Concentration and Dilution Pharmacy Calculations Guide

Concentration and Dilution Calculations for Pharmacy Technicians

Concentration and dilution calculations are fundamental skills for pharmacy technicians and commonly tested topics on the PTCB exam. Whether you are preparing IV solutions, compounding topical preparations, or verifying prescription concentrations, these mathematical concepts apply daily in pharmacy practice. This guide breaks down each calculation type with clear examples and step-by-step solutions.

Understanding Concentration Expressions

Concentration describes the amount of drug (solute) present in a given amount of preparation (solution or mixture). Pharmacy uses several ways to express concentration:

Percent Strength

Percent strength is the most common concentration expression. There are three types based on the physical states of the solute and solvent:

• Weight/Volume (w/v): Grams of solute per 100 mL of solution. Example: 0.9% NaCl means 0.9 g NaCl per 100 mL of solution.
• Volume/Volume (v/v): Milliliters of solute per 100 mL of solution. Example: 70% isopropyl alcohol means 70 mL alcohol per 100 mL of solution.
• Weight/Weight (w/w): Grams of solute per 100 g of preparation. Example: 1% hydrocortisone cream means 1 g hydrocortisone per 100 g of cream.

Ratio Strength

Ratio strength expresses concentration as a ratio of one part solute to a specified number of parts solution. For example, epinephrine 1:1000 means 1 g of epinephrine per 1000 mL of solution. To convert ratio strength to percent strength, divide the first number by the second and multiply by 100.

Example: Convert 1:1000 to percent strength. 1 divided by 1000 equals 0.001, multiplied by 100 equals 0.1%. So epinephrine 1:1000 is the same as 0.1%.

Milligrams per Milliliter (mg/mL)

This is a straightforward concentration expression commonly used for injectable medications. For example, morphine 2 mg/mL means each milliliter contains 2 mg of morphine. To convert percent strength to mg/mL, multiply the percent by 10. For instance, 1% lidocaine equals 10 mg/mL.

The Dilution Equation: C1V1 = C2V2

The dilution equation is the most important formula for concentration and dilution problems. It states that the amount of solute before dilution equals the amount after dilution:

C1 x V1 = C2 x V2

• C1 = initial (stock) concentration
• V1 = initial (stock) volume
• C2 = final (desired) concentration
• V2 = final (desired) volume

Example Problem 1

How many milliliters of a 50% dextrose solution are needed to prepare 500 mL of a 5% dextrose solution?

Using C1V1 = C2V2: 50% x V1 = 5% x 500 mL. Solving for V1: V1 = (5 x 500) / 50 = 50 mL. You need 50 mL of the 50% stock solution, then add enough sterile water to reach a final volume of 500 mL.

Example Problem 2

You have 250 mL of a 10% povidone-iodine solution. If you dilute it to 1000 mL with purified water, what is the resulting concentration?

Using C1V1 = C2V2: 10% x 250 mL = C2 x 1000 mL. Solving for C2: C2 = (10 x 250) / 1000 = 2.5%. The resulting solution is 2.5% povidone-iodine.

Alligation Method

Alligation is used when mixing two different concentrations to achieve a desired intermediate concentration. The alligation alternate method uses a simple grid pattern:

Place the higher concentration in the upper left corner and the lower concentration (or zero for a diluent) in the lower left corner. Place the desired concentration in the center. Subtract diagonally (desired minus lower, higher minus desired) to find the number of parts of each component needed.

Example Problem 3

How would you mix 20% and 5% cream to make 100 g of a 12% cream?

Using alligation: Higher concentration (20%) gets 12 minus 5 = 7 parts. Lower concentration (5%) gets 20 minus 12 = 8 parts. Total parts = 15. Amount of 20% cream: (7/15) x 100 g = 46.7 g. Amount of 5% cream: (8/15) x 100 g = 53.3 g.

Serial Dilutions

Serial dilutions involve performing multiple sequential dilutions to achieve very low concentrations. Each step dilutes the previous solution by a fixed ratio. This technique is useful in compounding when a single dilution step would be impractical.

For example, to prepare a 1:10,000 solution from a 1:100 solution, you could perform two 1:10 dilutions. First dilution: 1:100 becomes 1:1,000. Second dilution: 1:1,000 becomes 1:10,000. Each dilution involves taking one part of the current solution and adding nine parts of diluent.

Practice Tips for the PTCB Exam

When solving concentration and dilution problems on the PTCB exam, follow these strategies:

• Always identify what the question is asking before starting calculations
• Make sure all units match before plugging values into formulas
• Remember that percent strength to mg/mL conversion uses a factor of 10
• Double-check your answer by verifying the final concentration is between the two starting concentrations (for mixing problems)
• Practice converting between percent strength, ratio strength, and mg/mL

Concentration and dilution calculations become intuitive with practice. Work through multiple problems daily during your PTCB exam preparation, and these concepts will feel natural by test day. Understanding the underlying logic rather than just memorizing formulas will help you adapt to any variation the exam presents.