Dilution Concentration Calculator

Calculate Dilutions Using C₁V₁ = C₂V₂ — Calculate final concentration or volume from initial values.

Final Volume (V₂)

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Solvent to Add —

GUIDE

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Basic Principles of Dilution Formula

Dilution formula C₁V₁ = C₂V₂ is the basic formula for calculating solution concentration and volume. C₁ = initial concentration, V₁ = initial volume, C₂ = final concentration, V₂ = final volume. Example: to dilute 1000 ppm solution 10 mL to 100 ppm: 1000 × 10 = 100 × V₂ → V₂ = 100 mL. Add 90 mL water. This formula is based on conservation of solute amount. The moles of solute remain constant before and after dilution, only the solvent volume increases. Concentration units: ppm, M (molarity), %, mg/L, μg/mL. Must maintain unit consistency in calculations.

Serial Dilution Calculation Methods

Serial dilution is a stepwise dilution method to create very low concentrations from high concentration solutions. Example 1 (1:10 dilution 3 times): 1000 ppm solution diluted 1:10 three times → 100 ppm → 10 ppm → 1 ppm. Each step: 1mL solution + 9mL water. Example 2 (1:100 dilution): 10,000 ppm solution 1mL + 99mL water = 100 ppm. Or perform 1:10 dilution twice. Microbial culture: To dilute bacteria from 10⁹ CFU/mL to 10² CFU/mL requires 10⁷-fold dilution. Perform 1:10 dilution 7 times or 1:100 dilution 3.5 times.

Laboratory Solution Preparation Guide

1M NaCl solution 1L preparation: NaCl molecular weight = 58.44 g/mol. 1M = 1 mol/L, so dissolve 58.44g NaCl in water and dilute to 1L. Volumetric flask required. Dilute to 0.1M: Dilute 1M solution 100mL to 1L (add 900mL water) → 0.1M. % concentration: For 10% sugar solution 500mL: sugar 50g + 450mL water (w/v%). ppm solution: 1000 ppm = 1000 mg/L = 0.1%. For 1000 ppm salt water 1L: salt 1g + 1L water.

Concentration Unit Conversion

ppm ↔ %: 1% = 10,000 ppm. Example: 500 ppm = 0.05%. Molarity (M) ↔ g/L: M = (g/L) ÷ molecular weight. Example: NaCl 58.44 g/L = 1M. ppm ↔ mg/L: 1 ppm = 1 mg/L (water basis). ppb ↔ μg/L: 1 ppb = 1 μg/L. 100 ppb = 0.1 ppm. w/v% ↔ g/L: 5% w/v = 50 g/L. v/v%: 70% alcohol v/v = 700 mL/L.

Error Management and Accuracy

Pipette error: 10mL pipette with ±0.05mL accuracy = ±0.5% error. Precision experiments require micropipettes (within ±1%). Volumetric flask use: For 100mL dilution, use volumetric flask not beaker. Beaker: ±5% error, volumetric flask: ±0.1% error. Dilution order: Add high concentration solution first, then add solvent. Reverse order causes concentration non-uniformity. Mixing method: After dilution, mix thoroughly with vortex mixer or stirrer.

Industry-Specific Dilution Applications

Water quality: To maintain tap water chlorine 0.5~1.0 ppm, dilute sodium hypochlorite (10% stock). 10% = 100,000 ppm, so for 1 ppm requires 100,000-fold dilution. Stock 1mL → dilute in 100L water. Pesticide application: Herbicide stock (48% glyphosate) diluted 1000-fold for application. 100mL stock + 100L water = 0.048% = 480 ppm. Cleaning agents: Kitchen detergent diluted 100~500-fold. Medical disinfection: 70% alcohol = 99% ethanol 707mL + distilled water 293mL.