How can you calculate 1000 out of 1000

Calculate dilutions and mixing ratios

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There are detergents and disinfectants in concentrated form, which must be mixed with water in a certain ratio before use. The information is given in percent or in proportion.

Calculate the dilution with percentages

Figure 1: Dilution in percent

example 1: A 1% dilution must be made for a ready-to-use solution. Let's take the simplest case first: We need 1 liter of solution, i.e. 1000 ml. Now 1% of 1000 ml has to be calculated, which is 10 ml. If you cannot calculate that in your head, just take a pen and paper. To obtain a 1% solution, 10 ml of concentrate are diluted with 990 ml of water, the total is 1000 ml.

Example 2: 5 liters of a solution with a 2.5% dilution should be prepared.

  • Step 1: Convert the liters to milliliters, 5 liters are 5000 ml.
  • Step 2: calculate 2.5% of 5000 ml, you get 125 ml.
  • 3rd step: Calculate the amount of water: 5000 ml - 125 ml = 4875 ml.

Practical procedure: 125 ml of concentrate are measured and then made up to 5000 ml (5 liters).

Calculation of the quantities with proportions

When specifying ratios, e.g. 1:10, between the dilution and the mixture can be distinguished. At a dilution becomes 1 1 unit of a solvent (usually water) is added to the unit of volume of a substance (e.g. a cleaning agent concentrate) to achieve the desired concentration. Example: 1000 ml cleaning agent concentrate + 1000 ml water = 2000 ml, corresponds to a dilution factor of 1:2. Another example: with a dilution of 1: 6, 5 volume units of the solvent water are added to one volume unit of detergent concentrate (1 + 5 = 6).
At a 1: 1 mixture the mixture of one volume unit of one substance with one volume unit of another substance results in two volume units. A 1:1 Mixture corresponds to one 1:2 Dilution.
The following table should clarify the differences:

Final quantityThe final quantity must be 10 times the initial quantity:
1*10 = 10
The sum of the proportions results in the final quantity:
1 part + 10 parts = 11 parts
End shares1011
exampleDilution of cleaning agent concentrate in a ratio of 1:10:
100 ml concentrate
+ 900 ml of water = 1000 ml.
Mixture of a cleaning agent solution in a ratio of 1:10:
100 ml concentrate
+ 1000 ml of water = 1100 ml.

Figure 2: Difference between dilution and mixing

Calculation of the dilution

In this case the information reads: The concentrate must be diluted in a ratio of 1: 5 or 1:10. Let's take a relatively simple case again first, we want to make a 1:10 dilution. This means that 1 ml of concentrate has to be diluted with 9 ml of water, or a multiple thereof e.g. B. 10 ml concentrate diluted with 90 ml water etc.

In general, you want a certain amount of solution at the end, for example 1 or 5 liters. This is relatively easy: We stick to the 1:10 dilution, 1 ml concentrate must be diluted with 9 ml water, or in other words: 1 part concentrate + 9 parts water = 10 parts. If a total of 5 liters of solution are to be prepared, the 10 parts = 5 liters or 5000 ml. One part is calculated as follows: 5000 ml: 10 = 500 ml (= 1/10 part).

1 part = 500 ml,
9 parts = 4500 ml.

500 ml of concentrate are measured in a measuring cup and then, if the measuring cup is large enough, it is made up to 5 liters. Otherwise the concentrate is poured into a bucket with a marking and then topped up to 5 liters in the bucket.

Example: 1 liter of solution should be made up with a dilution of 1: 4. That means 1 part concentrate is diluted with 3 parts water, together that's 4 parts. The calculation is 1000 ml: 4 = 250 ml (= 1/4 part).

1 part = 250 ml,
3 parts = 750 ml.

For 1 liter of solution, 250 ml of concentrate must be diluted with 750 ml of water.

Calculation of the quantities for a mixture

You should mix a cleaning agent in a ratio of 1: 1 with water. In this case, take 1 part detergent + 1 part water = 2 parts solution.
example: Calculate the amounts of detergent and water if you are to mix the detergent in a ratio of 1: 2 and want a total of 3 liters of solution.

1 part detergent = 1 liter
2 parts of water = 2 liters
Total = 3 liters.

Calculation of a solution with a mixing cross

A 2.5% use solution of a cleaning agent is to be produced. The concentrate is a 20% solution to which water should be added. The mixing ratio can be calculated with a mixing cross.

The difference between 20% and 2.5% is 17.5.

Water (= 0%) is added to the starting solution.

The difference from 0% (water) to 2.5% is 2.5.

To get a 2.5% solution, you need to take 2.5 parts of the 20% starting solution and mix it with 17.5 parts of water (0%).


Mixing ratio:

Starting solution 20% → 2.5 parts
Water 0% → 17.5 parts
Total = 20 parts

5 liters (= 5000 ml) of a 2.5% working solution should be made up. A total of 20 parts are required.
5000 ml: 20 = 250.

2.5 x 250 = 625 ml the 20% starting solution
17.5 x 250 = 4375 ml Water (0%)
Total = 5000 ml

To the exercises


Mixing ratio for mixtures: calculate the amount, Heinz Becker Neumünster
Ruhr University Bochum: Mixture cross simple. Accessed on August 17, 2017
Mitch Fry, Elizabeth Page: Starting Knowledge Chemistry. A crash course for life sciences and medicine students. Elsevier GmbH, Munich 2007
Prof. Dr. Volker Wiskamp: Inorganic Chemistry. A practical textbook. Publisher Harri Deutsch. Unchanged reprint of the first edition in 1996, 2007

Detailed references

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