# Dilution of solutions

This online calculator allows you to find one of four parameters: volume before dilution, molar concentration before dilution, volume after dilution, molar concentration after dilution - based on the other three. It is intended for solving problems on dilution of solutions.

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#### Timur

Created: 2023-11-17 19:19:28, Last updated: 2023-11-18 08:02:36

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Problems on dilution of solutions usually sound like the following: "To what volume should 10 mL of a 5.0M solution be diluted so that its molarity becomes 1.0M" or "Determine the molarity of the solution obtained by diluting 100 mL of a 1.0M solution to 1.0 liter". The calculation formulas are given below the calculator. If no volumes are given in the problem and only mixing proportions are required, the Mixing solutions of different concentrations calculator can be used.

#### Dilution of solutions

Molar concentration before dilution, M (mol/liter)

Volume before dilution, ml

Molar concentration after dilution, M (mol/liter)

Volume after dilution, ml

Digits after the decimal point: 2

### Dilution of solutions by adding solvent

In example problems, solutions are specified in terms of the molarity, or molar concentration of a solution, Cₘ, measured in mol/L (the letter M is used instead of mol/L), and showing the number of moles of dissolved solute in 1 liter of solution.
$C_m=\frac{n}{V}$

Note that the amount of substance per liter of solution, not solvent. So, for example, to get 1 liter of solution, you do not add the substance to 1 liter of solvent (in this case the volume of the solution will be slightly more than 1 liter), but you add solvent (usually water) to the substance until you get the given volume of 1 liter.

As for the dilution of solutions, it should be understood that the addition of diluent does not change the number of moles of the dissolved substance in any way, and therefore we can write the following proportion:
$n=c_1v_1=c_2v_2$,
where
c₁ is the molar concentration or molarity of the solution before dilution
v₁ - volume of the solution before dilution
c₂ - molar concentration or molarity of the solution after dilution
v₂ - volume of solution after dilution

In the proportion $c_1v_1=c_2v_2$ knowing any three quantities, you can find the fourth, which is what the calculator above does.

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