Balancing Chemical Equations & Reaction Types – Comprehensive Study Notes

Chemical Equations: What the Symbols Mean

• Every chemical reaction is written as a reactants → products statement.
• The arrow (→) shows the direction of change, NOT an equals sign.
• Immediately after each formula a set of parentheses may appear to denote physical state:
  • (g) gas
  • (l) liquid
  • (s) solid
  • (aq) aqueous (dissolved in water)

Coefficients, Subscripts & Conservation of Mass

• Subscript (small number inside the formula)
  • Refers to atoms inside one formula unit / molecule.
  • Example: \text{CaCl}_2 contains 1 Ca and 2 Cl per unit.
• Coefficient (big number in front)
  • Refers to the number of whole formula‐units.
  • Example: 3\text{CaCl}_2 means 3 whole units → 3(1)=3 Ca and 3(2)=6 Cl.
• If no coefficient or subscript is shown, it is understood to be 1.
• Law of Conservation of Mass: atoms are neither created nor destroyed in a closed system.
  • Balancing ensures “same kinds & numbers of atoms” on both sides.
  • Only coefficients may be changed while balancing; subscripts are untouchable.

General Strategy for Balancing Equations

• Treat balancing as simple multiplication problems.
• Practical hints
  1. Tackle elements that appear in only one compound per side first (they are “easy”).
  2. Leave elements that appear in many places (often O or H) for last.
  3. Keep polyatomic ions intact if they appear unchanged on both sides (e.g.
     \text{SO}_4^{2-} stays together).
  4. Use the smallest whole–number set of coefficients (divide by the greatest common divisor at the end if necessary).
• Two organisational techniques
  • T-chart: write a reactant column vs. product column and list counts under each.
  • Inline annotation: write coefficients directly on the equation, repeatedly recount.

Counting Atoms: Worked Mini-Examples

• 3\text{Al(ClO}3)3
  • 3 units overall
  • Per unit: 1 Al, 3 Cl, 9 O.
  • Total: 3 Al, 9 Cl, 27 O.
• 2\text{CaCl}_2 → 2\times1=2 Ca and 2\times2=4 Cl.

Fully Worked Balancing Example ①

“Make gold(III) oxide from gold metal and oxygen gas.”

\boxed{?}\;\text{Au} + ?\;\text{O}2 \;→\; ?\;\text{Au}2\text{O}_3

1. Count initial atoms: Reactants \text{Au}=1, \text{O}=2 | Products \text{Au}=2, \text{O}=3.
2. Balance Au by multiplying Au metal by 2 → 2\text{Au}.
3. O no longer matches (Reactant O=2, Product O=3). Find LCM of 2 and 3 which is 6.
   • Need 6 O on each side.
   • Multiply \text{O}2 by 3 (gives 6 O) and \text{Au}2\text{O}_3 by 2 (gives 6 O).
4. Au count after step 3 ⇒ 2(2)=4 Au in product; set 4 Au metal reactant.

Final balanced form
\boxed{4}\text{Au} + \boxed{3}\text{O}2 → \boxed{2}\text{Au}2\text{O}_3

Fully Worked Balancing Example ② (Complex & Uses “Deal-with-O-last” Trick)

\text{H}3\text{PO}4 + \text{HNO}_3 → \text{???} (generic classroom demo)

1. Balance P first (appears once each side).
2. Balance H next.
3. Tackle O at the very end.
4. If a coefficient choice breaks an earlier element, revisit and multiply by whole numbers (6, 4, etc.) until all align.
5. Reduce coefficients if they share a common factor.

Classification of Reactions

• Various textbook schemes exist; lecturer condenses into 3 big functional classes but recognises “classic” 5+2 pattern.
  • Classical list used in lecture:
  1. Synthesis (Combination)
  2. Decomposition
  3. Combustion
  4. Single-Replacement (Displacement)
  5. Double-Replacement (Metathesis)
  6. Acid–Base (special case of double replacement)
  7. Precipitation (outcome-oriented label, also double replacement)

1. Synthesis (Combination)

• Two simpler species merge into one product.
• Must apply correct compound-building rules (ionic charges, covalent prefixes, diatomic element memory).
  Example: \text{N}2 + 3\text{H}2 → 2\text{NH}_3 (formation of ammonia).

2. Decomposition

• One reactant splits into two or more simpler substances.
• Again obey ionic vs. molecular rules & watch the seven diatomic elements (H2, N2, O2, F2, Cl2, Br2, I2). Example: 2\text{KNO}3 (s) → 2\text{KNO}2 (s) + \text{O}2 (g).

3. Combustion

• Hydrocarbon (CxHy or CxHyOz) + \text{O}2 → \text{CO}2 + \text{H}_2\text{O} (both usually gases).
• Presence of both \text{CO}2 and \text{H}2\text{O} in products is a diagnostic signature.

4. Single-Replacement (Displacement)

• General pattern A + BC → AC + B (where A & B are usually metals OR A & B are halogens).
• “Like replaces like”: a metal displaces a metal cation; a halogen displaces a halide.
• Need activity series (not covered in transcript) to know if swap actually occurs.
  • Example (metal): \text{Rb} + \text{LiCl} → \text{RbCl} + \text{Li}.
  • Example (non-metal): \text{Cl}2 + 2\text{KBr} → 2\text{KCl} + \text{Br}2.

5. Double-Replacement (Metathesis)

• Two ionic compounds exchange partners: AB + CD → AD + CB.
• Always swap either both positives or both negatives, stay consistent.
• Each new compound must be rebuilt via criss-cross-applesauce (charge criss-cross) and simplified.
  • Example: \text{MgCl}2 + \text{Ca(NO}3)2 → \text{Mg(NO}3)2 + \text{CaCl}2.

6. Acid–Base Neutralisation (special DR)

• Acid + base → salt + water.
  • Example: \text{HCl} + \text{NaOH} → \text{NaCl} + \text{H}_2\text{O}.

7. Precipitation (outcome-based DR)

• Two soluble salts → one insoluble solid (ppt) + one aqueous ion pair.
  • Requires solubility rules.

Predicting & Writing Products: Key Reminders

• Identify compound type (ionic, molecular, acid) before writing product formulae.
• Criss-cross charges for ionic products; use prefixes for molecular; apply acid naming rules for acids.
• Remember diatomic elements when they appear alone.
• After writing products, balance the entire equation.

In-Class Word-Problem Examples

• Decompose silver(I) oxide:
  1. Build formula: \text{Ag}_2\text{O} (ionic, Ag^+ & O^{2-}).
  2. Decompose: 2\text{Ag}2\text{O} → 4\text{Ag} + \text{O}2 (balance Ag first, O second).
• Reaction of aqueous barium hydroxide with aqueous perchloric acid:
  • Reactants: \text{Ba(OH)}2 (aq) + 2\text{HClO}4 (aq).
  • Swap partners → products: \text{Ba(ClO}4)2 (aq) + 2\text{H}_2\text{O} (l).
  • Already balanced once stoichiometric coefficients (1 : 2 : 1 : 2) are assigned.

Practical / Philosophical Notes

• Balancing is skill‐based; no universal step-list works for every equation—practice is paramount.
• If you become stuck, draw molecular pictures or use the T-chart to keep atoms straight.
• Coefficients occasionally balloon (e.g.
  25 or 27) if one follows the “draw & add one more” method; aim for smallest set by stepping back and looking for common multiples.
• Ethically, balancing reinforces the principle of matter conservation—a cornerstone of modern science.
• In real-world applications (industrial synthesis, biochemistry, environmental modeling) balanced equations feed directly into stoichiometric calculations, reactor design, and mass-balance audits.