed). Example: If equation is A + 2B → C and you start with 1.0 mol A and 3.0 mol B, A is limiting (needs 2.0 mol B but only 3.0 mol B available? actually B excess). Wait—work it each time with mole ratios. Remember to report theoretical yield, then percent yield if you have actual product. For step-by-step practice and AP-aligned examples, see the Topic 4.5 study guide (https://library.fiveable.me/ap-chemistry/unit-4/stoichiometry/study-guide/GjwCuhOQRvWLb4rKjYD2), the Unit 4 overview (https://library.fiveable.me/ap-chemistry/unit-4), and tons of practice problems (https://library.fiveable.me/practice/ap-chemistry).

Think in chains of canceling units. Start by writing what you’re given and what you need, then build a series of conversion factors that cancel units until you’re left with the answer. Step-by-step: 1. Convert any mass/particles/volume/molarity to moles first (g ÷ molar mass; atoms ÷ Avogadro’s number; V_gas → n with PV = nRT; M × L → moles). 2. Use the balanced equation’s stoichiometric coefficients as a mole ratio to go from moles of one substance to moles of another. Example: grams A → mol A → mol B (× coefficient ratio) → grams B. 3. For solutions or gases combine molarity or ideal-gas conversions in the chain (e.g., L solution → mol solute → mol product → grams product). 4. For multi-reactant problems find the limiting reagent by computing product yield from each reactant. The smallest theoretical yield wins. 5. Finish: compute percent yield = (actual ÷ theoretical)×100, and include units and reasonable sig figs. On the AP exam show each conversion factor (molar mass, mole ratios, PV=nRT, M conversions) so graders can follow your math. For more worked examples and practice, check the Topic 4.5 study guide (https://library.fiveable.me/ap-chemistry/unit-4/stoichiometry/study-guide/GjwCuhOQRvWLb4rKjYD2) and thousands of practice problems (https://library.fiveable.me/practice/ap-chemistry).