Pharmaceutical Calculations

• Pharmaceutical calculation involves altering product strength, using stock solutions, and problem-solving.
• A preparation can be strengthened by adding active ingredients, by admixture with a stronger preparation, or by evaporating its liquid vehicle.
• A preparation can be diluted by adding a diluent or by mixing with a weaker preparation.

Compounding Considerations

• Altering the strength of a pharmaceutical preparation may be necessary or desirable in pharmacy practice.
• Diluting liquid dosage forms can help create a product strength suitable for specific patients like pediatric or elderly individuals.
• Diluents should be compatible with the vehicle of the original product such as aqueous, alcoholic, or hydro-alcoholic solutions.
• Dilution can also be performed on solid dosage forms like powders or creams.
• The diluent should still be compatible with the original formulation.
• Concentrating a liquid via solvent evaporation is not common.
• Fortifying liquid, solid, or semi-solid dosage forms by adding a calculated quantity of therapeutic agent remains viable for compounding.
• Ratio strengths should be converted to percentage strengths when setting up a proportion.
• Proportional parts should be reduced to the lowest term during calculations.

Strength and Quantity Relationships

• If a mixture's strength is diluted to twice its original quantity, its active ingredient will be contained in twice as many parts, and its strength will be halved.
• If a mixture is concentrated by evaporation to one-half its original quantity, its active ingredient will be contained in one-half as many parts, and its strength will be doubled.
• If the amount of active ingredient is constant, changes in the quantity of a solution/mixture are inversely proportional to the percentage or ratio strength.
• 50mL solution with 10g active ingredient at 20% strength diluted to 100mL reduces strength to 10% or 1:10w/v.
• Reducing the volume of a solution to 25mL from 50mL via evaporation will yield a strength of 40% or 1:2.5w/v.
• Problems can be solved using inverse proportion, equations [(1st quantity)x(1st concentration)=(2nd quantity)x(2nd concentration)], or by determining the quantity of active ingredient.

Liquid Dilution and Concentration

• If 500 mL of a 15% v/v solution is diluted to 1500 mL, the percentage strength becomes 5%.
• 50 mL of a 1:20 w/v solution diluted to 1000 mL results in a ratio strength of 1:400 w/v.
• 125 mL of a 0.2% solution can create 1250 mL of a 1:5000 w/v lauralkonium chloride solution.
• If a syrup with 65% w/v sucrose is evaporated to 85% of its volume, the resulting percentage will be 76.47% w/v.
• If 1 gallon of a 30% w/v solution is evaporated to achieve a 50% w/v strength, the final volume is 2271 mL.
• Diluting an injection of 50 mg/10 mL to 1L results in a 0.005% strength solution.
• Doubling the strength of cough syrup containing 1 mg of chlorpheniramine maleate per teaspoonful in a 60-mL container requires adding 12 mg of chlorpheniramine maleate.

Stock Solutions

• Stock solutions are concentrated forms of active or inactive substances that prepare less concentrated solutions.
• To make 4 liters of a 1:2000 w/v solution from a 1:400 w/v stock solution, 800 mL are needed.
• Preparing 4000 mL of a mouthwash with 1:20,000 w/v from a 1% stock solution of red dye requires 20 mL of the stock solution.
• When compounding a prescription with Phenylephrine HCl 0.25%, Rose Water ad 30 mL using a 1:50 stock solution, 3.75 mL of the stock solution are needed.
• Preparing 500 mL of a sodium chloride stock solution, such that 50 mL diluted to 1000 mL yields "½ normal saline" (0.3% w/v), requires 30 grams of sodium chloride.
• Preparing 300 mL of a stock benzalkonium chloride solution from a 17% w/v concentrate, so 15 mL diluted to 1 liter yields 1:5000 solution, needs 23.5 ml concentrate.

Alligation

• Alligation is an arithmetical method to solve problems involving the mixing of solutions or solids with different percentage strengths.
• Alligation medial is a method to calculate the "weighted average" percentage strength of a mixture using the quantity and concentration of two or more substances.

Alligation Medial Calculations

• The percentage strength 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 is 50%.
• The percentage of zinc oxide in an ointment prepared by mixing 200 g of 10% ointment, 50 g of 20% ointment, and 100 g of 5% ointment is 10%.