Rucete ✏ AP Chemistry In a Nutshell
5. Stoichiometry
This chapter introduces the quantitative relationships in chemical reactions, allowing chemists to calculate reactant and product quantities, determine formulas, and perform titration or limiting-reactant analysis using dimensional analysis.
Dimensional Analysis Method
• Uses conversion factors to transform units without changing quantities.
• Conversion factors are derived from defined equalities (e.g., 1 yard = 36 inches).
• Always cancel units and ensure only the desired unit remains.
Metric Units and Prefixes
• SI base units include kilogram (kg), meter (m), second (s), kelvin (K), mole (mol), etc.
• Prefixes like kilo-, milli-, micro-, nano- modify base units for convenience (e.g., 1 cm = 1 × 10⁻² m).
Converting Complex Units
• For square/cubic units, apply the conversion factor multiple times (e.g., m² → cm²).
• For compound units like m/s or kg·m²/s², convert numerator and denominator separately.
The Mole and Avogadro’s Constant
• 1 mol = 6.02 × 10²³ particles (atoms, molecules, formula units).
• Used to count particles and relate chemical quantities in reactions.
Molar Mass
• For elements: molar mass = atomic mass in grams (e.g., C = 12.01 g/mol).
• For compounds: sum of the atomic masses of all atoms in the formula.
• Enables conversion between grams ↔ moles.
Conversion Factors from Formulas
• Chemical formulas provide ratios to construct conversion factors (e.g., C₁₂H₂₂O₁₁ → 12 mol C/mol compound).
• Multiply by Avogadro’s constant for mole-to-particle conversions.
Conversion Factors from Balanced Equations
• Mole ratios between reactants and products are derived from balanced equations.
• Used for inter-substance conversions (e.g., mol A → mol B).
Molarity and Density as Conversion Factors
• Molarity (mol/L) is used for solution stoichiometry.
• Density (g/cm³ or g/mL) converts between volume and mass.
• 1 mol of ideal gas at STP occupies 22.4 L.
Stoichiometric Conversion Sequence
• Steps: grams → moles → mole ratios → moles → grams.
• Diagram-based flow helps visualize sequence and required conversion factors.
One-Substance Conversions
• Use molar mass or molarity to convert grams ↔ moles or L ↔ moles.
• Examples include grams to moles, liters to moles, molarity × volume.
Two-Substance Conversions
• Must include mole-to-mole step using balanced equation.
• Example: grams A → moles A → moles B → grams B.
Limiting Reactant
• The reactant completely consumed first limits the reaction.
• Determine by calculating how much of the other reactant is needed.
• All product and excess reactant calculations must be based on the limiting reactant.
Theoretical Yield
• Maximum amount of product that can form from given reactants.
• Calculated from limiting reactant using mole ratios and molar masses.
Converting Complex Units
• Square and cubic conversions require applying the conversion factor multiple times (e.g., twice for m² → cm², three times for m³ → cm³).
• For compound units like m/s or kg·m²/s², convert numerator and denominator units separately.
Chemical Equalities and Equivalences
• Equalities allow creation of conversion factors (e.g., 1 mol = 6.02 × 10²³ particles).
• Equivalences can be interpreted chemically, even if they’re not strict mathematical equalities.
The Mole and Avogadro’s Constant
• 1 mol = 6.02 × 10²³ atoms, molecules, or formula units.
• Use “n” as the variable for moles in equations.
Molar Mass
• Molar mass = sum of atomic masses in a compound, in g/mol.
• Atomic mass and molar mass values are used to convert between mass and moles.
Mole Relationships in Formulas
• Each chemical formula represents fixed ratios of atoms or ions.
• These relationships can be scaled to moles to construct conversion factors.
Mole Relationships in Equations
• Balanced chemical equations yield mole ratios (e.g., 2H₂ + O₂ → 2H₂O means 2 mol H₂ reacts with 1 mol O₂).
Concentration and Density
• Molarity (M) = moles of solute / liters of solution.
• Density (g/mL) is used to convert between volume and mass of substances.
Gas Volume at STP
• 1 mol of gas occupies 22.4 L at STP (0 °C, 1 atm).
Stoichiometric Conversion Sequence
• Step-by-step logic using conversion factors: mass ↔ moles ↔ particles ↔ volume ↔ concentration.
• Most problems involve 1 to 3 steps (e.g., mass → moles → moles → mass).
Calculations Involving One Substance
• Mass ↔ Moles (via molar mass)
• Moles ↔ Volume (via molarity or gas volume at STP)
• Examples include converting between grams, liters, and moles.
Calculations Involving Two Substances
• Use mole-to-mole conversions from balanced chemical equations.
• Often involve mass A → mol A → mol B → mass B.
• Practice estimating answers using approximate multiples (1/5× to 5× rule).
Limiting-Reactant Calculations
• When two reactant quantities are given, determine which limits the reaction by converting one into the needed quantity of the other.
• The limiting reactant is completely used; excess reactants remain after the reaction.
• All subsequent calculations must use the limiting reactant as the base.
Percent Yield
• Percent yield = (actual yield / theoretical yield) × 100%
• Actual yield: amount of product actually obtained from the experiment.
• Theoretical yield: amount predicted using stoichiometry and limiting reactant.
Empirical Formulas
• Show the simplest whole-number ratio of atoms in a compound.
• Convert mass % → grams → moles → simplest ratio.
• If needed, multiply all subscripts by a small whole number to eliminate fractions.
Molecular Formulas
• Actual formula showing the number of each atom in a molecule.
• Molecular formula = (empirical formula) × n
• Use molar mass to determine n = (molar mass / empirical mass).
Titrations
• Used to determine unknown concentration of a solution.
• A solution of known concentration (titrant) is added to a solution of unknown concentration until the reaction reaches equivalence.
• Often uses acid–base neutralization reactions.
Back Titration
• Used when the analyte is not directly titratable.
• Add excess of a known reagent to react completely with the analyte, then titrate the remaining unreacted reagent.
Gravimetric Analysis
• Involves forming and isolating a solid precipitate.
• Filter, dry, and weigh the precipitate to determine the amount of a component in the original sample.
Gas Stoichiometry
• Use PV = nRT when gas is not at STP.
• Convert volume ↔ moles ↔ mass using the ideal gas law.
• Often used in combustion or decomposition reactions involving gases.
In a Nutshell
Stoichiometry allows chemists to relate quantities in chemical reactions using mole ratios, limiting reactants, and dimensional analysis. Mastery of molar mass, concentration, gas laws, and yield calculations enables precise control over laboratory outcomes and real-world applications in industrial chemistry.