Chapter Review

Basic Concepts

Mole Concept and Molar Mass · Stoichiometry and Mole Ratios · Limiting Reactant and Yield

The Mole — A Chemical Counting Unit

The mole is the SI unit for amount of substance, defined as exactly particles. Like a dozen always means 12, a mole always means the same particle count — but the mass differs per substance.

Key Points

  • •
    Gram atom: atomic mass in grams = 1 mole of atoms (e.g., 23 g Na = 1 mol Na atoms)
  • •
    Gram molecule: molecular mass in grams = 1 mole of molecules (e.g., 18 g H₂O = 1 mol H₂O)
  • •
    Gram formula: formula mass in grams = 1 mole of ionic formula units (e.g., 58.5 g NaCl = 1 mol)
  • •
    Gram ion: ionic mass in grams = 1 mole of ions (e.g., 96 g SO₄²⁻ = 1 mol)
  • •
    1 mole of any substance always contains particles regardless of identity
Formula

Avogadro's Number and Particle Calculations

Avogadro's number ( mol⁻¹) links the macroscopic mass scale to the microscopic particle count. It converts between moles and individual atoms, molecules, or ions.

Key Points

  • •
    — multiply moles by Avogadro's number to get particle count
  • •
    — combined formula for mass-to-particle conversion
  • •
    For atoms within a compound, multiply molecule count by the subscript of the target element
  • •
    In H₂SO₄, 1 mole gives 2 mol H atoms, 1 mol S atoms, and 4 mol O atoms
  • •
    Always check whether the question asks for molecules or individual atoms before answering
Formula

Molar Volume of Gases at STP

One mole of any ideal gas at STP (0 °C, 1 atm) occupies exactly 22.414 dm³. This holds regardless of the gas's molar mass because intermolecular distances dwarf molecular sizes in the gaseous state.

Key Points

  • •
    STP = 0 °C (273 K) and 1 atm (101.325 kPa)
  • •
    Molar volume = 22.414 dm³ mol⁻¹ at STP only
  • •
    1 dm³ = 1000 cm³ = 1 litre — always check and convert units
  • •
    gives moles from gas volume at STP
  • •
    Molar mass can be found from gas mass and volume:
  • •
    Applies only to ideal gases at STP — not to solids, liquids, or non-standard conditions
Formula

Ion Calculations from Dissociation

When a compound dissolves and dissociates, the number of each type of ion, their individual masses, and total charges are all calculated from the balanced dissociation equation and the original amount of substance.

Key Points

  • •
    Multiply moles of the original compound by each ion's coefficient to get ion moles
  • •
    Total positive charges must always equal total negative charges in solution
  • •
    A polyatomic ion like PO₄³⁻ contributes 3 charges per ion, not 1
  • •
    Mass of each ion after dissociation:
  • •
    For H₃PO₄ → 3H⁺ + PO₄³⁻: 1 mol gives 3 mol H⁺ and 1 mol PO₄³⁻

Stoichiometry and Balanced Equations

Stoichiometry uses balanced chemical equations to calculate quantitative relationships between reactants and products. The coefficients represent the relative number of moles of each substance involved.

Key Points

  • •
    Coefficients in a balanced equation give the mole ratio between any pair of substances
  • •
    Mole ratios can be simplified: KOH:H₂O = 2:2 simplifies to 1:1
  • •
    Ratios work between any two substances — not just reactant-product pairs
  • •
    Always balance the equation before extracting mole ratios
  • •
    Stoichiometry assumes complete conversion and no side reactions

Three-Step Stoichiometric Method

All stoichiometric calculations follow the same framework: convert given quantity to moles, apply the mole ratio from the balanced equation, then convert to the desired unit (mass, volume, or particle count).

Key Points

  • •
    Step 1: Convert given quantity to moles using or
  • •
    Step 2: Apply mole ratio — multiply by (coefficient of target / coefficient of given)
  • •
    Step 3: Convert result to desired unit — mass (), particles (), or volume ()
  • •
    Mass-mass:
  • •
    Track units at every step — if they cancel correctly, the setup is likely right

Solution-Based Stoichiometry

When the target is a solution with known percentage concentration and density, additional conversion steps are needed: solute mass → solution mass (÷ % as decimal) → solution volume (÷ density).

Key Points

  • •
    Percentage concentration: 27% HCl means 27 g HCl in 100 g of solution, not 100 g of HCl
  • •
    Always convert percentage to decimal before dividing (27% → 0.27)
  • •
    Work in strict order: solute mass → solution mass → solution volume
  • •
    gives volume of solution needed
  • •
    Solution volume should always be larger than the solute volume alone
Formula

Limiting Reactant

The limiting reactant is the substance completely consumed first in a reaction, controlling the maximum amount of product. The excess reactant remains partially unreacted. Identification requires comparing moles using the balanced equation, not raw masses.

Key Points

  • •
    Convert all given masses to moles before comparing
  • •
    The reactant producing fewer moles of product is the limiting reactant
  • •
    Shortcut: divide each reactant's moles by its coefficient — smaller result is limiting
  • •
    Smaller mass or fewer moles does NOT automatically mean limiting — stoichiometric coefficients matter
  • •
    Excess remaining = initial moles − moles that actually reacted (using mole ratio)
  • •
    Convert leftover moles back to mass when asked for excess mass

Percentage Yield

Percentage yield measures reaction efficiency by comparing actual product obtained to the theoretical maximum predicted by stoichiometry. It is always ≤ 100% due to practical losses.

Key Points

  • •
    Theoretical yield is calculated from the limiting reactant assuming perfect conditions
  • •
    Actual yield is always less than theoretical due to side reactions, incomplete conversion, and handling losses
  • •
  • •
    Both yields must be in the same units before calculating
  • •
    To find actual yield: multiply theoretical yield by (% yield / 100)
  • •
    To find theoretical yield: divide actual yield by (% yield / 100)
Formula

Formulas

Moles from Mass

Convert mass (g) to moles by dividing by molar mass (g mol⁻¹). First step in most stoichiometric problems.

Particles from Mass

Find the count of atoms, molecules, or ions from a given mass using molar mass and Avogadro's number.

Mass from Moles

Convert moles to mass (g) by multiplying by molar mass. Used for final answer conversion.

Gas Moles from Volume at STP

Convert gas volume (dm³) to moles at standard temperature and pressure. Valid only for ideal gases at STP.

Solution Volume from Solute Mass

Convert mass of pure solute to volume of solution using percentage concentration and density.

Percentage Yield

Calculate reaction efficiency. Actual yield and theoretical yield must be in the same units. Always ≤ 100%.

Volume from Mass and Density

Convert mass of a substance or solution to volume using its density.