How to Calculate Dilutions (C₁V₁ = C₂V₂)
Dilution is the process of reducing the concentration of a solution by adding more solvent. The fundamental dilution equation C₁V₁ = C₂V₂ states that the amount of solute before dilution equals the amount after — only the concentration and volume change. This equation is used daily in laboratories, pharmacies, and industrial chemical production.
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Formula
Dilution Calculator (C₁V₁ = C₂V₂)
Calculate dilution using C₁V₁ = C₂V₂ — solve for any one unknown.
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Worked Example
Given:
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FAQs
How do I prepare a diluted solution step by step?
Calculate V₁ = C₂V₂/C₁. Measure that volume of stock solution. Transfer to a volumetric flask. Add solvent until the final volume V₂ is reached. Mix thoroughly. For example, to make 500 mL of 0.1 M HCl from 1 M HCl: V₁ = (0.1)(500)/1 = 50 mL stock, then fill to 500 mL.
What is a serial dilution?
A serial dilution performs multiple sequential dilutions, each reducing concentration by the same factor. For example, a 1:10 serial dilution takes 1 mL of sample and adds 9 mL of diluent, then repeats. After 6 steps, concentration is reduced by 10⁶ = one million times. Used in microbiology to count bacteria.
Why does diluting a solution change concentration but not the amount of solute?
Dilution only adds more solvent — no solute is removed or added. The amount of solute (moles = C × V) remains constant. More solvent simply spreads the same number of solute molecules through a larger volume, reducing concentration.