This all-in-one online Dilution Calculator performs calculations using the formula linking the concentration (or molarity) of a solution with the volume of the solution before and after dilution. You can enter the values of any three parameters in the fields of the calculator and find the missing parameter.
C1·V1 = C2·V2
Dilution Formula
Dilution is the process of decreasing the concentration of a solute in a solution, simply by adding more solvent to the solution. This process keeps the amount of solute constant, but decreases its final concentration by increasing the total amount of solution.
Diluting solutions is used in the laboratory, as stock solutions are often stored in concentrated forms. For the solutions to be usable in the lab, they must be accurately diluted to a desired, lesser concentration.
Dilution equation can be represented by the following dilution formula:
C1·V1 = C2·V2 ,
where
• C1 – initial concentration or molarity,
• V1 – initial volume,
• C2 – final concentration or molarity,
• V2 – final volume.
This dilution formula is based on the principle of conservation of mass. When a solution is diluted, the number of moles of solute (the substance being dissolved) remains constant, while the number of moles of solvent (the substance doing the dissolving) increases. But the formula itself includes volumes, not masses.
The dilution equation is a convenient way to express the relationship between concentrations and volumes of solutions, but it is only valid under some assumption. This assumption is that the volumes of the substances being used are additive, i.e. the final volume is the sum of the initial volumes, so no volume is lost or gained.
Ideal Solutions
A solution that has the property of additive volumes and for which the above dilution formula is valid is called an ideal solution. An ideal solution is similar to an ideal gas, with the important difference that intermolecular interactions in liquids are very strong and cannot simply be neglected, as in the case of ideal gases.
Further, we assume that the average interaction forces are the same between all the molecules in the solution, i.e. both between the molecules themselves of each of the substances in the mixture, as well as between the molecules of different substances in the mixture.
Unlike ideal solutions, where volumes are strictly additive and mixing is always complete, the volume of a non-ideal solution, in general, is not a simple sum of the volumes of the constituent liquids.
It is important to note that the above assumptions are generally valid for dilutions performed at low concentrations and moderate dilutions and under standard laboratory conditions.
This is true because in such a case the molar fraction of one component approaches unity, and the other, respectively, approaches zero. So, it is obvious that the behavior of the solution approaches ideality. This is a simple consequence of the fact that under these conditions each molecule of one of the substances is surrounded mainly by its own kind, and the few interactions with the molecules of the second substance will have little effect.
In some cases, where the above assumptions are not met, such as dilutions in non-ideal solutions or dilutions at high concentrations, other methods may need to be used to calculate dilutions.
Dilution Calculations
Our solution dilution calculator will easily help you to calculate how to dilute a stock solution of known concentration to obtain a desired volume of diluted solution.
Let’s consider an example. Suppose 250 mL of a 0.5 M aqueous solution of NaCl is diluted with water to a final concentration of 100 mM. What is the final volume of the diluted solution? What is the volume of water to be added to the initial solution?
Plugging all the numbers into the dilution calculator we can instantly get: 1.25 L is the final volume of solution. So, as much as 1.25 L – 250 mL = 1 L of water is to be added to the initial solution to achieve the desired concentration.
Related calculators
Check out our other chemistry calculators such as Molality Calculator or Mole Calculator.