[{"data":1,"prerenderedAt":113},["ShallowReactive",2],{"cheatsheet-solutions-and-concentration":3},{"sheet":4},{"sheetSlug":5,"topicSlugs":6,"primaryTopic":7,"title":8,"subtitle":9,"sections":10},"solutions-and-concentration",[5],9,"Solutions & Concentration","Percent, molarity, molality, dilution, mixing, and the concepts behind dissolving.",[11,23,31,39,47,55,63,71,79,87,97,105],{"heading":12,"kind":13,"items":14},"Mass percent","rules",[15],{"ref":16,"mode":19,"provenance":20,"text":21,"source_hash":22},{"type":17,"topic":7,"id":18,"field":17},"rule","SC-R001","transform","owned_workbook","Mass % = (mass of component / mass of solution) × 100, where mass of solution = solute + solvent. For an ion target, convert ion mass ↔ compound mass with mole ratios and molar masses.","f5918807c3cf5a9eacc548a2681f5af58876acb610a102ac20dc58e4db045e9f",{"heading":24,"kind":13,"items":25},"Volume percent",[26],{"ref":27,"mode":19,"provenance":20,"text":29,"source_hash":30},{"type":17,"topic":7,"id":28,"field":17},"SC-R002","Volume % = (component volume / total solution volume) × 100. Given one volume and a target %, solve x / (x + V_other) = target/100.","442704269b406789880e30e4cd30eb126f5136412d937c820d9d90206eb89605",{"heading":32,"kind":13,"items":33},"Solubility & saturation",[34],{"ref":35,"mode":19,"provenance":20,"text":37,"source_hash":38},{"type":17,"topic":7,"id":36,"field":17},"SC-R004","Solubility = grams of solute per 100 g water at a stated temperature (supplied). Saturated-solution mass % = solubility / (solubility + 100) × 100.","28501c80c3ee9dc9321b392f9fad52278268ac6416839c2705acfb817b649ca1",{"heading":40,"kind":13,"items":41},"Molarity",[42],{"ref":43,"mode":19,"provenance":20,"text":45,"source_hash":46},{"type":17,"topic":7,"id":44,"field":17},"SC-R006","Molarity M = moles solute / litres of solution. Convert mL → L (÷1000); mass → moles via molar mass. For hydrates use the full hydrate molar mass.","2463c428ade2087c57e9629eaf1169c10eb05c4274a0272503cb20f7a43f4e65",{"heading":48,"kind":13,"items":49},"Molarity of each ion",[50],{"ref":51,"mode":19,"provenance":20,"text":53,"source_hash":54},{"type":17,"topic":7,"id":52,"field":17},"SC-R007","For a soluble strong electrolyte (complete dissociation): write the dissociation equation, then multiply the compound molarity by each ion's coefficient. 0.10 M CaCl₂ → 0.10 M Ca²⁺ and 0.20 M Cl⁻.","882c79f5a5e52224e3574b13a6deec9bd784bef1db4c6d64e7525089226847cd",{"heading":56,"kind":13,"items":57},"Dilution",[58],{"ref":59,"mode":19,"provenance":20,"text":61,"source_hash":62},{"type":17,"topic":7,"id":60,"field":17},"SC-R010","M₁V₁ = M₂V₂ (moles conserved). 'Diluted to' a volume → V₂ is the final total; water 'added' → V₂ = V₁ + V_water. Units just have to match (they cancel).","877856f42013a3d96c836fab7374c9eb9408ea6b5e8477ddd8efff6c5d930699",{"heading":64,"kind":13,"items":65},"Stock solutions",[66],{"ref":67,"mode":19,"provenance":20,"text":69,"source_hash":70},{"type":17,"topic":7,"id":68,"field":17},"SC-R011","Use M₁V₁ = M₂V₂ with 1 = stock (concentrated), 2 = target (dilute). Volume of stock V₁ = M₂V₂ / M₁; stock concentration M₁ = M₂V₂ / V₁.","1d7ba7315056f1e94ba329ade0228c66aa355a7b9c2b12b7efad1b83424c2874",{"heading":72,"kind":13,"items":73},"Mixing same-compound solutions",[74],{"ref":75,"mode":19,"provenance":20,"text":77,"source_hash":78},{"type":17,"topic":7,"id":76,"field":17},"SC-R012","Final M = (M₁V₁ + M₂V₂) / (V₁ + V₂). The result lands between the two, nearer the larger-volume solution (a quick sanity check).","a32f6fe63a3726123556075a7382c7c41d4c70ac676e3353a1c1480f113dc047",{"heading":80,"kind":13,"items":81},"Molality",[82],{"ref":83,"mode":19,"provenance":20,"text":85,"source_hash":86},{"type":17,"topic":7,"id":84,"field":17},"SC-R014","Molality m = moles solute / kg of solvent (mass, not volume; solvent, not solution). Add hydrate water to the solvent mass. Unlike molarity, m is temperature-independent.","750694a203f6c57adef5edcb2c25426e82c9ac42c73358f8c617f2db31e66164",{"heading":88,"kind":89,"items":90},"Molarity ↔ molality","steps",[91],{"ref":92,"mode":19,"provenance":94,"text":95,"source_hash":96},{"type":17,"topic":7,"id":93,"field":17},"SC-R017","original","You need the density ρ. Take a reference amount (1 L for M, 1 kg solvent for m); mass of solution = ρ × V; solvent mass = solution − solute. Then m = n/kg_solvent, M = n/L_solution. No density → not convertible.","5b996909a092dcaffd288ffdd2bf124b3b49676e5dc3b6f4c4939e187885164f",{"heading":98,"kind":13,"items":99},"ppm & ppb",[100],{"ref":101,"mode":19,"provenance":94,"text":103,"source_hash":104},{"type":17,"topic":7,"id":102,"field":17},"SC-R021","ppm = (mass solute / mass solution) × 10⁶; ppb = (mass solute / mass solution) × 10⁹. For dilute water, 1 ppm ≈ 1 mg/L. Use these for trace levels where mass % is inconveniently small.","e1698db61d90cb386e41ca7ec96c214b210edcd6062a1a4e40c928c1dd01bd4f",{"heading":106,"kind":13,"items":107},"Like dissolves like",[108],{"ref":109,"mode":19,"provenance":94,"text":111,"source_hash":112},{"type":17,"topic":7,"id":110,"field":17},"SC-R020","Polar dissolves polar; non-polar dissolves non-polar. Ionic solids dissolve in polar solvents via ion-dipole forces. Mismatched polarity → immiscible layers or an insoluble solid.","6c7b6eda8d8295b84d18cf076a315050605a03ac8268d7f9104ee816bcdc83d7",1787246033575]