Dilution Calculator
What is Dilution?
Dilution is the process of adding solvent to a concentrated solution to decrease its concentration.
Dilution Equation:
c₁V₁ = c₂V₂
The amount of substance remains constant!
c₁V₁ = c₂V₂
The amount of substance remains constant!
Variables:
- c₁: initial concentration
- V₁: volume of stock solution
- c₂: final concentration
- V₂: final total volume
Formulas
Dilution Equation:
c₁V₁ = c₂V₂
c₁V₁ = c₂V₂
Final Concentration:
c₂ = (c₁·V₁) / V₂
c₂ = (c₁·V₁) / V₂
Final Volume:
V₂ = (c₁·V₁) / c₂
V₂ = (c₁·V₁) / c₂
Initial Concentration:
c₁ = (c₂·V₂) / V₁
c₁ = (c₂·V₂) / V₁
Important: The dilution equation is valid only when the amount of substance n remains constant. The number of molecules stays the same; only the concentration changes.
Practical Examples
Example 1: Diluting Hydrochloric Acid
You have 100 mL of a 2 mol/L HCl solution and dilute it to 500 mL.
c₁ = 2 mol/L, V₁ = 100 mL, V₂ = 500 mL
c₂ = (2 × 100) / 500 = 0.4 mol/L
You have 100 mL of a 2 mol/L HCl solution and dilute it to 500 mL.
c₁ = 2 mol/L, V₁ = 100 mL, V₂ = 500 mL
c₂ = (2 × 100) / 500 = 0.4 mol/L
Example 2: Calculating Final Volume
You want to prepare a 0.1 mol/L solution from 50 mL of a 1 mol/L solution.
c₁ = 1 mol/L, V₁ = 50 mL, c₂ = 0.1 mol/L
V₂ = (1 × 50) / 0.1 = 500 mL
You want to prepare a 0.1 mol/L solution from 50 mL of a 1 mol/L solution.
c₁ = 1 mol/L, V₁ = 50 mL, c₂ = 0.1 mol/L
V₂ = (1 × 50) / 0.1 = 500 mL
Example 3: Laboratory Practice
A stock solution of unknown concentration is diluted from 25 mL to 250 mL to obtain a 0.05 mol/L solution.
V₁ = 25 mL, V₂ = 250 mL, c₂ = 0.05 mol/L
c₁ = (0.05 × 250) / 25 = 0.5 mol/L
A stock solution of unknown concentration is diluted from 25 mL to 250 mL to obtain a 0.05 mol/L solution.
V₁ = 25 mL, V₂ = 250 mL, c₂ = 0.05 mol/L
c₁ = (0.05 × 250) / 25 = 0.5 mol/L
Technical Background
Practical Tips for Dilution:
- Safety: When diluting acids, always add acid to water, never the reverse!
- Volume Contraction: When mixing, volumes do not simply add (volume contraction occurs)
- Temperature: Dilution is often exothermic; the solution becomes hot!
- Dilution Factor: The ratio V₂/V₁ describes how many times the solution was diluted
Serial Dilutions in Analytics:
- Laboratory Diagnostics: Serial dilutions for concentration determination
- Microbiology: Dilution series for colony counting and viability testing
- Pharmacology: Dose-dependent test series
- Immunology: Antigen-antibody reactions at various concentrations
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