When a product is diluted there is a change in the amount of product, although at the same time the amount of ingredient in the product remains the same.
In practice, a pharmaceutical product may be supplied in a concentrated form. This has many advantages as the product may be more stable in the concentrated form, it takes up less space in the pharmacy and, most importantly, the pharmacist can then dilute the preparation to produce several different final strengths of product. However, failure by the pharmacist to correctly calculate the dilution will result in the patient receiving too much or too little of the active ingredient.
If a solution containing 5 g of an ingredient in 200 mL of product is diluted to 400 mL with vehicle, the final product becomes 400 mL containing 5 g of ingredient. The volume of product has changed (it has doubled) and the amount of ingredient is still 5 g.
The amount strength has therefore changed from 5 g/200 mL to 5 g/400 mL.
Example 5.2 shows the method of calculating the final concentration of the diluted product starting with a ratio strength.
Rather than keeping large amounts of products in the dispensary it is usual to keep concentrated products. These stock solutions can then be diluted to the desired concentration for the final product.
Example 5.3 starts with a ratio strength.
Example 5.4 starts with a percentage strength.
Sometimes we are required to calculate the amount of diluent required to produce a stated final concentration.
Concentrated waters, such as rose water, peppermint water and chloroform water, are used to produce single-strength products. They are intended for dilution in the ratio 1 part of concentrated water with 39 parts of water. To produce the single-strength product, we take one part of the concentrate and dilute it to 40 parts with water.
Suppose that we have to make volumes of single-strength chloroform water (50 mL, 100 mL, 200 mL, 300 mL, 500 mL) from chloroform water concentrate. Since chloroform water concentrate is in the ratio 1 : 40, we have to take 1 mL and dilute it to 40 mL with water in order to obtain single-strength chloroform water.
Setting up proportional sets:
chloroform water concentrate (mL)
1
a
b
c
d
e
water (mL) to
40
50
100
200
300
500
If we calculate the value for c:
We therefore require 5 mL of chloroform water concentrate made up to 200 mL with water to produce 200 mL of single-strength chloroform water.
This calculation can be repeated for a, b, d and e. Alternatively, these values can be obtained from the value for c by ‘spotting’, as follows:
Thus, the following proportional sets are obtained for single-strength chloroform water:
chloroform water concentrate (mL)
1
1.25
2.5
5
7.5
12.5
water (mL) to
40
50
100
200
300
500
In most formulae the chloroform water is expressed as double strength for half the total volume. To make double-strength chloroform water we have to take twice the volume of the chloroform water concentrate.
One of the problems when weighing ingredients for preparations is that amounts of less than 100 mg cannot be weighed with sufficient accuracy. We have to use trituration to get the required amount.
The Pharmaceutical Codex states that powders must weigh a minimum of 120 mg. No maximum weight is stated. If the amount of drug in the powder is less than 120 mg, it is necessary to include an inert powder to bulk up the powder to the minimum weight.
