C₁V₁ = C₂V₂ — solve for any variable
Solution dilution uses the conservation of solute: C₁V₁ = C₂V₂. To prepare a diluted solution: calculate V₁ = C₂V₂/C₁, pipette V₁ of stock into a flask, add solvent up to V₂. Example: to make 500 mL of 1 M HCl from 12 M stock: V₁ = 1×500/12 = 41.7 mL. Take 41.7 mL concentrated HCl and dilute to 500 mL with water. Safety: always add acid to water (never the reverse) to safely dissipate heat. Use volumetric flasks for accuracy. For very small volumes, prepare intermediate dilutions rather than trying to measure < 0.1 mL. Always label diluted solutions with concentration, date, solvent, and preparer.