# Mixing solutions of different concentrations

The concentration of a chemical in a solution can be reduced by mixing it with a less concentrated solution of the same substance. The calculator below allows you to determine the proportions in which two solutions need to be mixed to obtain the desired concentration.

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#### Timur

Created: 2023-11-04 05:57:27, Last updated: 2023-11-04 05:57:27

To obtain the proportion, you only need to know the concentrations of the solutions being mixed and the target concentration. The result is given as the percentage of each of the mixed solutions in the resulting solution. For example, values 25 and 75 will mean that you need to take 25 parts of the first solution and 75 parts of the second. If the first solution is mixed with pure diluent, specify the second concentration as zero. Calculation formulas are given below the calculator.

#### Proportions of diluted solution and diluent

Digits after the decimal point: 2
Solution ratio

Diluent ratio

### Dilution by mixing solutions of different concentrations

Obviously, the total amount of substance is conserved during mixing. Thus we can write (using, for example, molar concentration)
$C_x=\frac{n_x}{V_x}=\frac{n_1+n_2}{V_1+V_2}=\frac{C_1V_1+C_2V_2}{V_1+V2}$, where
Cₓ is the target molar concentration
nₓ is the amount of substance in the resulting solution
Vₓ - volume of the solution obtained
n₁ - amount of substance in the first solution to be mixed
C₁ - molarity of the first miscible solution
V₁ - volume of the first miscible solution
n₂ - quantity of substance of the second miscible solution
C₂ - molarity of the second miscible solution
V₂ - volume of the second miscible solution

It should be noted that in the above formula, replacing the volume of the resulting solution by the sum of the volumes of the mixed solutions is possible if the rule of additivity of volumes is satisfied for the dissolved substance, otherwise the calculation will be inaccurate.

From the obtained formula we express the ratio of volumes of mixed solutions
$C_x=\frac{C_1V_1+C_2V_2}{V_1+V2}\\C_xV_1+C_xV_2=C_1V_1+C_2V_2\\C_x\frac{V_1}{V_2}+C_x=C_1\frac{V_1}{V_2}+C_2\\C_x\frac{V_1}{V_2}- C_1\frac{V_1}{V_2}=C_2-C_x\\\frac{V_1}{V_2}(C_x-C_1)=C_2-C_x\\\frac{V_1}{V_2}=\frac{C_2-C_x}{C_x-C_1}$
This formula is what is used in the calculator.

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