1. Yewande Dayo Student Pharmacist
Altering Product Strength, Use of Stock Solutions, and Problem Solving by Alligations
Yewande Dayo
Student Pharmacist

2. Objectives
Upon completion of this chapter, the student will be able to:
Perform calculations for altering product strength by dilution, concentration, or fortification.
Perform calculations for the preparation and use of stock solutions.
Apply alligation medial and alligation alternate in problem- solving.

3. Altering Product Strength
If a mixture of a given strength is diluted to twice its original quantity, its strength will be reduced by one half because the active ingredient will be contained in twice as many parts of the whole
5 grams in 100 mL = 5%
5 grams in 200 mL = ?%

4. Dilution and Concentration
If a mixture is concentrated to one half its original quantity, the active ingredient will be contained in one-half as many parts of the whole and the strength will be doubled.
5 grams in 100 mL = 5%
5 grams in 50 mL = ?%
The percentage or ratio strength decreases as the quantity of solution increases (active ingredient remains constant)
The reverse is also true

5. Multiple Ways to Solve a Problem
A problem can be solved in several ways. The best way is not necessarily the shortest: the best way is the one that is clearly understood.
Problems in this section may be solved by:
Inverse proportion
Q1 x C1 = Q2 x C2
By determining the quantity of active solute needed and then calculating the quantity of the available solution (usually concentrated or stock solution) that will provide the needed amount of constituent.

6. Stock Solutions
Solutions of known concentration. Usually strong solutions from which weaker ones are easily made.
Stock solutions are prepared on a weight in volume basis.

7. Dilution of Alcohol
Because of a noticeable contraction in volume when alcohol and water are mixed, we cannot calculate the precise volume of water needed to dilute alcohol to a desired volume in volume strength. However, we may “qs” with water to the appropriate volume.
Because the contraction of liquids does not affect the weights of the components, the weight of water needed to dilute alcohol to a desired weight in weight strength may be calculated.

8. Example 1
If 500 mL of a 15% v/v solution of methyl salicylate in alcohol are diluted to 1500 mL, what will be the percentage strength v/v?
Ans: 5%

9. Example 2
If a 0.067% (w/v) methylbezethonium chloride lotion is diluted with an equal volume of water, what will be the ratio strength (w/v) of the dilution?
Ans: 1:2985 0r % (w/v)

10. Example 3
What is the strength of a sodium chloride solution obtained by evaporating 800 g of a 10% (w/w) solution to 250 g?
Ans= 32%

11. Example 4
How many milliliters of water for injection must be added to 10 liters of a 50%(w/v) dextrose injection to reduce the concentration to 30% (w/v)
Ans: 6670 mL

12. Example 5
How many milliliters of a 5% (w/v) solution of menthol in alcohol should be used to obtain the amount of menthol needed in preparing the lotion?
Menthol %
Hexachlorphene %
Glycerin %
Alcohol 70% to make mL
Ans: 10 mL

13. Example 6
How many milliliters of a 1:400 (w/v) stock solution should be used to make 4 liters of a 1:2000 (w/v) solution?
Ans: 800 mL

14. Example 7
How many milliliters of a 1:50 (w/v) stock solution of a chemical should be used to prepare 1 liter of a 1:4000 (w/v) solution?
Ans: 12.5 mL

15. Example 8
How many milliliters of water must be added to 250 mL of a 25% (w/v) stock solution of sodium chloride to prepare a 0.9% (w/v) sodium chloride solution?
Ans: mL

16. Example 9
If a syrup containing 65% (w/v) of sucrose is evaporated to 85% of its volume, what percent (w/v) of sucrose will it contain?
Ans: mL

17. Dilution of Acids
The strength of an official concentrated acid is expressed as percentage weight-in-weight, e.g., HCl, NF contains 36.5% w/w
The strength of an official diluted acid is expressed as percentage weight-in-volume, e.g., Dil HCl, NF contains 9.5% w/v

18. Example 10
How many milliliters of 37% (w/w) hydrochloric acid having a specific gravity of 1.20 are required to make mL of diluted hydrochloric acid 10% (w/v)?
Ans: 225 mL

19. Example 11
How many milliliters of 85% w/w phosphoric acid having a specific gravity of 1.71 should be used in preparing 1 gallon of ¼% w/v phosphoric acid solution to be used for bladder irrigation?
Ans: 6.5 mL

20. Dilution and concentration of solids
Drug + Diluent = Product
How much drug present in or needed for the product?
How much diluent present in or needed in the product?
How much drug present in the stock solution?
How much diluent present in the stock solution?
Finally how much stock solution needed to get the desired drug for the finished product?

21. Example 12
How many grams of opium containing 15% (w/w) of morphine and how many grams of lactose should be used to prepare 150 g of opium containing 10% (w/w) of morphine?
Ans: 100 g of Opium and 50 g of Lactose

22. Example 12
If some moist crude drug contains 7.2% of active ingredient and 21.6% of water, what will be the percentage (w/w) of active ingredient after the drug is dried?
Ans: 9.18%

23. Example 13
How many grams of 20% benzocaine ointment and how many grams of ointment base (diluent) should be used in preparing 5 lb of 2.5% benzocaine ointment?
Ans: 284 g benzocaine and 1989 g of diluent

24. Example 14
How many grams of coal tar should be added to 3200 g of 5% coal tar ointment to prepare an ointment containing 20% of coal tar?
Ans: 600 g

25. Example 15
How many milliliters of water should be added to 100 mL of a 1:125 (w/v) solution to make a solution such that 25 mL diluted to 100 mL will yield a 1:4000 dilution?
Ans: 700 mL

26. ALLIGATION
It is a short-cut arithmetical method (based on algebraic summation) for solving problems that involve mixing of
Solutions or mixtures of solids possessing different percentage (%) strengths
Mixtures of liquids with different specific gravity, provided there is no change in volume when liquids are combined. There are two types
Alligation Medial
Alligation Alternate

27. Alligation Medial
It is a method by which the “weighted average” percentage strength of a mixture of two or more substances of known quantity and concentration may be quickly calculated.

28. Example 16
What is the percentage (v/v) of alcohol in a mixture of mL of 40% (v/v) alcohol, 1000 mL of 60% (v/v) alcohol, and 1000 mL of 70% (v/v) alcohol (assume no contraction of volume)?
Ans: 50%

29. Alligation Alternate
It is a method by which we may calculate the number of parts of two or more components of a given strength when they are to be mixed to prepare a mixture of desired strength.

30. Example 17
In what proportion should 20% benzocaine ointment be mixed with an ointment base to produce a 2.5% benzocaine ointment?
Ans: benz: dil = 2.5:17.5 or 1:7

31. Example 18
A hospital pharmacist wants to use three lots of ichthammol ointment containing, respectively, 50%, 20%, and 5% ichthammol. In what proportion should they be mixed to prepare a 10% ichthammol ointment?
Ans: 50%:20%:5% = 1:1:10 or 5:5:50

32. Example 19
How many milliliters of each of two liquids with specific gravities of and should be used to prepare mL of a liquid having a specific gravity of 0.925?

33. Example 20
The formula for a buffer solution contains 1.24% (w/v) of boric acid. How many milliliters of a 5% (w/v) boric acid solution should be used to obtain the boric acid needed in preparing 1 liter of the buffer solution?

34. Example 21
If a pharmacist adds 3 g of hydrocortisone to 60 g of a 5% (w/w) hydrocortisone cream, what is the final percentage strength of hydrocortisone in the product?

35. Example 22 Rx
Castor Oil 5.0 mL
Euresol mL
Alcohol 85% ad mL
How many milliliters each of 95% (v/v) alcohol and water should be used in preparing the prescription?

36. Example 23
Phenobarbital elixir contains 400 mg of phenobarbital in each 100 mL. A physician wants to increase the phenobarbital content to 30 mg per teaspoonsful and to prescribe the dose twice a day for 24 days. How many milligrams of phenobarbital should be added to the prescribed volume of the prescription to provide the amount needed for the dosage regimen?

37. Example 24
If a pharmacist mixed 1 pint of propylene glycol having a specific gravity of 1.20 with 500 mL of water, how many milliliters additional propylene glycol should be added to change the specific gravity to 1.15?

38. Example 25
How many grams of sorbitol solution having a specific gravity of and how many grams (milliliters) of water should be used in preparing 500 g of a sorbitol solution having a specific gravity of 1.225?

39. Example 26
A manufacturing pharmacist has on hand four lots of belladonna tincture, containing 25 mg, 27 mg, 33 mg, and 35 mg of alkaloids per 100 mL. How many gallons of each lot should be used to prepare 16 gallons of belladonna tincture containing 30 mg of alkaloids per 100 mL?

40. Example 27
How many grams of silver nitrate should be used in preparing 500 mL of a solution such that 10 mL diluted to a liter will yield a 1:5000 solution?

41. Example 28
Express a patient’s uric acid level of 5.0 mg/dL in terms of milligrams percent.

42. Example 29
You have prepared a solution by dissolving 120 mg of a drug in 3 mL of water and diluted the solution to 6 mL. What is the concentration of the drug in solution in terms of % w/v. If the specific gravity of the diluted solution is then calculate the concentration in % w/w.

43. Example 30 Rx Zinc Oxide Starch aa 2 g Petrolatum 60 g
After compounding the formula above, the pharmacist received a call from the prescriber to change the concentration of zinc oxide to 7.5 % (w/w). How many grams of zinc oxide should the pharmacist add to the original formula?

44. Case 1 Rx Hydrocortisone 0.6% AQUAPHOR q.s. ad 15 g
Sig: Apply to child’s affected area t.i.d.
The pharmacist has no hydrocortisone powder but does have a hydrocortisone cream, 1%. How many grams each of hydrocortisone Cream and Aquaphor should be used in filling the prescription?