[{"data":1,"prerenderedAt":97},["ShallowReactive",2],{"cheatsheet-solubility-and-complex-ion-equilibria":3},{"sheet":4},{"sheetSlug":5,"topicSlugs":6,"primaryTopic":7,"title":8,"subtitle":9,"sections":10},"solubility-and-complex-ion-equilibria",[5],24,"Solubility & Complex-Ion Equilibria","Ksp, molar solubility, the common-ion effect, Q vs Ksp, selective precipitation, and coupled equilibria.",[11,23,47,56,64,72,81,89],{"heading":12,"kind":13,"items":14},"Ksp expression","rules",[15],{"ref":16,"mode":19,"provenance":20,"text":21,"source_hash":22},{"type":17,"topic":7,"id":18,"field":17},"rule","SE-R001","transform","owned_workbook","Ksp = product of ion concentrations, each to its coefficient, in a saturated solution. The pure solid is excluded. AgCl ⇌ Ag⁺ + Cl⁻: Ksp = [Ag⁺][Cl⁻].","58fa914069fe3c25cb66161894e91ddec2751b1ced74c3422077ae2230bdaa92",{"heading":24,"kind":25,"columns":26,"items":29},"Ksp in terms of solubility s","data",[27,28],"Salt type","Ksp",[30],{"ref":31,"mode":19,"provenance":20,"rows":33,"source_hash":46},{"type":17,"topic":7,"id":32,"field":17},"SE-R002",[34,37,40,43],[35,36],"MX","s²",[38,39],"MX₂ or M₂X","4s³",[41,42],"MX₃ or M₃X","27s⁴",[44,45],"M₂X₃","108s⁵","4ecad31660a41a358bee4fe094c7b4de183dfeee468764da9d352b4afa7bdb20",{"heading":48,"kind":49,"items":50},"Molar solubility from Ksp","steps",[51],{"ref":52,"mode":19,"provenance":20,"text":54,"source_hash":55},{"type":17,"topic":7,"id":53,"field":17},"SE-R004","ICE with x for the reference ion, write the Ksp polynomial, solve for x. If solubility is given in g/L, convert to mol/L (÷ molar mass) before using Ksp.","f3a7fead31f3e799c10f6cf259a3483c8fed696a21e4db71760019fa178e03c9",{"heading":57,"kind":13,"items":58},"Insoluble hydroxides & pH",[59],{"ref":60,"mode":19,"provenance":20,"text":62,"source_hash":63},{"type":17,"topic":7,"id":61,"field":17},"SE-R005","For M(OH)ₙ, [OH⁻] = n·s, so pOH = −log[OH⁻], pH = 14 − pOH. Given pH instead: [OH⁻] = 10^(−(14−pH)), then solve Ksp for the metal-ion concentration.","fff66b2ac5188742b4bd7dc6f5b55c21f9aa0f36a1666c7f2ec8c507e39000a2",{"heading":65,"kind":13,"items":66},"Common-ion effect",[67],{"ref":68,"mode":19,"provenance":20,"text":70,"source_hash":71},{"type":17,"topic":7,"id":69,"field":17},"SE-R008","A shared ion already in solution goes into the ICE initial row, lowering molar solubility vs pure water. The x-small approximation (x ≪ common-ion concentration) is usually valid; check x \u003C 5%.","80f9687768cd4a7674ef78abd21c10625abdaf58d9f50fdd58ebc9aeaba21ba4",{"heading":73,"kind":13,"items":74},"Q vs Ksp (will it precipitate?)",[75],{"ref":76,"mode":19,"provenance":78,"text":79,"source_hash":80},{"type":17,"topic":7,"id":77,"field":17},"SC-R011","original","Compute Q from initial ion concentrations (apply dilution when mixing: [ion] × V_part/V_total). Q \u003C Ksp → no precipitate; Q > Ksp → precipitates until Q = Ksp; Q = Ksp → just saturated.","8c11276f4d974d4964f73401d88ad87965925743a51f44a2c817bf0f74672ad7",{"heading":82,"kind":13,"items":83},"Selective precipitation",[84],{"ref":85,"mode":19,"provenance":20,"text":87,"source_hash":88},{"type":17,"topic":7,"id":86,"field":17},"SE-R007","Find the counter-ion concentration each salt needs to hit Q = Ksp; the lowest threshold precipitates first. Comparing Ksp values directly is valid only for the same salt stoichiometry.","f309e2063a515d2428946af4d5875d04eb7fcfa13851ac949b54ef5c6c9f7051",{"heading":90,"kind":13,"items":91},"Complex-ion / coupled equilibria",[92],{"ref":93,"mode":19,"provenance":78,"text":95,"source_hash":96},{"type":17,"topic":7,"id":94,"field":17},"SC-R010","Coupling dissolution to complex formation raises solubility: K_overall = Ksp × Kf. E.g. Al(OH)₃(s) + OH⁻ ⇌ Al(OH)₄⁻. With excess ligand ([L] ≈ [L]₀), a 1:1 salt gives s = √(K_overall·[L]ʲ). Acid-coupled M(OH)ₙ: K = Ksp/Kwⁿ.","e1095ccb934d8d8104a3753a601bdbbe7024fbf5a7e153aa3362af5cb56e9436",1787246033550]