Balancing Chemical Equations
High-Yield Summary
- Physical changes preserve chemical composition (e.g., phase changes); chemical changes rearrange atoms into new substances.
- Law of conservation of mass: atoms are neither created nor destroyed, so equations must balance — same atom count on both sides.
- Balance with coefficients (not subscripts, which are fixed): most complex substance first, simplest (often O₂) last; use smallest whole-number coefficients.
- Stoichiometric pathway: mass of X → moles of X (÷ molar mass) → moles of Y (× mole ratio from balanced equation) → mass of Y (× molar mass) → particles of Y (× Avogadro's number, optional).
- Limiting reagent caps product formation and is fully consumed; excess reagent is left over. Percent yield = (actual ÷ theoretical) × 100%.
Steps to Balance an Equation
- 1Determine what reaction is occurring — identify reactants, products, and physical states.
- 2Write the unbalanced equation.
- 3Balance one atom at a time, starting with the substance with the most elements, saving the simplest substance for last.
- 4Use the smallest whole-number coefficients that balance the equation.
- 5Check every atom to confirm full balance.
Stoichiometric Conversion Pathway & Percent Yield
mass X →(÷MM) moles X →(×mole ratio) moles Y →(×MM) mass Y →(×Nₐ) particles Y | % Yield = (Actual/Theoretical) × 100%
- MM = Molar mass (g/mol)
- Nₐ = Avogadro's number, 6.022 × 10²³ particles/mol
- mole ratio = Read from the coefficients of the balanced equation
- Worked example (propane combustion): C₃H₈ + 5 O₂ → 3 CO₂ + 4 H₂O — balance carbon (3), then hydrogen (4 H₂O for 8 H), then oxygen last (10 O total → 5 O₂).
- Worked example (aspirin synthesis): 2 g salicylic acid (138.12 g/mol) → 0.0145 mol → 0.0145 mol aspirin (1:1, 180.16 g/mol) → 2.61 g theoretical; 1.6 g actual → 61.3% yield.
Key Terms
- Limiting reagent
- The reactant that is completely consumed first, capping how much product can form.
- Excess reagent
- The reactant that is not fully used up; some remains after the reaction stops.
- Theoretical yield
- The amount of product predicted by stoichiometry, assuming no losses.
- Actual yield
- The amount of product actually collected — almost always less than theoretical, due to error/loss.
Common MCAT Trap
- Never balance by changing subscripts (e.g., turning H₂O into H₂O₂) — that changes the substance's identity. Only coefficients can be adjusted.
- Balance the most complex/multi-element substance first and diatomic elements (O₂, H₂, N₂) last — balancing in the wrong order creates extra rework.
- The limiting reagent isn't necessarily the one present in the smallest amount — it's the one that runs out first based on the stoichiometric ratio required, not raw quantity.
Quick Recall
What are the four signs that a chemical change (not physical) has occurred?
In the propane combustion C₃H₈ + 5 O₂ → 3 CO₂ + 4 H₂O, why is oxygen balanced last?
If theoretical yield is 2.61 g and actual yield is 1.6 g, what is the percent yield?