Solutions & Concentration Cheat Sheet

Mass percent

CORE RULE

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.

Volume percent

CORE RULE

Volume % = (component volume / total solution volume) × 100. Given one volume and a target %, solve x / (x + V_other) = target/100.

Solubility & saturation

CORE RULE

Solubility = grams of solute per 100 g water at a stated temperature (supplied). Saturated-solution mass % = solubility / (solubility + 100) × 100.

Molarity

CORE RULE

Molarity M = moles solute / litres of solution. Convert mL → L (÷1000); mass → moles via molar mass. For hydrates use the full hydrate molar mass.

Molarity of each ion

CORE RULE

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⁻.

Dilution

CORE RULE

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).

Stock solutions

CORE RULE

Use M₁V₁ = M₂V₂ with 1 = stock (concentrated), 2 = target (dilute). Volume of stock V₁ = M₂V₂ / M₁; stock concentration M₁ = M₂V₂ / V₁.

Mixing same-compound solutions

CORE RULE

Final M = (M₁V₁ + M₂V₂) / (V₁ + V₂). The result lands between the two, nearer the larger-volume solution (a quick sanity check).

Molality

CORE RULE

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.

Molarity ↔ molality

METHOD

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.

ppm & ppb

CORE RULE

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.

Like dissolves like

CORE RULE

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.