You assign the units to the parts depending on whether you are dealing with w/w, w/v, or v/v preparations.
2. The very same default rules based on weighing of solids and volumetric measurement of liquids used for percentage strength applies here. Thus, the cinnamon oil solution is assumed to be v/v since no other indication is given. Both liquids must have the same units. We can express this concentration as a percentage by first converting the ratio to a decimal value.
What is the percentage strength of a 1:400 solution of an oil in alcohol?
Solution. 0.25% v/v
CALCULATIONS
1:400 = 1 mL oil in 400 mL solution Using proportion,
j = 0.25 mL oil
Since percent is defined as parts per 100, the strength of the solution is 0.25% v/v.
3. A viral vaccine is preserved with 1:10,000 solution of benzalkonium chloride (a solid). How would we express this concentration as percentage?
Solution. 0.01% w/v
CALCULATIONS
1:10,000 = 1 g benz. in 10,000 mL solution
4. A 1:40 dilution of atropine in a solid mixture means that 1 g of atropine is contained in 40 g of the mixture. In systems of this type, the other solid material usually has no medicinal action. It is called a diluent. This type of solid mixture, containing only an active drug and diluent, is called a drug trituration. Triturations provide a convenient means for handling materials used in very small quantities. The concentration of drug in the trituration is generally specified in terms of ratio strength.
The inert substance (or diluent) that is used most frequently in preparing triturations is lactose, otherwise known as milk sugar. Lactose has no drug action or ill effects and is pleasant tasting. In preparing a trituration, the drug and the diluent must be thoroughly mixed so that the resulting powder is completely uniform.
Notice that when both components are solids, they must have the same units.
The concentration in this case is
What is the percentage strength of a 1:50 w/w mixture?
Solution. 2% w/w
CALCULATIONS
j = 2; 2 parts per 100 defines a 2% mixture.
5. What is the percentage strength of a 1:500 zinc oxide ointment?
Solution. 0.2% (w/w)
CALCULATIONS
j = 0.2 = 0.2% w/w
6. Express each of the following as a percentage strength:
A. 1:400(w/w)
B. 1:250(w/w)
C. 1:6600(w/w)
Solutions.
A. 0.25% (w/w)
B. 0.4% (w/w)
C. 0.015% (w/w)
7. Other expressions of concentration may be changed to ratio strength. The concentration is written as a fraction, reduced (so that the numerator has a value of “1”), and then converted to a ratio.
A doctor prescribed an ointment to contain 5 mg of hydrocortisone per gram of ointment. How would the pharmacist express this as a ratio strength?
Solution. 1:200 (w/w)
CALCULATIONS
j = 200 g ointment; 1 part per 200 parts defines 1:200 ratio strength.
8. Express the following concentrations as ratio strength.
A. 5 mg drug in 50 mL of solution
B. 0.25 mL of drug in 10 mL of solution
C. 500 μg of drug per gram of solution
D. 40 mg of drug in 0.5 mL Of solution
Solutions.
A. 1:10,000 (w/v)
B. 1:40(v/v)
C. 1:2000(w/w)
D. 1:12.5 (w/v)
9. A 1:1000 solution of thimerosal (a solid) means that 1 g of thimerosal is contained in each 1000 mL of the solution. As with percentage solutions, the ratio strength of w/v systems is defined in terms of grams (of solid) and milliliters (of liquid). The concentration is
What is the percentage strength of a 1:2000 w/v solution?
Solution. 0.05% w/v
CALCULATIONS
j = 0.05 g; thus the concentration is 0.05%
10. If an injection contains 5 mg of drug per milliliter, what would be its ratio strength?
Solution. 1:200 w/v
CALCULATIONS
j = 200 mL; thus the ratio strength is 1:200
11. What is the ratio strength of a 1/4% (w/v) solution?
Solution. 1:400 w/v
CALCULATIONS
j = 400; thus the ratio strength is 1:400 w/v
12. If 150 mg of strychnine sulfate are intimately mixed with 7.35 g of lactose, an inert substance, what is the ratio strength of strychnine sulfate in the mixture?
Solution. 1:50 w/w
CALCULATIONS
Total weight of the mixture:
7.35 g + 0.15 g = 7.50 g
j = 50; the ratio strength is 1:50
13. What is the ratio strength of a 0.01% w/v solution? (Remember that w/v systems are defined in terms of grams and milliliters.)
Solution. 1:10,000 w/v
CALCULATIONS
j = 10,000; the ratio strength is 1:10,000.
14. What is the ratio strength of a 0.5% solution of eucalyptus oil in mineral oil?
Solution. 1:200 v/v
CALCULATIONS
j = 200 mL of solution
The solution is therefore 1:200 v/v.
15. How many milligrams of mercury bichloride are needed to make 200 mL of a 1:500 w/v solution?
Solution. 400 mg
CALCULATIONS
By definition, 500 mL of solution contain 1 g.
j = 0.4 g = 400 mg
16. A pharmacist has 3.0 mL of an oil. How many milliliters of a 1:25 solution in alcohol can she prepare?
Solution. 75 mL
CALCULATIONS
j = 75 mL solution
17. A 1:4 mixture containing codeine sulfate, with lactose as an inert diluent, is prepared. How many milligrams of lactose are present in 1.25 g of the mixture?
