Chapter 27: Concentrations and Dilutions

Concentrations and Dilutions in Pharmaceuticals

Potency Definition

  • Percent Strength: A method of defining the potency of pharmaceuticals. It indicates the grams of the active ingredient per 100 mL of the solution, allowing for clarity when determining dosages.

  • Conversion for Calculation Simplicity: Percent strength can be expressed as a fraction or a decimal for ease of calculation.

Weight/Weight Concentrations

  • Definition: Weight/Weight (w/w) concentration involves mixing a solid active ingredient (like a powder) with a solid base (like an ointment).

  • Calculation Steps:

    1. Establish a Ratio: This is done by taking the amount of active ingredient (in grams) over the total quantity of the mixture (in grams).

    2. Convert to Decimal: Divide the numerator (grams of the active ingredient) by the denominator (total grams).

    3. Convert to Percentage: To calculate the final concentration, convert the decimal to a percentage by multiplying it by 100.

Weight/Weight Practice Problems

  1. Active Ingredient in Cream: If there is 12g of an active ingredient in a 120g cream, calculate the concentration.

  2. Neomycin Sulfate in Ointment: A 30g ointment contains 105 mg of neomycin sulfate; determine the concentration.

  3. Bactroban® Ointment: Contains 0.6g of mupirocin in a 30g tube; calculate the percent strength.

Weight/Volume Concentrations

  • Definition: In this type of concentration, a solid active ingredient (like powder) is combined with a liquid base (such as syrup).

  • Calculation Steps:

    1. Construct a Ratio: This involves using the weight (grams) of the active ingredient over the volume (mL) of the liquid.

    2. Convert to Decimal: Divide the weight by the volume.

    3. Find the Percentage: Multiply the decimal form by 100 to express it as a percentage.

Weight/Volume Practice Problems

  1. Active Ingredient in Water: When 25g of an active ingredient is combined with 250 mL of water, calculate the strength.

  2. Lidocaine HCL in Xylocaine®: 30 mL contains 1.5g; determine its concentration.

  3. Clindamycin Phosphate in Cleocin T®: Contains 10mg per mL; calculate the percentage strength.

Volume/Volume Concentrations

  • Definition: Volume/Volume (v/v) concentration denotes a liquid active ingredient mixed with a liquid base, commonly seen in emulsions.

  • Calculation Steps:

    1. Formulate a Ratio: Create a ratio of the active ingredient’s volume to the total volume of the mixture.

    2. Transform to Decimal: Convert this ratio into decimal form through division.

    3. Final Concentration in Percentage: Multiply the decimal value by 100 to achieve the final percentage concentration.

Volume/Volume Practice Problems

  1. Dilution of an Active Ingredient: Mixing 10 mL of an active ingredient with enough water to make a total of 200 mL; calculate the concentration.

  2. Alcohol Strength from a Mixture: 180 mL of an ingredient with 820 mL alcohol solution; find the strength.

  3. Normal Saline Mixture: Combining 150 mL of an ingredient with 350 mL normal saline; calculate the strength.

Sample Poll Questions

  1. If 20 grams of salt (NaCl) is mixed with 80 grams of water, what is the weight/weight percent concentration of salt in the solution?

  2. Mix 5 grams of sugar (C12H22O11) with 15 grams of water; determine the weight/weight percent concentration of sugar.

  3. When 50 mL of ethanol is mixed with 150 mL of water, calculate the volume/volume percent concentration of ethanol in the mixture.

  4. A solution prepared by mixing 25 mL of acetic acid (CH3COOH) with 75 mL of water; find the volume/volume percent concentration of acetic acid.

  5. Calculate the weight/weight percent concentration for a solution containing 30 grams of solute and 70 grams of solvent.

Understanding Dilutions

  • Stock Solutions: Highly concentrated solutions that are diluted to achieve the desired strength of a medication.

  • Diluent: The substance—typically of larger volume—used to dilute the stock solution, thereby achieving a specific final concentration.

Stock Solutions and Dilution Formula

  • Dilution Calculation Formula: The following formula helps maintain the consistency of the active ingredient when diluting stock solutions: Q1 imes C1 = Q2 imes C2 Where:

    • Q_1 = volume/quantity of the stock solution used.

    • C_1 = concentration of the stock solution (in percentage).

    • Q_2 = desired final volume/quantity of the diluted solution.

    • C_2 = desired final concentration of the diluted solution (in percentage).

Dilutions Practice Scenarios

  1. Hydrogen Peroxide Solution: Preparing 480 mL of a 3% hydrogen peroxide solution from a stock solution of 12%. The known values are:

    • C_1 = 12 ext{%, initial concentration}

    • Q_2 = 480 ext{ mL, desired final volume}

    • C_2 = 3 ext{%, desired final concentration}

    • Question: How many mL of the 12% hydrogen peroxide stock solution will you need?

  2. Coal Tar Solution Dilution: Beginning with 60 g of a 20% coal tar solution diluted to obtain a total of 100 g. The data is:

    • Q_1 = 60 ext{ g, initial quantity}

    • C_1 = 20 ext{%, initial concentration}

    • Q_2 = 100 ext{ g, final quantity after dilution}

    • Question: What is the final concentration of the diluted product?

  3. Dilution of a Medication: A nurse is preparing 10 mL of a 1:2 v/v dilution of a medication. Question: How many mL of the 3:4 v/v stock solution should be used for preparation?

  4. Syrup Dilution: Compounding a medication requiring a 30% v/v dilution of a concentrated syrup. Question: How many mL of the 50% syrup should be used to prepare 90 mL of the diluted solution?

  5. Ointment Size Calculation: Preparing a 1:5 w/w dilution of a concentrated active ingredient needs calculating Question: how many grams of the 1:4 concentrated active ingredient should be used to prepare 100 g of the diluted ointment?

  6. Ointment Strength Calculation: Compounding a 25% w/w dilution of a concentrated ointment. Question: How many grams of the 50% concentrated ointment should be used to prepare 80 g of the diluted ointment?

Summary on Concentrations and Dilutions

  • The concepts of concentrations and dilutions are fundamentally related to the basic principles of ratios and proportions.

  • Their application is crucial in various pharmacy contexts for ensuring accurate dosages and safe preparation of medications, ultimately contributing to effective patient care.