Solubility Product ( K sp ), Ionic Product ( Q sp ) & Common Ion Effect Why this matters Some ionic solids dissolve only a little — they are sparingly soluble. Their dissolution is an equilibrium. The solubility product K sp tells us how much can dissolve. If we mix solutions, we use the ionic product Q sp to decide if a precipitate will form. Adding a common ion often reduces solubility — a standard NEET numericals theme and the backbone of selective precipitation in qualitative analysis. A sparingly soluble salt at the bottom establishes equilibrium with its ions in solution. The K sp expression depends only on dissolved ion concentrations at a given temperature. Defining K sp and the dissolution equilibrium Treat the solid as a reservoir that can release ions until equilibrium is reached. The equilibrium expression excludes the pure solid (activity = 1), so K sp involves only ion concentrations. Temperature fixes K sp ; adding more solid does not change K sp — it only ensures saturation. General dissolution K sp is an equilibrium constant that depends only on temperature. Solubility product An ionic solid with low solubility in water (often much less than 0.01 M), establishing a dissolution–precipitation equilibrium. Sparingly soluble salt Solubility product ( K sp ) Product of equilibrium molar concentrations of ions, each raised to its stoichiometric coefficient, for the dissolution of a sparingly soluble salt. Moles of solute that dissolve per litre of solution to reach saturation at a given temperature (mol L -1 ). Molar solubility (s) Product of the current ion concentrations (not necessarily at equilibrium), used to predict precipitation by comparison with K sp . Ionic product ( Q sp ) Decrease in the solubility of a sparingly soluble electrolyte due to the addition of a strong electrolyte that provides a common ion. Common ion effect Precipitating one ion from a mixture while leaving others in solution by controlling the concentration of a precipitating ion based on K sp differences. Selective precipitation All ionic compounds dissolve completely in water. Many ionic salts (e.g., AgCl, BaSO4, CaCO3) are sparingly soluble with very small K sp values, so they remain mostly undissolved. K sp changes if we add more solid. K sp depends only on temperature. Adding more solid does not change K sp ; it only helps maintain saturation. Relating K sp to molar solubility s Let s be the molar solubility (mol L -1 ). Use stoichiometry of ions formed per formula unit to write ion concentrations at saturation in terms of s, then substitute into K sp . This is a high-yield path from K sp to s and back. General s– K sp relation AB type A2B or AB2 type Type K sp –s formulas by salt type Salt type Dissolution stoichiometry K sp in terms of s s in terms of K sp AB AB(s) ⇌ A + + B - K sp = s 2 s = ( K sp ) 1/2 A2B A2B(s) ⇌ 2A + + B 2- K sp = (2s) 2(s) = 4s 3 s = ( K sp /4) 1/3 AB2 AB2(s) ⇌ A 2+ + 2B - K sp = (s)(2s) 2 = 4s 3 s = ( K sp /4) 1/3 AB3 AB3(s) ⇌ A 3+ + 3B - K sp = s(3s) 3 = 27s 4 s = ( K sp /27) 1/4 A2B3 A2B3(s) ⇌ 2A 3+ + 3B 2- K sp = (2s) 2(3s) 3 = 108s 5 s = ( K sp /108) 1/5 Worked examples (assuming 298 K): • AgCl (AB), K sp = 1.8× 10 -10 ⇒ s = √(1.8× 10 -10 ) ≈ 1.34× 10 -5 M. • PbI2 (AB2), K sp = 7.1× 10 -9 ⇒ s = ( K sp /4) 1/3 ≈ (1.775× 10 -9 ) 1/3 ≈ 1.21× 10 -3 M. These magnitudes explain why AgCl is far less soluble than PbI2. Check your s– K sp algebra against stoichiometry first. Count how many of each ion one formula unit gives, then raise s accordingly. tip K sp is an equilibrium constant (unit depends on expression form) fixed by temperature, while s is the amount that dissolves to saturate the solution at that temperature. Students often confuse solubility 's' (mol L -1 or g L -1 ) with solubility product 'Ksp'. Incorrect stoichiometry when writing K sp for salts like CaF2. For CaF2: [ Ca 2+ ] = s but [ F - ] = 2s, so K sp = s(2s) 2 = 4s 3 . Do not write K sp = s× s 2 or s×(2s). Ionic product Q sp and precipitation test Ionic product Compare Q sp with K sp : • If Q sp > K sp : the solution is supersaturated with respect to the salt, so precipitation occurs until equilibrium is reached. • If Q sp = K sp : saturated solution at equilibrium. • If Q sp < K sp : unsaturated; more solid can dissolve. To compute Q sp on mixing, first find the new ion concentrations after dilution (use moles/total volume), then apply the product. Formation of a solid when the ionic product exceeds K sp . Graphical guide: region where Q sp exceeds K sp leads to precipitation; at the boundary Q sp = K sp is saturation. 2026-05-26T17:04:34.863Z Precipitation threshold plot: x-axis [ A y+ ], y-axis [ B x- ]. Draw boundary curve [A] x[B] y = K sp . Shade the region above ( Q sp > K sp ) as 'precipitation'. Clean 2D vector style, red boundary, neutral palette, no embedded text labels. gpt-image-2 Common ion effect: numerical backbone Adding a strong electrolyte that shares an ion with the sparingly soluble salt reduces its solubility (Le Ch a telier's principle). When a large common-ion concentration C is present, the extra contribution from dissolution (≈ s) is often negligible compared to C, allowing a simple calculation. Common-ion relation (AB case) Example: AgCl(s) in 0.10 M NaCl. K sp (AgCl) = 1.8× 10 -10 . Let [ Cl - ] ≈ 0.10 M (since s ≪ 0.10). Then [ Ag + ] = K sp /[ Cl - ] = (1.8× 10 -10 )/0.10 = 1.8× 10 -9 M. Compare to pure water solubility ≈ 1.34× 10 -5 M — a huge reduction due to the common ion. Adding a common ion (Cl− from NaCl) to saturated AgCl reduces [Ag+] until the K sp expression is satisfied at a much lower solubility. Small-x check: After solving, verify s ≪ C (the added common-ion concentration). If not, redo without the approximation. tip Selective precipitation — choosing the right reagent Because different salts have very different K sp values, one ion can be precipitated from a mixture while another stays dissolved by carefully adjusting the concentration of the precipitating ion. This is used for cation group separation in qualitative analysis (covered in NTCH20). Example: Separate Ag + and Pb 2+ using I - . Given equal initial [ Ag + ] = [ Pb 2+ ] = 0.010 M. • For AgI (AB): precipitation begins when [ Ag + ][ I - ] = K sp (AgI) = 8.5× 10 -17 ⇒ [ I - ] crit(AgI) = 8.5× 10 -15 M. • For PbI2 (AB2): precipitation begins when [ Pb 2+ ][ I - ] 2 = K sp (PbI2) = 7.1× 10 -9 ⇒ [ I - ] crit(PbI2) = √(7.1× 10 -9 /0.010) ≈ 8.4× 10 -4 M. Thus, there is a wide window 8.5× 10 -15 ≪ [ I - ] ≪ 8.4× 10 -4 M where only AgI precipitates — enabling selective precipitation of Ag + . Selective precipitation window: as [I−] increases, AgI starts precipitating far earlier than PbI2 due to its much smaller K sp . 2026-05-26T17:04:35.062Z Two-threshold diagram on white background: x-axis [I−] (log scale). Vertical line at very low [I−] for AgI start; another at much higher [I−] for PbI2 start. Shade the region where only AgI precipitates. Clean vector style, red/blue markers for AgI/PbI2. gpt-image-2 How pH affects solubility If the anion of the salt is the conjugate base of a weak acid ( CO3 2− , S 2- , OH − , PO4 3− ), added H3O + converts that anion to a weakly ionized form ( HCO3 − /H2CO3 → CO2↑, HS − /H2S, H2O, HPO4 2− / H2PO4 − ). This removes the anion from solution and shifts dissolution to the right — increasing solubility in acid. In contrast, salts with anions of strong acids ( Cl − , NO3 − ) show little pH dependence. Examples you know CaCO3 (limestone, chalk) dissolves in dilute acids: CO3 2− + 2H3O + → H2CO3 + 2H2O; H2CO3 → CO2(g) + H2O. Metal sulfides become more soluble in acidic medium as S 2- is protonated to HS − /H2S. Hydroxides like Mg(OH)2 dissolve more in acid as OH − is consumed by H3O + . Real-life and industrial applications Kidney stones: Calcium oxalate (CaC2O4) precipitates when [ Ca 2+ ][ C2O4 2− ] exceeds K sp . Hydration and citrate therapy reduce ionic product. Water hardness: Ca 2+ / Mg 2+ removal by precipitation as carbonates/hydroxides in softening processes. Photographic/X-ray film: AgBr ( K sp ≈ 5.4×10 −13 ) forms light-sensitive microcrystals. Barium meal: BaSO4 ( K sp ≈ 1.1×10 −10 ) is so insoluble it’s safe as a radiocontrast agent; free Ba 2+ is otherwise toxic. Silver recovery: Precipitating Ag + from waste streams as AgCl/Ag2S for recycling. Kidney stone formation: when [ Ca 2+ ] and [ C2O4 2− ] in urine exceed K sp (CaC2O4), crystals nucleate and grow, forming stones. In kidney physiology, if [ Ca 2+ ][ C2O4 2− ] > K sp (CaC2O4), calcium oxalate precipitates. Controlling dietary oxalate, ensuring hydration, and using citrate (which complexes Ca 2+ ) help keep the ionic product below K sp . clinical Data you must know for NEET AgCl 1.8× 10 -10 AgBr 5.4× 10 -13 AgI 8.5× 10 -17 BaSO4 1.1× 10 -10 PbI2 7.1× 10 -9 Ca(OH)2 5.5× 10 -6 Mg(OH)2 5.6× 10 -12 CaCO3 3.4× 10 -9 K sp of common sparingly soluble salts (approx., 298 K) Salt K sp Compound neet-alert High-yield: Convert between K sp and s correctly (mind stoichiometry), apply common ion effect numerically (e.g., [ Ag + ] = K sp /[ Cl - ] for AgCl), and choose reagents for selective precipitation using K sp thresholds. Glossary Equilibrium constant for dissolution of a sparingly soluble salt; product of ion concentrations raised to stoichiometric powers. Solubility product ( K sp ) Equilibrium amount of solute dissolved per litre (mol L -1 ) to form a saturated solution. Molar solubility (s) Instantaneous product of ion concentrations; compared to K sp to assess precipitation. Ionic product ( Q sp ) Lowering of a salt’s solubility by adding a strong electrolyte sharing a common ion with the salt. Common ion effect Using K sp differences to precipitate one ion from a mixture by adjusting the precipitating ion concentration. Selective precipitation Salt with very small solubility in water ( K sp small), e.g., AgCl, BaSO4. Sparingly soluble salt