Pharmaceutical preparations consist of a number of different ingredients in a vehicle to produce a product. The ingredients and vehicles used in a product can be solid, liquid or gas.
Concentration is an expression of the ratio of the amount of an ingredient to the amount of product. It can be expressed in several ways:
In the case of a solid ingredient in a liquid vehicle the ratio is expressed as a weight in volume, denoted by w/v (for example sugar granules dissolved in a cup of coffee)
For a liquid ingredient in a solid vehicle the ratio is expressed as a volume in weight, denoted by v/w (for example lemon juice drizzled on the top of a cake)
If both ingredient and vehicle are liquids the ratio is expressed as a volume in volume, denoted by v/v (for example milk added to a cup of coffee)
When the ingredient and vehicle are both solid the ratio is expressed as a weight in weight, denoted by w/w (for example the blueberries as a proportion of the whole blueberry muffin)
The concentration of pharmaceutical preparations usually describes the strength of the drug in the preparations. In practice it is important that the patient receives the correct amount of the drug
If a patient receives too much of the drug they are likely to experience side-effects; side-effects are often dose-related, so the higher the amount of the drug the stronger the side-effect
If a patient receives too little of the drug, then their treatment is likely to be less effective than the prescriber intended. This can lead to a deterioration in the health of the patient.
We know that rational numbers can be expressed as ratios, fractions, decimals or percentages. As concentrations are expressions of ratios, they can also be expressed in different forms. The forms traditionally used are those of amount strengths, ratio strengths, parts per million and percentage strength.
Each of these four forms can be expressions of w/w, v/v, w/v or v/w, depending on whether solids or liquids are involved.
For ratio strengths, parts per million and percentage strengths in w/w or v/v the amounts of ingredients and product must be expressed in the same units:
a ratio of 7 mL to 12 mL is the ratio 7 : 12 v/v
a ratio of 3 mg to 5 mg is the ratio 3 : 5 w/w.
As long as the units used are the same, they lead to the same ratio.
For a concentration of 3 mg to 5 g, we need to change to the same units before we can express the w/w ratio.
Converting 5 g to milligrams:
g
–
–
mg
5 g =
5
0
0
0
= 5000 mg
The ratio becomes 3 mg to 5000 mg, which is the ratio 3 : 5000 w/w.
In the case of w/v and v/w there is an agreed convention that states that weight is expressed in grams and volume is expressed in millilitres.
Let us now examine each of the traditional ways of expressing concentrations in more detail.
Amount strengths can appear in any of the four forms, w/w, v/v, w/v or v/w. The amount strength is a ratio of the quantities and any units can be used, i.e. g/mL, mg/mL, mg/g, mL/mL, g/g, g/mL, etc. The units are stated in all cases.
Let us first consider a solid dissolved in a liquid to produce a solution.
Ratio strength is expressed as a ratio in the form 1 in r. The corresponding fraction would have a numerator of 1.
The agreed convention states that, when ratio strength represents a solid in a liquid involving units of weight and volume, the weight is expressed in grams and the volume in millilitres.
1 in 500 potassium permanganate in water is a solid in a liquid and is therefore a weight in volume (w/v) ratio strength. This means that the solution contains 1 g of potassium permanganate made up to 500 mL with water.
Example 4.3 illustrates the calculation of a ratio strength for a solid in a solid.
Parts per million (ppm) is used to denote concentrations in cases when the ratio of ingredient to product is very small. It is equivalent to a ratio in the form of p in 1000 000 or a fraction in which the denominator is 1000 000.
By the agreed convention, 1 ppm weight in volume is 1 g in 1000 000 mL; 1 ppm weight in weight is 1 mg per 1000 000 mg or 1 g per 1000 000 g. In volume in volume it is 1 mL in 1000 000 mL or 1 L in 1000 000 L.
In terms of parts, a percentage is the amount of ingredient in 100 parts of the product. In the w/v and v/w cases, using the convention, the units are grams per 100 mL and millilitres per 100 g.
