Limiting Reactant Basics – Unit 7B Part 4 Lecture

Key Definitions & Concepts

• When two reactants are mixed, they may not be present in the exact stoichiometric ratio required by the balanced chemical equation.
  • One reagent will be consumed first (the Limiting Reactant, LR) and stops the reaction.
  • The other reagent(s) remain in Excess (ER) and are left over once the LR is gone.
• Limiting Reactant (LR)
  • "Runs out first" ⟶ limits the maximum amount of product that can form.
  • Determining the LR is the first and most critical step in any limiting-reactant calculation; every subsequent answer depends on it.
• Product Yields
  • Theoretical Yield (TY): the mass, moles, or count of product predicted if the LR were converted 100 % to product via stoichiometry.
  • Actual Yield (AY): the amount of product actually isolated in the laboratory (or counted in real-life scenarios).
  • Percent Yield (PY): a performance metric comparing AY with TY.
    \text{Percent Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100\%
  • Real PY values are almost always < 100\% because of spills, incomplete reactions, side reactions, product stuck to glassware, impure reactants, etc.

Logical Approach to Limiting-Reactant (LR) Problems

• Step 1 Identify the LR.

  • Option 1 (Product Comparison)
  1. Pick one product.
  2. Use stoichiometry to convert each reactant’s starting amount to an amount of that product.
  3. The smaller product value indicates the LR.
  • Option 2 (Reactant-to-Reactant Comparison)
  1. Pick one reactant.
  2. Use stoichiometry to find how much of the other reactant would be needed to consume it.
  3. Compare that required amount with what is actually available.
     • If you do not have enough of the second reactant, it is the LR.
     • If you have more than enough, the first reactant you picked is the LR.
  • Perform only one of these options—doing both wastes time and can create confusion.

• Step 2 Answer Product-Related Questions

  • Always find TY from the LR via stoichiometry.
  • If PY is requested, insert TY and the provided AY into the formula above.

• Step 3 Answer Reactant-Related Questions (Leftovers)

  • LR: 0 left—by definition it is used up.
  • ER: always a two-step process
  1. Stoichiometry to compute how much ER reacts.
  2. Subtract "used" from "initial" to obtain "left over".
  • Three interchangeable methods exist for the stoichiometry–subtraction pair:
    • Option 1 – start with initial LR.
    • Option 2 – start with TY of product.
    • Option 3 – (only if Option 1 was used for LR) convert the difference between the two product amounts calculated during LR identification.

Example 1 Holiday Goody Bags (Small Numbers)

Reaction: 2L + 3K \;\longrightarrow\; 1B

• Initial inventory: 6 lollipops (L), 10 kisses (K).
• Questions & Answers
  • a LR? Lollipops (run out after 3 bags).
  • b Bags produced? 3.
  • c Leftovers? 0 L, 1 K.
• Visual Walk-Through (one bag at a time)
  1 Bag ⟶ 4 L, 7 K left.
  2 Bags ⟶ 2 L, 4 K left.
  3 Bags ⟶ 0 L, 1 K left. Reaction stops.

Example 2 Holiday Goody Bags (Larger Numbers)

Reaction: 2L + 3K \;\longrightarrow\; 1B

• Initial inventory: 180 L, 300 K.
• a Identify LR
  • Product comparison (Option 1)
    • 180 L \Rightarrow 90 bags.
    • 300 K \Rightarrow 100 bags.
    → Smaller (90) comes from L → Lollipops are LR.
  • Reactant comparison (Option 2) gives same conclusion.
• b Theoretical Yield (TY)
  • From LR: 180\,L \times \frac{1\,B}{2\,L} = 90\,B
• c Percent Yield (PY) if 85 complete bags are obtained
  \text{PY} = \frac{85}{90} \times 100\% \approx 94\%
• d Leftovers
  • LR (L): 0 left.
  • ER (K): choose any option
    • Option 1 (LR-based):
    180\,L \times \frac{3\,K}{2\,L} = 270\,K \text{ used}
    300\,K - 270\,K = 30\,K left over.
    • Option 2 (TY-based) or Option 3 produce the same 30 K.

Example 3 Bead Necklaces

Reaction: 13B + 9G \;\longrightarrow\; 1N (B = blue bead, G = green bead, N = necklace)

• Initial inventory: 156 B, 126 G.
• a Identify LR
  • Product comparison
    • 156 B \Rightarrow 12 necklaces.
    • 126 G \Rightarrow 14 necklaces.
    → Blue beads are LR (even though numerically more than greens).
• b Theoretical Yield
  156\,B \times \frac{1\,N}{13\,B} = 12\,N
• c Blue beads leftover: 0 (LR).
• d Green beads leftover (Option 1 shown)
  Stoichiometry for usage:
  156\,B \times \frac{9\,G}{13\,B} = 108\,G \text{ used}
  Subtraction:
  126\,G - 108\,G = 18\,G left over.
  (Options 2 & 3 arrive at same answer.)

Summary of Strategies

• Always locate the LR before doing anything else; every later calculation depends on it.
• Product questions = TY (and possibly PY).
• Reactant questions = leftovers.
  1. LR → none left.
  2. ER → (stoichiometry amount used) then (initial – used).
• Multiple calculation pathways exist; choose whichever aligns with data you already have to minimize work.

Additional Learning Resources

• Tyler DeWitt, "Introduction to Limiting & Excess Reactants" (16 min) – uses cooking metaphors.
• Easy Engineering, "Limiting Reactant Reactions – Animation" (5 min) – demonstrates a tabular bookkeeping method.

What’s Next

• The subsequent presentation (Unit 7B – Part 5) transitions from candy & bead analogies to genuine chemistry limiting-reactant calculations, applying the exact same logical framework outlined above.