Dilution to a Target Concentration
Dilution to a Target Concentration
Diluting a concentrated stock solution to a working concentration is one of the most frequently performed calculations in a chemistry or process lab, underpinning everything from reagent prep to feed makeup tanks, and it rests on a single conservation law: the amount of solute does not change when you add solvent, only its concentration does. Getting the target volume wrong is a common and consequential lab error — too little solvent leaves the solution over-strength and can throw off a titration or reaction stoichiometry, while too much wastes reagent and dilutes below the intended working range — so this simple C1V1 = C2V2 relationship is worth writing out explicitly rather than doing by memory.
Conservation of solute mass gives C1·V1 = C2·V2, so the final volume is V2 = C1·V1/C2. where C1 and V1 are the concentration and volume of the concentrated stock solution, and C2 is the target (diluted) concentration.
Inputs
C_1 := 5 mol/L=5000 mol/m^3
V_1 := 0.1 L=1e-04 m^3
C_2 := 0.5 mol/L=500 mol/m^3
Because the total moles of solute stay fixed as solvent is added, the same moles that were in the small stock volume must end up in the larger final volume, which rearranges directly to the target volume needed.
V_2 := C_1·V_1/C_2=1e-03 m^3
Results
Here the stock must be diluted tenfold, to a final volume of 1 L, meaning 0.9 L of solvent gets added to the original 0.1 L of stock. This dilution factor (V2/V1 = 10, or equivalently C1/C2) is the number worth sanity-checking against the intended use — a factor far outside a normal working range for the application is usually a sign the stock concentration or target was mistyped. In practice the diluted volume is often made up to the mark in a volumetric flask rather than adding a separately measured volume of solvent, which avoids small volume-of-mixing errors.
Assumptions & limitations
- Ideal mixing with no volume contraction or expansion on dilution.
- Solute assumed to remain fully dissolved at both concentrations.
- Isothermal dilution (no significant heat of dilution effects).
- Concentrations expressed on a consistent volume basis (molarity).