Adjust parameters and observe how the result changes in real time · C₁·V₁ = C₂·V₂
Concentration of the concentrated stock solution
Volume to take from the stock solution
Target concentration after dilution
250
mL150
mL — concentration and volume of the stock solution.
— concentration and volume of the final diluted solution.
Algebraic rearrangement of the dilution law to isolate the current unknown variable ().
Dimensionless ratio indicating how many times the original concentration has been diluted. Fundamental for planning serial dilutions in microbiology and biochemistry.
The equation is based on the principle of conservation of mass. When solvent is added to a solution, the amount of solute (moles or mass) remains strictly constant (). Since the amount of solute is the product of concentration and volume (), the equality follows directly.
Mathematically, the solvent to add is . However, in practical laboratory analysis, volumes of real mixtures are rarely additive due to intermolecular interactions (such as hydrogen bonding). For instance, mixing 50 mL of ethanol and 50 mL of water yields ~96 mL of solution, not 100 mL, due to the contraction of partial molar volumes.
The dilution of highly concentrated solutions (especially strong acids or bases) is not a thermo-neutral process. Ion hydration releases a large amount of thermal energy. To prevent localized boiling and splashing, the universal safety rule dictates that the concentrated solute must always be added slowly to a fraction of the solvent, and never the reverse.
This suite performs predictive analysis on the inputs. If the algorithm detects that or that, it will issue a formal warning. Physically, increasing concentration or reducing volume requires evaporation, precipitation, or the addition of pure solute, which breaks the simple dilution mathematical modeland requires a more complex mass balance.