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Solubility product questions look like plug-and-play algebra, but they hide three traps: comparing Ksp values for salts of different formulas, squaring the wrong concentration with a common ion, and forgetting that mixing two solutions dilutes both. This post works through each with numbers from the NCERT textbook and ends with a practice routine.
What does the syllabus ask for?
The JEE (Main) 2026 syllabus and the NEET (UG) 2026 syllabus include "the solubility of sparingly soluble salts and solubility products" and the common ion effect. The CBSE Chemistry curriculum for 2026-27 lists "Solubility Equilibria of Sparingly Soluble Salts" in Class 11, and the JEE (Advanced) 2026 brochure lists "Solubility product and its applications, common ion effect". Check the current documents for your exam.
What is Ksp?
For barium sulphate in contact with its saturated solution, BaSO₄(s) ⇌ Ba²⁺(aq) + SO₄²⁻(aq), the NCERT chapter Equilibrium writes Ksp = [Ba²⁺][SO₄²⁻], with the solid left out because its concentration is constant. NCERT gives Ksp = 1.1 × 10⁻¹⁰ at 298 K, so the molar solubility S satisfies S² = 1.1 × 10⁻¹⁰ and S = 1.05 × 10⁻⁵ mol/L.
For a general salt MₓXᵧ, NCERT gives Ksp = (xS)ˣ(yS)ʸ = xˣyʸS⁽ˣ⁺ʸ⁾. Write the stoichiometry before you write any numbers.
Research on this topic shows why it is hard. Raviolo (2001) designed a problem that asks students to link what they see in the beaker, the particles in solution and the symbols in the equation, and found students struggled to connect the three. When you solve, picture the solid, the dissolved ions and the expression together.
Worked example 1: is a smaller Ksp always less soluble?
Compare BaSO₄ (Ksp = 1.1 × 10⁻¹⁰) with Ag₂CrO₄ (Ksp = 1.1 × 10⁻¹², from NCERT exercise 6.68).
BaSO₄: S = √(1.1 × 10⁻¹⁰) = 1.05 × 10⁻⁵ mol/L.
Ag₂CrO₄ ⇌ 2Ag⁺ + CrO₄²⁻, so Ksp = (2S)²(S) = 4S³. Then S³ = 2.75 × 10⁻¹³ and S = 6.5 × 10⁻⁵ mol/L.
Silver chromate has a Ksp a hundred times smaller, yet it is about six times more soluble. Ksp values can be compared directly only for salts with the same formula type, such as AgBr and BaSO₄ (both 1:1).
Worked example 2: the common ion effect
What is the solubility of Ag₂CrO₄ in 0.10 M K₂CrO₄?
Let S dissolve. Then [Ag⁺] = 2S and [CrO₄²⁻] = 0.10 + S ≈ 0.10.
Ksp = (2S)²(0.10) = 0.40S² = 1.1 × 10⁻¹².
S² = 2.75 × 10⁻¹², so S = 1.7 × 10⁻⁶ mol/L.
Now in 0.10 M AgNO₃ instead: Ksp = (0.10)²S, so S = 1.1 × 10⁻¹⁰ mol/L. A common Ag⁺ cuts solubility far more than a common CrO₄²⁻, because [Ag⁺] is squared. Always check the approximation: here S is tiny compared with 0.10, so it holds. NCERT's Problem 6.28 uses the same method for Ni(OH)₂ in 0.10 M NaOH.
Worked example 3: will a precipitate form?
Equal volumes of 2.0 × 10⁻⁵ M BaCl₂ and 2.0 × 10⁻⁵ M Na₂SO₄ are mixed. Does BaSO₄ precipitate?
Mixing equal volumes halves each concentration: [Ba²⁺] = [SO₄²⁻] = 1.0 × 10⁻⁵ M.
Ionic product Q = (1.0 × 10⁻⁵)² = 1.0 × 10⁻¹⁰.
Q < Ksp (1.1 × 10⁻¹⁰), so no precipitate.
If you forget the dilution, you get Q = 4.0 × 10⁻¹⁰, which is above Ksp, and the wrong answer. NCERT states the rule: when Q is not equal to Ksp, it gives the direction of precipitation or dissolution.
Where is this used?
NCERT gives two real uses of the common ion effect. Passing HCl gas through saturated sodium chloride solution precipitates very pure NaCl. Adding an excess of a common ion makes precipitation almost complete in gravimetric analysis, for example of silver as AgCl or barium as BaSO₄. The same idea drives group separation in salt analysis in the chemistry practical. NCERT also notes that salts of weak acids, such as phosphates, become more soluble at low pH because the anion gets protonated.
Which mistakes cost marks?
Comparing Ksp values across different formula types.
Writing Ksp = S² for every salt.
Forgetting the dilution when two solutions are mixed.
Dropping the coefficient: writing [Ag⁺] = S instead of 2S.
Not checking that S is small enough for the approximation.
A practice routine
Derive S for 1:1, 1:2 and 2:3 salts from the general formula, then check against NCERT Problem 6.26.
Solve NCERT exercise 6.68 (Ag₂CrO₄ against AgBr) and explain why the ratio is so large.
Do two common ion problems a day for a week, one with the squared ion common and one without.
Link this chapter to pH. Our guide to ionic equilibrium, pH and buffers covers the acid side.
If you get a Ksp answer wrong and cannot see why, the Fermi Problem Library has a step-by-step solver that explains the reasoning, so you can find the exact line where your set-up went off.
This week, redo worked example 3 with 4.0 × 10⁻⁵ M solutions and decide whether a precipitate forms.
