University of Sulaimani College of Pharmacy 2nd Stage Pharmaceutical Orientation Altering Product Strength, Use of Stock Solutions, and Problem- Solving by Alligation Lec (8) Shahen S. Mohammed BSc pharmacy MSc pharmaceutics

Concentration/Quantity Relationship The percentage or ratio strength (concentration) of a component in a pharmaceutical preparation is based on its quantity relative to the total quantity of the preparation. If the quantity of the component remains constant, any change in the total quantity of the preparation, through dilution or concentration, changes the concentration of the component in the preparation inversely. An equation useful in these calculations is: (1st quantity) × (1st concentration) = (2nd quantity) × (2nd concentration)

Problems in this section generally may be solved by any of the following methods: 1. Inverse proportion. 2. The equation: (1st quantity)(1st concentration)=(2nd quantity)(2nd concentration), or Q1 C1 Q2 C2. 3. By determining the quantity of active ingredient (solute) present or required and relating that quantity to the known or desired quantity of the preparation.

Dilution and Concentration of Liquids Example Calculations of the Dilution and Concentration of Liquids If 500 mL of a 15% v/v solution are diluted to 1500 mL, what will be the percentage strength (v/v)?

If 50 mL of a 1:20 w/v solution are diluted to 1000 mL, what is the ratio strength (w/v)?

If a syrup containing 65% w/v of sucrose is evaporated to 85% of its volume, what percentage (w/v) of sucrose will it contain? Any convenient amount of the syrup, for example, 100 mL, may be used in the calculation. If we evaporate 100 mL of the syrup to 85% of its volume, we will have 85 mL.

How many grams of 10% w/w ammonia solution can be made from 1800 g of 28% w/w strong ammonia solution?

How many milliliters of a 1:5000 w/v solution of the preservative lauralkonium chloride can be made from 125 mL of a 0.2% solution? Q1 C1 = Q2 C2 125ml * 0.2%= Q2 * 0.02% Q2 = 1250 ml

Strengthening of a Pharmaceutical Product As noted previously, there is occasion in which a pharmacist may be called upon to strengthen an existing pharmaceutical product. This may be accomplished by the addition of active ingredient or by the admixture with a calculated quantity of a like-product of greater concentration.

Example If a cough syrup contains in each teaspoonful, 1 mg of chlorpheniramine maleate and if a pharmacist desired to double the strength, how many milligrams of that ingredient would need to be added to a 60-mL container of the syrup. Assume no increase in volume.

Stock Solutions Stock solutions are concentrated solutions of active (e.g., drug) or inactive (e.g., colorant) substances and are used by pharmacists as a convenience to prepare solutions of lesser concentration.

Example Calculations of Stock Solutions 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?

How many milliliters of a 1:400 w/v stock solution should be used in preparing 1 gallon of a 1:2000 w/v solution?

Some interesting calculations are used in pharmacy practice in which the strength of a diluted portion of a solution is defined, but the strength of the concentrated stock solution used to prepare it must be determined.

How much drug should be used in preparing 50 mL of a solution such that 5 mL diluted to 500 mL will yield a 1:1000 solution? 1:1000 means 1 g of drug in 1000 mL of solution

The accompanying diagrammatic sketch should prove helpful in solving the problem.

How many grams of sodium chloride should be used in preparing 500 mL of a stock solution such that 50 mL diluted to 1000 mL will yield a (0.3% w/v) for irrigation? 1000 (mL) × 0.003 = 3 g of sodium chloride in 1000 mL of (0.3% w/v), which is also the amount in 50 mL of the stronger (stock) solution to be prepared.

How many milliliters of water should be added to 300 mL of a 1:750 w/v solution of benzalkonium chloride to make a 1:2500 w/v solution? The difference between the volume of diluted (weaker) solution prepared and the volume of stronger solution used represents the volume of water (diluent) to be used. 1000 mL - 300 mL = 700 mL, answer.

How many milliliters of water should be added to a pint of a 5% w/v solution to make a 2% w/v solution?

Dilution of Alcohol Example How much water should be mixed with 5000 mL of 85% v/v alcohol to make 50% v/v alcohol? Therefore, use 5000 mL of 85% v/v alcohol and enough water to make 8500 mL, answer.

How many milliliters of 95% v/v alcohol and how much water should be used in compounding the following prescription? R X caine 1 g Alcohol 70% 30 mL Sig. Ear drops. Therefore, use 22.1 mL of 95% v/v alcohol and enough water to make 30 mL, answer.

Dilution and Fortification of Solids and Semisolids The dilution of solids in pharmacy occurs when there is need to achieve a lower concentration of an active component in a more concentrated preparation.

Example Calculations of Solid and Semisolid Dilutions If 30 g of a 1% hydrocortisone ointment were diluted with 12 g of Vaseline, what would be the concentration of hydrocortisone in the mixture? Or

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?

Triturations Triturations are dilutions of potent medicinal substances. They were prepared by diluting one part by weight of the drug with nine parts of finely powdered lactose. They are, therefore, 10% or 1:10 w/w mixtures. These dilutions offer a means of obtaining conveniently and accurately small quantities of potent drugs for compounding purposes. Although no longer official as such, triturations exemplify a method for the calculation and use of dilutions of solid medicinal substances in compounding and manufacturing procedures.

Example Calculations of Triturations How many grams of a 1:10 trituration are required to obtain 25 mg of drug? 10 g of trituration contain 1 g of drug 25 mg = 0.025 g

Alligation Alligation is an arithmetical method of solving problems that involves the mixing of solutions or mixtures of solids possessing different percentage strengths. Alligation Medial is a method by which the percentage strength of a mixture of two or more substances of known quantity and concentration may be easily calculated. By this method, the percentage strength of each component, expressed as a decimal fraction, is multiplied by its corresponding quantity; then the sum of the products is divided by the total quantity of the mixture; and the resultant decimal fraction is multiplied by 100 to give the percentage strength of the mixture. Of course, the quantities must be expressed in a common denomination, whether of weight or volume.

Example Calculations Using Alligation Medial What is the percentage strength (v/v) of alcohol in a mixture of 3000 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 after mixing.

In some problems, the addition of a solvent or vehicle must be considered. It is generally best to consider the diluent as of zero percentage strength, as in the following problem. What is the percentage strength of alcohol in a mixture of 500 mL of a solution containing 40% v/v alcohol, 400 mL of a second solution containing 21% v/v alcohol, and a sufficient quantity of a nonalcoholic third solution to make a total of 1000 mL?

Alligation Alternate 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. A final proportion permits us to translate relative parts to any specific denomination. The strength of a mixture must lie somewhere between the strengths of its components; that is, the mixture must be somewhat stronger than its weakest component and somewhat weaker than its strongest.

Example Calculations Using Alligation Alternate In what proportion should alcohols of 95% and 50% strengths be mixed to make 70% alcohol? Note that the difference between the strength of the stronger component (95%) and the desired strength (70%) indicates the number of parts of the weaker to be used (25 parts), and the difference between the desired strength (70%) and the strength of the weaker component (50%) indicates the number of parts of the stronger to be used (20 parts).

How many milliliters of 50% w/v dextrose solution and how many milliliters of 5% w/v dextrose solution are required to prepare 4500 mL of a 10% w/v solution?

Specific Gravity of Mixtures The methods of alligation medial and alligation alternate may be used in solving problems involving the specific gravities of different quantities of liquids of known specific gravities, provided no change in volume occurs when the liquids are mixed and that they are measured in a common denomination of volume.

Example Calculations of Specific Gravity Using Alligation What is the specific gravity of a mixture of 1000 mL of syrup with a specific gravity of 1.300, 400 mL of glycerin with a specific gravity of 1.250, and 1000 mL of an elixir with a specific gravity of 0.950?

In what proportion must glycerin with a specific gravity of 1 In what proportion must glycerin with a specific gravity of 1.25 and water be mixed to prepare a liquid having a specific gravity of 1.10?