Pharm. Calc./Compounding
Sherif S. Ebada, Ph.D.
Contact information:Assoc. Prof. Dr. Sherif S. EbadaPharmaceutical Chemistry Dept.Office hours:
Tuesdays and Thuresdays: 10:00 am–12:00 pmE-mail: [email protected]
Lecture 7
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Required Textbook
Howard C. Ansel and Shelly J. Stockton Pharmaceutical Calculations. 15th Ed.
15 Altering Product Strength, Useof Stock Solutions, andProblem Solving by Alligation
objectives
• Perform calculations for altering product strength through dilution or fortification.
• Perform calculations for the preparation and use of stock solutions.
• Apply alligation medial and alligationalternate in problem solving.
headline and syllabus
1. Introduction
2. Relationship between Strength and Total Quantity
3. Dilution of Liquids
4. Strengthening of a Pharmaceutical Product
5. Stock Solutions
6. Dilution and Fortification of Semisolids
7. Alligation
8. Specific Gravity of Mixtures
introduction
The strength of a pharmaceutical preparation may be increased or decreased by changing the proportion of active ingredient to the whole. A preparation may be strengthened or made more concentrated by the addition of active ingredient, by admixture with a like preparation of greater strength, or through the evaporation of its vehicle, if liquid. The strength of a preparation may be decreased or diluted by the addition of diluent or by admixture with a like preparation of lesser strength.
• In the course of pharmacy practice, the reduction in the strength of a commercially available pharmaceutical product may be desired to treat a particular patient, based on the patient’s age (e.g., pediatric or elderly) or medical status, or to assess a patient’s initial response to a new medication. The strengthening of a product may be desired to meet the specific medication needs of an individual patient.
• Various methods of calculation for the alteration of the strength of pharmaceutical preparations are presented in this chapter.
Relationship between Strength and Total Quantity
• 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)?
• 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
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Strengthening of a Pharmaceutical Product
• 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.
A pharmacist received a prescription for 100 mL of a cefuroximeaxetil suspension to contain 300 mg of drug in each 5 mL. The pharmacist has 100 mL of a suspension containing 250 mg/5 mLand also has 250-mg scored tablets of the drug. How many tablets should be pulverized and added to the suspension to achieve the desired strength? Assume noincrease in the volume of the suspension.
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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.
• For example if I am supposed to prepare 1 molar NaOH stock solution which is one mole of NaOH in 1000ml water. I will weigh it accurately for one mole of NaOH .ie 40grams by the atomic weight or molar mass of the elements in NaOH and then transfer it to volumetric flask making up the volume upto 1000 ml.Thus my standard stock solution is prepared.
Advantages of stock solution:
1. Since stock solution is highly concentrated, its storage requires less space.
2. It is also convenient to transport stock solution due to its small volume.
3. Stock solutions which contains any active biological substances (e.g., enzymes, inhibitors, DNA, RNA etc.) are more stable in highly concentrated form
4. Stock solutions are used to save preparation time
Disadvantages of stock solution:
1. Since stock solution is highly concentrated, often to dissolve them requires more time and effort. Sometime, heating of solution is required to dissolve the substance completely.
2. Long term storage of stock solution (especially salt solution, at cold room) may leads to precipitation of solute.
Note:• To dilute means to add a certain amount of solvent(water)
to a certain amount of concentrated stock solution. If you add a certain amount of solvent to a certain amount of concentrated stock solution, you will notice that the amount of solute present in the stock solution is the same amount present in the dilute solution. The only difference is that the dilute solution now contains more water than the stock from which it was prepared. In real life, what you just read is similar to you adding more water to your coffee or tea to lighten its taste. As you add more water, you are only increasing the amount of water in the solution, but not the amount of coffee or tea molecules present in it. Here is an illustration of a dilute solution prepared from a stock solution:
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 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.
•Semi-solid dosage forms are normallypresented in the form of creams, gels, ointments, or pastes. They contain one\more active ingredients dissolved or uniformly dispersed in a suitablebase
•The choice of a base for semi-solid dosage forms depends on many factors: the therapeutic effect desired, the nature of active ingredient(s) to be incorporated, the availability of the active ingredient(s) at the site of action, the shelf-life of the finished product, and the environmental conditions in which the product is intended to beadministered.
•In many cases, a compromise has to be made in order to achieve the required stability. For example, drugs that hydrolyse rapidly are more stable in hydrophobic bases than in water-containing bases, even though they may be more effective in the latter.
•As for the dilution of semisolid preparations, in order
to tailor the formulations to the needs of the patients,
was thought to be associated with a number of
dangers, one of which is the unpredictable alteration
of activity.
Semi-solid dosage forms should not be diluted. If a
dilution is nevertheless necessary, this requires
special attention; the same type of base should be
used in order to obtain a homogeneous mixture.
•When calculating solid dilutions, the following formula is useful
and should be committed to memory:
Q1(quantity 1) × C1(concentration 1) =Q2(quantity 2) ×C2
(concentration2)
•Example:
A 0.05% fluocinonide 30 gm ointment is combined with 15 gm
of ointment base. What is the new percent strength?
30 gm+15 gm=45 gm
(30 gm)(0.05%) = (45 gm)(C2)
(30)(0.05) = (45)(X)
= 0.03%
Example Calculations of Solid andSemisolid 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
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• 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?
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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.
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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.
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• 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?
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Alligation
• Alligation Alternate is a method by which wemay calculate the number of parts of two ormore components of a given strength when theyare to be mixed to prepare a mixture of desiredstrength. A final proportion permits us totranslate relative parts to any specificdenomination. The strength of a mixture must liesomewhere between the strengths of itscomponents; that is, the mixture must besomewhat stronger than its weakest componentand somewhat weaker than its strongest.
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Example
• An order of 240 ml of 56% solution has been given
• You have 70% and 50% solutions need to be mixed together in order to make 56% solution.
• How much of each do you need in order to make 240 ml of the new strength ?
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Alligation grid
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Alligation grid
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Alligation Alternate
• We can use alligation when you are diluting with water and sludge .
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Water and sludge are of a 0% of A.I
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Example
• 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).
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• Example • 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?
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Example
• A hospital pharmacist wants to use three lots of zinc oxide containing, respectively, 50%, 20% and 5% zinc oxide. In what proportion should they be mixed to prepare a 10% zinc oxide ointment?
50%
20%
5%
10%
5 parts
5 parts
10 parts + 40 parts = 50 parts
60 parts total ointment
The 50%, 20% and 5% lots should be mixed in a 5:5:50
proportion (or 1:1:10)
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problems
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A pharmacist fills a prescription for 30 g of a 0.1% w/w hydrocortisone cream by combining a 1% w/w hydrocortisone cream and a cream base. How many grams of each were used?3 g hydrocortisone cream (1% w/w)27 g cream baseHow many grams of an 8% w/w progesterone gel must be mixed with 1.45 g of a 4% w/w progesterone gel to prepare a 5.5% w/w gel?0.87g
problems
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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?6694.4 mL water
30 g ointment base
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How many milliliters of sterile water for injection should be added to a vial containing 5 mg/mL of a drug to prepare a solution containing 1.5 mg/mL of the drug?2.33 mL sterile water for injection
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.
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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?
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• 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?
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problems
problems
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