9.4 Balancing, Solubility Rules & Types of Reactions
Key Takeaways
- Balance equations by atom count on each side — conserve mass and atoms; never change subscripts, only coefficients.
- Six reaction types: synthesis (A + B → AB), decomposition (AB → A + B), single replacement (A + BC → AC + B), double replacement (AB + CD → AD + CB), combustion (CxHy + O2 → CO2 + H2O), and oxidation-reduction (redox).
- Solubility rules: all Group 1 and ammonium salts are soluble; all nitrates, acetates, and most chlorates are soluble; chlorides are soluble except Ag+, Pb2+, Hg2²⁻; sulfates are soluble except Ba2+, Pb2+, Sr2+, Ca2+ (slightly); most sulfides, carbonates, phosphates, and hydroxides are insoluble except Group 1 and ammonium.
- A net-ionic equation shows only the species that change; spectator ions (unchanged on both sides) are canceled.
- Precipitation forms when mixing two soluble ionic compounds produces an insoluble product; identify the precipitate by combining ions crosswise and applying solubility rules.
Why Balance?
Quick Answer: A balanced equation obeys the law of conservation of mass — the same number of each atom on both sides. Balance by adjusting coefficients only; never change a subscript, because that changes the substance.
The Six Reaction Types
| Type | Pattern | Example |
|---|---|---|
| Synthesis (combination) | A + B → AB | 2 H2 + O2 → 2 H2O |
| Decomposition | AB → A + B | 2 H2O → 2 H2 + O2 (electrolysis) |
| Single replacement | A + BC → AC + B | Zn + 2 HCl → ZnCl2 + H2 |
| Double replacement (metathesis) | AB + CD → AD + CB | AgNO3 + NaCl → AgCl + NaNO3 |
| Combustion | CxHy + O2 → CO2 + H2O | C3H8 + 5 O2 → 3 CO2 + 4 H2O |
| Redox | electron transfer | 2 Na + Cl2 → 2 NaCl |
Single-replacement feasibility is checked with an activity series (Li > K > Na > … > Au): a metal displaces any metal below it from a compound. Halogen displacement follows F > Cl > Br > I.
Worked Balancing Example — Combustion of Propane
Balance C3H8 + O2 → CO2 + H2O.
- Carbons first: 3 C on left → coefficient 3 on CO2.
C3H8 + O2 → 3 CO2 + H2O - Hydrogens next: 8 H on left → coefficient 4 on H2O.
C3H8 + O2 → 3 CO2 + 4 H2O - Oxygens last (oxygen is most free): right side now has 3×2 + 4×1 = 10 O. Need 10/2 = 5 O2.
C3H8 + 5 O2 → 3 CO2 + 4 H2O - Verify: C 3=3, H 8=8, O 10=10 ✓.
Combustion of Compounds with Oxygen
For a hydrocarbon CxHy, the balanced combustion is:
CxHy + (x + y/4) O2 → x CO2 + (y/2) H2O
If (x + y/4) is not an integer, multiply the entire equation by 2.
Solubility Rules
These determine whether a precipitation occurs in a double-replacement reaction.
| Rule | Always soluble (exceptions) |
|---|---|
| Group 1 cations (Li+, Na+, K+, …) and NH4+ | All salts soluble |
| Nitrate NO3−, acetate CH3COO−, chlorate ClO3−, perchlorate ClO4− | All salts soluble |
| Chlorides, bromides, iodides | Soluble EXCEPT Ag+, Pb2+, Hg2²⁺ |
| Sulfates SO4²− | Soluble EXCEPT Ba2+, Pb2+, Sr2+; Ca2+ slightly soluble |
| Generally INSOLUBLE | |
| Carbonates CO3²−, phosphates PO4³−, sulfides S²−, hydroxides OH− | INSOLUBLE except Group 1 cations and NH4+ (and Ba(OH)2, Sr(OH)2, Ca(OH)2 slightly soluble) |
Precipitation and Net-Ionic Equations
Worked Example
Mix aqueous silver nitrate and sodium chloride. What precipitates? Write total, complete ionic, and net-ionic equations.
- Predict products (double replacement): AgNO3(aq) + NaCl(aq) → AgCl(?) + NaNO3(?).
- Apply solubility rules: NaNO3 — Na+ is Group 1 → soluble (spectator). AgCl — Ag+ is an exception to the chloride rule → insoluble; AgCl is the precipitate (white).
- Total equation:
AgNO3(aq) + NaCl(aq) → AgCl(s) + NaNO3(aq) - Complete ionic:
Ag+(aq) + NO3−(aq) + Na+(aq) + Cl−(aq) → AgCl(s) + Na+(aq) + NO3−(aq) - Cancel spectators (Na+, NO3−):
Ag+(aq) + Cl−(aq) → AgCl(s)— the net-ionic equation.
Why Net-Ionic Equations Matter on the PA-CAT
The Bulletin's chemistry sample item — increased solubility of carboxylic-acid compounds upon ionization — is essentially the reverse logic. A neutral carboxylic acid RCOOH is largely molecular in water; deprotonation gives RCOO−, which pairs with soluble cations to form ionic salts that dissociate freely. Knowing which species are spectators and which actually participate is a recurring skill across acid-base, precipitation, and redox items.
Stoichiometric Coefficients as Mole Ratios
Coefficients give mole ratios. For the propane combustion above, 1 mol C3H8 reacts with 5 mol O2 to produce 3 mol CO2 and 4 mol H2O. At STP, 5 mol O2 ≈ 5 × 22.4 = 112 L. These mole ratios feed directly into limiting-reactant, percent-yield, and gas-volume problems elsewhere on the exam.
Common Pitfalls
- Changing a subscript instead of a coefficient — turns H2O into H2O2, a different substance.
- Forgetting diatomic elements: H2, N2, O2, F2, Cl2, Br2, I2 must be written with subscript 2 when elemental.
- Treating all chlorides as soluble — AgCl, PbCl2, Hg2Cl2 are not.
- Ignoring state symbols — they tell you which species can be spectators (aq) and which are the precipitate (s) or gas (g).
Redox vs Metathesis — How to Tell Them Apart
PA-CAT reaction-classification items hinge on one question: do any oxidation states change? If yes, the reaction is redox; if no, it is metathesis (double replacement) or acid-base.
Disambiguation Table
| Reaction | Oxidation states change? | Classification |
|---|---|---|
| 2 Na + Cl₂ → 2 NaCl | Na 0 → +1, Cl 0 → −1 | Redox (synthesis) |
| AgNO₃ + NaCl → AgCl↓ + NaNO₃ | No change | Metathesis / precipitation |
| CH₄ + 2 O₂ → CO₂ + 2 H₂O | C −4 → +4, O 0 → −2 | Redox (combustion) |
| HCl + NaOH → NaCl + H₂O | No change | Acid-base (metathesis) |
| Zn + CuSO₄ → ZnSO₄ + Cu | Zn 0 → +2, Cu +2 → 0 | Redox (single replacement) |
Predicting the Precipitate — Cross-Ion Method
When two soluble ionic compounds mix, swap cation–anion pairs crosswise and apply the solubility rules to each new pair.
Worked example: Mix Fe₂(SO₄)₃(aq) and Ba(OH)₂(aq). Possible products are Fe(OH)₃ and BaSO₄. Hydroxides are insoluble except Group 1 cations and Ba/Sr/Ca, so Fe(OH)₃ is insoluble (reddish-brown precipitate); sulfates are insoluble for Ba²⁺, so BaSO₄ is also insoluble (white precipitate). Here two precipitates form — a case the PA-CAT uses to test whether you check every cross-pair rather than stopping at the first. The net-ionic equation is 2 Fe³⁺(aq) + 3 SO₄²⁻(aq) + 3 Ba²⁺(aq) + 6 OH⁻(aq) → 2 Fe(OH)₃(s) + 3 BaSO₄(s).
What are the correct coefficients to balance C4H10 + O2 → CO2 + H2O?
Mixing aqueous barium chloride with aqueous sodium sulfate produces a white precipitate. Which net-ionic equation is correct?