Definition
Dilution is the process of reducing the concentration of substances and mixtures. Dilutions are commonly used in pharmacy, especially for liquid and semisolid dosage forms, and play an important role in manufacturing. Solid dosage forms such as powders can also be diluted. For an optimal understanding of this topic, we also recommend the articles Mass, Volume, Concentration, and Density.
Implementation
Usually, solvent or base is added during dilution. Because this increases the volume and mass, the concentration decreases. In the following example with a mass concentration, the volume V is the divisor. If V increases, the concentration decreases:
- C (mass concentration) = m (mass) / V (volume).
Calculation of dilutions
The calculation of dilutions is based on the principle that the amount or number of dissolved or dispersed substance remains the same before and after dilution. For example, adding water to a syrup does not change the amount of sugar dissolved. Using the example of substance amount concentration:
- C (substance amount concentration) = n (substance amount) / V (volume).
So holds:
- N = C x V
The amount of substance of the substance is the same before (n1) and after dilution (n2):
- N1 = n2
So holds:
- C1 (concentration 1) x V1 (volume 1) = C2 (concentration 2) x V2 (volume 2).
This is the well-known formula that is often used in connection with dilutions.
Mass concentration
This formula is also used for a mass concentration:
- C (mass concentration) = m (mass) / V (volume).
The mass is the same before and after dilution:
- M1 = m2
Accordingly, the same is true here:
- C1 x V1 = C2 x V2
Mase percent
In mass percent, the volume is replaced by the total mass:
- C1 x m1 = C2 x m2
Mnemonic phrases such as “customer times customer by pharmacist” (doctor times doctor by pharmacy) and “I will i will i han” are based on this formula. This calculates the concentrated mass m1, which is needed for dilution:
- M1 = (C2 x m2) / C1
- M1 = (customer x customer) / pharmacist
- M1 = (I will x I will) / I han
Example: a customer orders 100 g of salicylaseline 10%. The pharmacy has salicylaseline 50% in stock. How much of the concentrated ointment is needed to make it? Solution:
- M1 = (10% x 100 g) / 50% = 20 g
For the preparation, 20 g of salicylaseline 50% (m1) is mixed with 80 g of petrolatum. This gives a total of 100 g salicylaseline 10% (m2).
Volume percent and alcohol dilutions
Things get more complicated when calculating with volume percentages. A typical example is alcohol dilution. Here, our dilution formula shown above (C1 x V1 = C2 x V2) cannot be applied directly. If 50 ml of water is mixed with 50 ml of water, the result is 100 ml of water. However, if 50 ml of water is mixed with 50 ml of ethanol 96% (V/V), the total is not 100 ml, but noticeably less! This phenomenon is called volume contraction. Therefore, it is not possible to calculate with the volumes. But with the masses, because they do not change, even with a different pressure. For the calculation of alcohol dilutions, therefore, both the volumes and the volume percentages must be converted into masses or mass percentages. A detailed ethanol table with the required data can be found in the European Pharmacopoeia.
Example of the calculation of an alcohol dilution
Ethanol 96% (V/V) and purified water are to be used to make 100 ml of ethanol 20% (V/V). How much ethanol and water are needed to do this? We set the temperature at 20°C. As already mentioned, the volume percentages and volumes must be converted to mass percentages and masses. The ethanol table of the European Pharmacopoeia is available for this purpose, in which the densities and mass percentages are listed.
- Ethanol 96% (V/V) corresponds to 93.84% (m/m) and has a density of 0.80742 grams per cubic centimeter.
- Ethanol 20% (V/V) corresponds to 16.21% (m/m) and has a density of 0.97356 grams per cubic centimeter.
- For water, we calculate a density of 1 gram per cubic centimeter.
It is valid:
- Mass = density x volume
So:
- Target size: 100 ml ethanol 16.21% (m/m) = 0.97356 grams per cubic centimeter x 100 ml = 97.356 g
Calculate dilution using our formula for mass percentages (see above):
- M1 = (C2 x m2) / C1 = (16.21% x 97.356 g) / 93.84% = 16.82 g ethanol 96%.
Solution: 16.82 g ethanol 96% is supplemented on the balance with water to 97.356 g. Tip: In the Formularium Helveticum (FH) is a table with the calculated values for the various alcohol dilutions. There are digital alcohol dilution calculators on the Internet.
Hydrogen peroxide
Hydrogen peroxide is also commonly diluted in pharmacies. It is monographed in the European Pharmacopoeia at percent by mass:
- Hydrogen peroxide 30% (m/m)
- Hydrogen peroxide 3% (m/m)
Hydrogen peroxide can therefore be diluted on the balance. The density of hydrogen peroxide (30%) is 1.1 grams per cubic centimeter, slightly higher than that of water.
