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Balancing Equations: Vocabulary (Practice Problems)

Key Concepts in Balancing Equations

  • Law of conservation of mass: atoms of each element must balance on both sides of a chemical equation.
  • Subscripts in chemical formulas cannot be changed to balance; only stoichiometric coefficients may be adjusted.
  • Stoichiometric coefficients are the smallest whole numbers that balance all elements.
  • Common methods:
    • Inspection (trial-and-error): balance one element at a time, often starting with those that appear in only one compound.
    • Algebraic method: assign unknown coefficients to each species and solve the resulting system of linear equations for each element.
    • Balancing polyatomic ions as a unit when they appear unchanged on both sides to reduce work.
  • Balancing strategy tips:
    • Balance elements that appear in only one reactant and one product first.
    • Balance hydrogen and oxygen last if possible, or use water, H+, or OH- as needed in aqueous solutions.
    • After balancing, recount all elements to verify correctness.
  • Quick check approach:
    • Count atoms of each element on both sides and ensure equality.
    • Confirm coefficients are in the smallest whole-number ratio.

Worked Example: Balancing Fe + O₂ → Fe₂O₃

  • Goal: Determine smallest integers a, b, c such that
    a\,\mathrm{Fe} + b\,\mathrm{O2} \rightarrow c\,\mathrm{Fe2O_3}.
  • Atom balance equations:
    • Iron (Fe): (a = 2c)
    • Oxygen (O): (2b = 3c)
  • Solve for integers: choose (c = 2). Then (a = 4) and (b = 3).
  • Balanced equation:
    4\,\mathrm{Fe} + 3\,\mathrm{O2} \rightarrow 2\,\mathrm{Fe2O_3}.

Practice Problems (transcribed from transcript; some items are garbled in the source)

  • (a) 2 Fe + 3 Cl₂ → 2 FeCl₃
  • (b) 2 Fe + 3 O₂ → 2 Fe₂O₃
    (Note: This item appears to be the common reactant/product pair; if the intended product is Fe₂O₃, the fully balanced form is 4 Fe + 3 O₂ → 2 Fe₂O₃. The given text shows an unbalanced form; please verify the intended coefficients.)
  • (c) 2 FeBr₃ + 3 H₂SO₄ → Fe₂(SO₄)₃ + 6 HBr
  • (d) C₄H₆O₃ + … (text garbled; unable to determine the full equation from transcript)
  • (e) … (garbled)
  • (f) … (garbled)
  • (g) … (garbled)
  • (h) … (garbled)
  • (i) … (garbled)
  • (j) … (garbled)
  • (k) … (garbled)

Notes on garbled items

  • Several items (d) through (k) in the transcript are incomplete or corrupted in the provided text, making it impossible to reconstruct their exact chemical equations.
  • Action needed: provide a clean, complete transcription of items (d)–(k) to include them accurately in the notes.

Additional balancing techniques (summary for quick study)

  • If a reaction contains diatomic elements (H₂, O₂, N₂, F₂, Cl₂, Br₂, I₂) on both sides, balance those molecules by adjusting their coefficients first where possible.
  • For combustion reactions (e.g., fuels with O₂ producing CO₂ and H₂O), balance C first (as CO₂), then H, then O.
  • When balancing complex formulas, consider balancing a whole polyatomic ion as a unit if it appears intact on both sides (e.g., SO₄²⁻, NO₃⁻).
  • If using the algebraic method:
    • Write a coefficient variable for each chemical species.
    • Create a system of equations for each element based on atom counts.
    • Solve (often you’ll have one degree of freedom; fix a coefficient to a convenient value to obtain the smallest integer solution).

Quick practice prompt (optional extension)

  • Balance the following (if text is clarified):
    • Fe + Cl₂ → FeCl₂ or FeCl₃ (choose the correct product to balance)
    • Fe + O₂ → Fe₂O₃
    • FeBr₃ + H₂SO₄ → FeSO₄ or Fe₂(SO₄)₃ + HBr (ensure atom balance)

If you want me to proceed with full balances

  • Please provide a clean version of items (d)–(k) from the transcript, or re-upload the PDF/transcript so I can complete the full set of balanced equations and include them here.