The Mole and Reaction Stoichiometry
Students use the mole concept, balanced equations, and dimensional analysis to calculate quantities of reactants and products while demonstrating conservation of mass.
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The Mole and Avogadro's Number
A mole is the amount of substance containing 6.022 × 10²³ representative particles, a value called Avogadro's number. Representative particles may be atoms, molecules, ions, or formula units. The mole lets chemists count extremely small particles by measuring a laboratory-sized quantity. For example, 2.00 mol of carbon contains 2.00 mol × 6.022 × 10²³ atoms/mol = 1.204 × 10²⁴ carbon atoms. To convert particles to moles, divide the number of particles by Avogadro's number. During a chemical reaction, atoms are rearranged rather than created or destroyed. Counting particles in moles therefore helps demonstrate that the number of each type of atom, and consequently total mass, remains constant in a closed system.
Molar Mass Conversions
Molar mass is the mass of one mole of a substance, expressed in grams per mole. Calculate it by adding the atomic masses of all atoms in the chemical formula. Water, H₂O, has a molar mass of 2(1.008) + 16.00 = 18.016 g/mol. Dimensional analysis uses this value as a conversion factor. For example, the number of moles in 36.0 g of water is 36.0 g H₂O × 1 mol H₂O/18.016 g H₂O = 2.00 mol H₂O. To convert moles to grams, multiply by molar mass. Units guide the setup: unwanted units cancel, leaving the desired unit. Because molar mass links particle amounts to measurable masses, it is essential for testing conservation of mass quantitatively.
Mole Ratios
Coefficients in a balanced chemical equation give mole ratios among reactants and products. In 2H₂ + O₂ → 2H₂O, two moles of hydrogen react with one mole of oxygen to form two moles of water. These ratios also represent proportional numbers of molecules, but they do not represent equal masses. If 3.00 mol O₂ reacts completely, dimensional analysis predicts 3.00 mol O₂ × 2 mol H₂O/1 mol O₂ = 6.00 mol H₂O. The equation is balanced because both sides contain four hydrogen atoms and two oxygen atoms for each reaction set. Thus, the mole ratio preserves the number of atoms of each element. Balanced equations are required before any stoichiometric calculation because incorrect coefficients would imply that atoms and mass were not conserved.
Mass-to-Mass Calculations
A mass-to-mass calculation converts the mass of one substance to the mass of another through moles. First balance the equation, then convert the given mass to moles, apply the mole ratio, and convert the resulting moles to grams. For propane combustion, C₃H₈ + 5O₂ → 3CO₂ + 4H₂O. If 44.10 g C₃H₈ burns completely, 44.10 g C₃H₈ × 1 mol C₃H₈/44.10 g C₃H₈ × 3 mol CO₂/1 mol C₃H₈ × 44.01 g CO₂/1 mol CO₂ = 132.0 g CO₂. Carbon dioxide is not the only product, so its mass alone does not equal the reactant mass. When all reactants and products in the closed system are included, their total masses are equal.
Limiting Reactants and Yield
The limiting reactant is consumed first and determines the maximum amount of product. Other reactants are present in excess. For 2H₂ + O₂ → 2H₂O, suppose 5.00 mol H₂ is mixed with 2.00 mol O₂. Two moles of O₂ require 4.00 mol H₂, so O₂ is limiting and 1.00 mol H₂ remains. The reaction can form 4.00 mol H₂O, or 4.00 mol × 18.016 g/mol = 72.1 g H₂O. This maximum calculated amount is the theoretical yield. If an experiment produces 61.3 g H₂O, the percent yield is 61.3 g/72.1 g × 100 = 85.0%. A yield below 100% may result from incomplete reaction or product loss, but atoms and mass are still conserved when all substances are counted.