Solubility Rules — Which Salts Dissolve and Why
Mix two clear solutions and sometimes nothing happens, sometimes a solid drops out. Every salt analysis question, every precipitation problem and every ionic equation you will write depends on knowing which combination gives a precipitate. Most students memorise the solubility rules and forget them within a month, because a list of exceptions with no reason behind it has nothing to hold on to. This article gives the rules as a usable table and the energetics that make them make sense, then converts "insoluble" into an actual number using Ksp.
The rules, in the order you should apply them
Work down this table and stop at the first row that matches. The earlier rows override the later ones — that ordering is what saves you from contradictions.
| # | Ion involved | Rule | Exceptions to remember |
|---|---|---|---|
| 1 | Group 1 cations (Li⁺, Na⁺, K⁺…) and NH4⁺ | All their salts are soluble | Effectively none at school level |
| 2 | NO3⁻, CH3COO⁻, ClO3⁻, ClO4⁻ | All nitrates, acetates, chlorates and perchlorates are soluble | None commonly met |
| 3 | Cl⁻, Br⁻, I⁻ | Soluble | Ag⁺, Pb²⁺, Hg2²⁺ are insoluble |
| 4 | SO4²⁻ | Soluble | Ba²⁺, Sr²⁺, Pb²⁺ insoluble; Ca²⁺ and Ag⁺ only slightly soluble |
| 5 | OH⁻ | Insoluble | Group 1 hydroxides soluble; Ba(OH)2 soluble; Ca(OH)2 and Sr(OH)2 slightly soluble |
| 6 | CO3²⁻, PO4³⁻, SO3²⁻, S²⁻ | Insoluble | Soluble with group 1 cations and NH4⁺ (rule 1 wins); group 2 sulphides also dissolve |
Two memory hooks make this stick. For halides: silver, lead and mercury(I) are the three that refuse. For sulphates: barium, strontium and lead are the three that refuse. Everything else in those two rows dissolves.
Why some salts dissolve — the energy balance
Dissolving an ionic solid is a competition between two energies. The crystal must first be pulled apart, which costs energy, and the freed ions are then surrounded by water molecules, which releases energy.
If hydration releases more than the lattice costs, dissolving is exothermic and the salt usually dissolves easily. If the lattice is far stronger than hydration, the salt stays put. But enthalpy is only half the story — the full criterion is free energy:
Breaking an ordered crystal into freely moving ions increases disorder, so ΔSsolution is usually positive and the −TΔS term helps dissolving. This is why several salts (NH4NO3 and KNO3 among them) dissolve even though the process is endothermic — the beaker gets noticeably colder, yet the solid still disappears. Entropy pays the bill.
The two group trends every syllabus asks for
Both lattice energy and hydration energy fall as the cation gets bigger down group 2. Which one falls faster decides the trend, and it depends on the size of the anion.
| Series | Trend down the group | Reason |
|---|---|---|
| Sulphates: BeSO4 → MgSO4 → CaSO4 → SrSO4 → BaSO4 | Solubility decreases | SO4²⁻ is large, so lattice energy changes little as the cation grows. Hydration energy of the cation falls sharply, so dissolving becomes less favourable. |
| Hydroxides: Mg(OH)2 → Ca(OH)2 → Sr(OH)2 → Ba(OH)2 | Solubility increases | OH⁻ is small, so lattice energy falls steeply as the cation grows — faster than the hydration energy falls. Dissolving becomes easier. |
Notice that the same two quantities explain opposite trends. The examiner is testing whether you can say which term dominates, not whether you can recite a direction.
Worked example 1 — predicting a precipitate
Lead(II) nitrate solution is added to potassium iodide solution. What happens?
Ions present: Pb²⁺, NO3⁻, K⁺, I⁻. Two new pairings are possible — PbI2 and KNO3.
KNO3: potassium salt (rule 1) and nitrate (rule 2) — soluble, stays in
solution.
PbI2: iodide is normally soluble (rule 3) but Pb²⁺ is one of the three
exceptions — insoluble.
Molecular equation: Pb(NO3)2(aq) + 2KI(aq) →
PbI2(s) + 2KNO3(aq)
Net ionic equation, with K⁺ and NO3⁻ removed as spectators:
Pb²⁺(aq) + 2I⁻(aq) → PbI2(s) — the familiar bright yellow precipitate.
Worked example 2 — will it actually precipitate? Q vs Ksp
100 mL of 0.010 M Pb(NO3)2 is mixed with 100 mL of 0.010 M KI.
Step 1 — dilution. The total volume becomes 200 mL, so each
concentration is halved:
[Pb²⁺] = 0.010 × (100/200) = 0.0050 M
[I⁻] = 0.010 × (100/200) = 0.0050 M
Step 2 — reaction quotient. For PbI2 ⇌ Pb²⁺ + 2I⁻,
Q = [Pb²⁺][I⁻]²
Q = 0.0050 × (0.0050)² = 0.0050 × 2.5 × 10−5 =
1.25 × 10−7
Step 3 — compare. Tabulated Ksp for PbI2 at 298 K is around 7 × 10−9 (different data tables quote slightly different values, so use the one given in your own question). Q is roughly 18 times larger than Ksp.
Q > Ksp, so a precipitate forms. If Q had come out smaller than Ksp, everything would have stayed dissolved.
Worked example 3 — "insoluble" is a number, not a wall
No salt is truly insoluble. Silver chloride, the standard example of an insoluble salt, still dissolves a little.
For AgCl ⇌ Ag⁺ + Cl⁻, with a commonly tabulated Ksp = 1.8 × 10−10 at 298 K. If solubility is s mol/L, then [Ag⁺] = [Cl⁻] = s, so Ksp = s².
s = √(1.8 × 10−10) = √1.8 × √(10−10) = 1.342 × 10−5 mol/L
Convert to grams per litre. M(AgCl) = 107.868 + 35.45 = 143.318 g/mol
Mass dissolved = 1.342 × 10−5 × 143.318 = 1.92 × 10−3 g/L =
about 1.9 mg per litre.
Compare barium sulphate, Ksp ≈ 1.1 × 10−10:
s = √(1.1 × 10−10) = 1.049 × 10−5 mol/L
M(BaSO4) = 137.327 + 32.06 + 4(15.999) = 137.327 + 32.06 + 63.996 =
233.383 g/mol
Mass = 1.049 × 10−5 × 233.383 = 2.45 × 10−3 g/L ≈
2.4 mg per litre — low enough that barium sulphate is safely swallowed as
an X-ray contrast agent even though barium ions are toxic.
Worked example 4 — a 1 : 2 salt needs a different algebra
Magnesium hydroxide, Mg(OH)2 ⇌ Mg²⁺ + 2OH⁻, with Ksp ≈ 1.8 × 10−11. If s mol/L dissolves, then [Mg²⁺] = s and [OH⁻] = 2s.
Ksp = s(2s)² = 4s³
s³ = 1.8 × 10−11 ÷ 4 = 4.5 × 10−12
s = (4.5 × 10−12)1/3 = 1.65 × 10−4 mol/L
Check: 4 × (1.65 × 10−4)³ = 4 × 4.50 × 10−12 = 1.80 × 10−11 ✓
Then [OH⁻] = 2s = 3.30 × 10−4 M, so pOH = −log(3.30 × 10−4) = 4 − 0.518 = 3.48 and pH = 14 − 3.48 = 10.52 — mildly basic, which is exactly why a suspension of magnesium hydroxide works as a gentle antacid.
Common mistakes that cost marks
- Forgetting to halve concentrations after mixing. In every "will it precipitate" question the volumes add, so both concentrations drop before Q is calculated.
- Writing Ksp = s² for every salt. The exponents come from the stoichiometry: AgCl gives s², Mg(OH)2 gives 4s³, Ca3(PO4)2 gives 108s⁵.
- Including the solid in the Ksp expression. A pure solid has constant activity and never appears.
- Treating "insoluble" as absolute. It means "very slightly soluble"; the Ksp value is the honest statement.
- Using someone else's Ksp table. Published values differ with temperature and measurement method — always use the value supplied in the question, and quote it.
- Ignoring the common ion effect. AgCl is even less soluble in dilute NaCl than in pure water, because the added Cl⁻ pushes the equilibrium back towards the solid.
Where solubility rules appear in exams
| Exam | Typical question |
|---|---|
| CBSE / ICSE Class 10 | Double displacement reactions; naming the precipitate and its colour |
| CBSE / ICSE Class 11–12 | Ionic equilibrium: Ksp, solubility, common ion effect, salt analysis practicals |
| JEE / NEET | Q vs Ksp precipitation problems; selective precipitation of sulphides |
| IIT-JAM / CUET-PG | Solubility from Ksp for 1:1, 1:2 and 1:3 salts |
| GATE / CSIR-NET | Gravimetric analysis, complexation effects on solubility |
Turn Ksp into a solubility in one step. The Ksp calculator handles the stoichiometry for you — 1:1, 1:2 and 1:3 salts — so you can check the cube-root working above instead of trusting your own arithmetic under exam pressure.
Open the Ksp & Solubility Calculator →Ionic equilibrium is one of the chapters where marks are lost to small algebra slips rather than to weak theory. ABC Chemistry covers it in Class 11–12 coaching at the Gurugram centre and in online classes across India — abcchemistry.in. For students in Delhi, Noida or Gurgaon who prefer one-to-one teaching at home, home tuition is available through delhihometutor.com.