Solution Dilution Calculator

The core principle behind solution dilution is the conservation of moles. Because adding solvent does not change the total number of solute particles present, the product of the initial concentration and initial volume must equal the product of the final concentration and final volume. This relationship is expressed universally by the standard dilution equation: C₁V₁ = C₂V₂. Here, C₁ represents the initial concentration of the stock solution, V₁ is the volume of the stock solution needed, C₂ is the desired final concentration, and V₂ is the total final volume of the diluted solution. By entering any three of these variables into the calculator, you can instantly solve for the remaining unknown parameter.

Imagine you need to prepare 500 mL of a 0.1 M sodium chloride solution (C₂ = 0.1 M, V₂ = 500 mL) using a concentrated stock solution of 2.0 M sodium chloride (C₁ = 2.0 M). You want to find out how much of the stock solution (V₁) you must measure out. Using the formula V₁ = (C₂ * V₂) / C₁, we plug in our known values: V₁ = (0.1 M * 500 mL) / 2.0 M. Multiplying the numerator yields 50, and dividing by 2.0 gives an initial volume of 25 mL. Therefore, you must measure 25 mL of your 2.0 M stock solution and add sufficient water to reach a final total volume of 500 mL.

Always maintain consistent units for your measurements; if your final volume is in milliliters, ensure your initial volume is calculated in milliliters as well. When preparing precise solutions, never add the final volume of solvent directly to your solute. Instead, add your calculated stock volume to a volumetric flask containing a portion of the solvent, mix thoroughly, and then carefully bring the total solution up to the calibration mark with the remaining solvent.