Dilution Factor Calculator

Calculate dilutions, concentrations, and volumes for laboratory work

Dilution Equation: C₁V₁ = C₂V₂

Calculate any one variable given the other three

Initial Solution

Final Solution

Understanding Dilutions

Dilution is the process of reducing the concentration of a solution by adding more solvent. This fundamental technique is used extensively in analytical chemistry, biology, and clinical laboratories. The key principle is that the amount of solute remains constant while the volume increases.

Key Formulas

Dilution Equation

C₁V₁ = C₂V₂

  • • C₁ = initial concentration
  • • V₁ = initial volume (volume to transfer)
  • • C₂ = final concentration
  • • V₂ = final volume (total volume)

Dilution Factor

DF = V_final / V_sample = C_initial / C_final

A dilution factor of 10 means the solution is 10 times less concentrated (1:10 dilution).

Serial Dilution

Total DF = DF₁ × DF₂ × DF₃ × ...

Three 1:10 dilutions give a total dilution factor of 1000 (10 × 10 × 10).

Example Problems

Example 1: Making a Dilution

Problem: You need 50 mL of 0.1 M NaCl. You have a 1 M stock solution. How much stock do you need?

Solution:

C₁V₁ = C₂V₂
(1 M)(V₁) = (0.1 M)(50 mL)
V₁ = 5 mL

Answer: Take 5 mL of stock and add water to 50 mL total

Example 2: Dilution Factor

Problem: You dilute 1 mL of sample to 10 mL total. What's the dilution factor?

Solution:

DF = V_final / V_sample
DF = 10 mL / 1 mL
DF = 10

Answer: This is a 1:10 dilution (dilution factor = 10)

Example 3: Serial Dilution

Problem: Starting with 100 mg/mL, perform three 1:10 dilutions. What's the final concentration?

Solution:

Total DF = 10 × 10 × 10 = 1000
C_final = C_initial / DF
C_final = 100 mg/mL / 1000
C_final = 0.1 mg/mL

Answer: Final concentration is 0.1 mg/mL (100 µg/mL)

Common Dilution Ratios

Dilution Ratio Dilution Factor Sample Volume Final Volume Diluent to Add
1:2 2 1 mL 2 mL 1 mL
1:5 5 1 mL 5 mL 4 mL
1:10 10 1 mL 10 mL 9 mL
1:100 100 1 mL 100 mL 99 mL
1:1000 1000 1 mL 1000 mL 999 mL

Applications of Dilutions

1. Analytical Chemistry

Preparing standard solutions for calibration curves, bringing samples into measurable range for spectrophotometry, and diluting concentrated acids and bases.

2. Microbiology

Serial dilutions for colony counting, preparing bacterial cultures to desired cell density, and diluting samples for plate counts.

3. Molecular Biology

Diluting DNA/RNA for PCR, preparing working concentrations of enzymes and buffers, and diluting protein samples for assays.

4. Clinical Chemistry

Diluting patient samples when analyte concentration exceeds instrument range, preparing quality control materials, and making reagent working solutions.

5. Pharmaceutical Sciences

Preparing drug formulations at specific concentrations, diluting stock solutions for dose-response studies, and making standard solutions for drug analysis.

References

Dilution calculations are based on fundamental analytical chemistry principles from reputable sources:

Note: Always use proper laboratory techniques when performing dilutions. Use calibrated pipettes and volumetric flasks for accurate results. Mix solutions thoroughly after dilution. Remember that the calculation assumes volumes are additive and temperature effects are negligible. For precision work, consider temperature-dependent volume changes and non-ideal solution behavior.

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