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    NAPLEX Dilution Practice Questions with Answers

    May 30, 202610 min read0 views
    NAPLEX Dilution Practice Questions with Answers

    NAPLEX Dilution Practice Questions with Answers

    Mastering pharmaceutical calculations is a cornerstone of passing the North American Pharmacist Licensure Examination, and NAPLEX Dilution remains one of the most frequently tested areas. Whether you are preparing for the clinical portions of the exam or the rigorous math section, understanding how to manipulate concentrations safely is vital for patient care. This guide provides comprehensive explanations, worked examples, and practice questions to ensure you are exam-ready.

    Concept Explanation

    NAPLEX dilution is the process of reducing the concentration of a solute in a solution by adding more solvent, usually calculated using the conservation of mass principle expressed as C 1 V 1 = C 2 V 2 C_1V_1 = C_2V_2 .

    In this fundamental formula, C 1 C_1 represents the initial concentration, V 1 V_1 is the initial volume, C 2 C_2 is the final concentration, and V 2 V_2 is the final total volume. This relationship is critical because the total amount of active ingredient (solute) remains constant; only the volume of the liquid holding it changes. Pharmacists use this to prepare specific strengths of medications from stock solutions or to reconstitute powders. For more complex scenarios involving the mixing of two different strengths to reach a third, the alligation method is often employed as a visual shortcut.

    To succeed in these calculations, you must also be comfortable converting between different units of concentration, such as percentage strength (w/v, v/v, w/w), ratio strength (1:1000), and milligrams per milliliter (mg/mL). If you are looking for a structured way to manage your study time for these topics, the AI MasterPlan can help organize your prep. Additionally, many dilution problems are found within medication safety contexts where precision prevents toxicities.

    Solved Examples

    1. Basic Dilution: How many milliliters of a 20 % 20\% dextrose solution are needed to prepare 500  mL 500 \text{ mL} of a 5 % 5\% dextrose solution?
      1. Identify the variables: C 1 = 20 % C_1 = 20\% , C 2 = 5 % C_2 = 5\% , V 2 = 500  mL V_2 = 500 \text{ mL} .
      2. Set up the equation: 20 % × V 1 = 5 % × 500  mL 20\% \times V_1 = 5\% \times 500 \text{ mL} .
      3. Solve for V 1 V_1 : V 1 = 5 × 500 20 V_1 = \frac{5 \times 500}{20} .
      4. Calculate: V 1 = 2500 20 = 125  mL V_1 = \frac{2500}{20} = 125 \text{ mL} .
      5. Answer: 125  mL 125 \text{ mL} of the 20 % 20\% solution is required.
    2. Ratio Strength Conversion: A pharmacist has 10  mL 10 \text{ mL} of a 1 : 200 1:200 (w/v) solution. If this is diluted to 100  mL 100 \text{ mL} , what is the final percentage strength?
      1. Convert ratio strength to percentage: 1 : 200 = 1 200 = 0.005 1:200 = \frac{1}{200} = 0.005 , which is 0.5 % 0.5\% .
      2. Identify variables: C 1 = 0.5 % C_1 = 0.5\% , V 1 = 10  mL V_1 = 10 \text{ mL} , V 2 = 100  mL V_2 = 100 \text{ mL} .
      3. Set up the equation: 0.5 % × 10  mL = C 2 × 100  mL 0.5\% \times 10 \text{ mL} = C_2 \times 100 \text{ mL} .
      4. Solve for C 2 C_2 : C 2 = 5 100 C_2 = \frac{5}{100} .
      5. Calculate: C 2 = 0.05 % C_2 = 0.05\% .
    3. Solving for Solvent Added: How much water should be added to 300  mL 300 \text{ mL} of a 70 % 70\% isopropyl alcohol solution to reduce the concentration to 40 % 40\% ?
      1. Identify variables: C 1 = 70 % C_1 = 70\% , V 1 = 300  mL V_1 = 300 \text{ mL} , C 2 = 40 % C_2 = 40\% .
      2. Solve for the final total volume ( V 2 V_2 ): 70 × 300 = 40 × V 2 70 \times 300 = 40 \times V_2 .
      3. V 2 = 21000 40 = 525  mL V_2 = \frac{21000}{40} = 525 \text{ mL} .
      4. Calculate the volume of water to be added: V 2 − V 1 = 525  mL − 300  mL V_2 - V_1 = 525 \text{ mL} - 300 \text{ mL} .
      5. Answer: 225  mL 225 \text{ mL} of water must be added.

    Practice Questions

    1. A stock solution of sodium chloride is 23.4 % 23.4\% . How many milliliters of this stock solution are needed to make 1  L 1 \text{ L} of 0.9 % 0.9\% normal saline?

    2. If you dilute 50  mL 50 \text{ mL} of a 4 % 4\% (w/v) solution to a total volume of 250  mL 250 \text{ mL} , what is the final concentration in mg/mL?

    3. How many grams of a 10 % 10\% (w/w) ammonia ointment can be prepared from 450  g 450 \text{ g} of a 25 % 25\% (w/w) ammonia ointment?

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    4. A physician orders a 0.5 % 0.5\% hydrocortisone cream. The pharmacy has 30  g 30 \text{ g} of a 2.5 % 2.5\% hydrocortisone cream. How much cream base (diluent) should be added to achieve the desired concentration?

    5. What is the final concentration (v/v) if 150  mL 150 \text{ mL} of pure ethanol is added to 850  mL 850 \text{ mL} of water? (Assume volumes are additive).

    6. How many milliliters of water must be added to 100  mL 100 \text{ mL} of a 1 : 10 1:10 (w/v) solution to make it a 1 : 50 1:50 (w/v) solution?

    7. A pharmacist mixes 200  mL 200 \text{ mL} of 10 % 10\% dextrose with 300  mL 300 \text{ mL} of 20 % 20\% dextrose. What is the final concentration of the mixture?

    8. You have a 50 % 50\% (w/v) magnesium sulfate solution. How many milliliters of this solution are required to provide 4  g 4 \text{ g} of magnesium sulfate?

    9. A 10  mL 10 \text{ mL} vial is labeled 2 % 2\% lidocaine. If this is diluted to 50  mL 50 \text{ mL} with normal saline, what is the new percentage strength?

    10. How many milliliters of a 1 : 1000 1:1000 epinephrine solution are needed to prepare 10  mL 10 \text{ mL} of a 1 : 10 , 000 1:10,000 solution?

    Answers & Explanations

    1. Answer: 38.46  mL 38.46 \text{ mL} . Using C 1 V 1 = C 2 V 2 C_1V_1 = C_2V_2 : 23.4 × V 1 = 0.9 × 1000 23.4 \times V_1 = 0.9 \times 1000 . V 1 = 900 / 23.4 = 38.46  mL V_1 = 900 / 23.4 = 38.46 \text{ mL} .
    2. Answer: 8  mg/mL 8 \text{ mg/mL} . First, find final %: 4 % × 50 = C 2 × 250 4\% \times 50 = C_2 \times 250 . C 2 = 200 / 250 = 0.8 % C_2 = 200 / 250 = 0.8\% . Since 0.8 % 0.8\% means 0.8  g / 100  mL 0.8 \text{ g} / 100 \text{ mL} , it equals 800  mg / 100  mL 800 \text{ mg} / 100 \text{ mL} , which is 8  mg/mL 8 \text{ mg/mL} .
    3. Answer: 1125  g 1125 \text{ g} . Use weight-based dilution: 25 % × 450  g = 10 % × V 2 25\% \times 450 \text{ g} = 10\% \times V_2 . V 2 = 11250 / 10 = 1125  g V_2 = 11250 / 10 = 1125 \text{ g} .
    4. Answer: 120  g 120 \text{ g} . First find total weight ( V 2 V_2 ): 2.5 % × 30  g = 0.5 % × V 2 2.5\% \times 30 \text{ g} = 0.5\% \times V_2 . V 2 = 75 / 0.5 = 150  g V_2 = 75 / 0.5 = 150 \text{ g} . Diluent to add = 150  g − 30  g = 120  g 150 \text{ g} - 30 \text{ g} = 120 \text{ g} .
    5. Answer: 15 % 15\% . Total volume = 150  mL + 850  mL = 1000  mL 150 \text{ mL} + 850 \text{ mL} = 1000 \text{ mL} . Concentration = ( 150 / 1000 ) × 100 = 15 % (150 / 1000) \times 100 = 15\% .
    6. Answer: 400  mL 400 \text{ mL} . Convert to %: 1 : 10 = 10 % 1:10 = 10\% ; 1 : 50 = 2 % 1:50 = 2\% . 10 % × 100 = 2 % × V 2 10\% \times 100 = 2\% \times V_2 . V 2 = 1000 / 2 = 500  mL V_2 = 1000 / 2 = 500 \text{ mL} . Water added = 500 − 100 = 400  mL 500 - 100 = 400 \text{ mL} .
    7. Answer: 16 % 16\% . Total mass of dextrose = ( 10 % × 200 ) + ( 20 % × 300 ) = 20 + 60 = 80  g (10\% \times 200) + (20\% \times 300) = 20 + 60 = 80 \text{ g} . Total volume = 500  mL 500 \text{ mL} . Concentration = ( 80 / 500 ) × 100 = 16 % (80 / 500) \times 100 = 16\% .
    8. Answer: 8  mL 8 \text{ mL} . 50 % 50\% means 50  g / 100  mL 50 \text{ g} / 100 \text{ mL} or 0.5  g/mL 0.5 \text{ g/mL} . 4  g / 0.5  g/mL = 8  mL 4 \text{ g} / 0.5 \text{ g/mL} = 8 \text{ mL} .
    9. Answer: 0.4 % 0.4\% . 2 % × 10  mL = C 2 × 50  mL 2\% \times 10 \text{ mL} = C_2 \times 50 \text{ mL} . C 2 = 20 / 50 = 0.4 % C_2 = 20 / 50 = 0.4\% .
    10. Answer: 1  mL 1 \text{ mL} . Convert to %: 1 : 1000 = 0.1 % 1:1000 = 0.1\% ; 1 : 10 , 000 = 0.01 % 1:10,000 = 0.01\% . 0.1 × V 1 = 0.01 × 10 0.1 \times V_1 = 0.01 \times 10 . V 1 = 0.1 / 0.1 = 1  mL V_1 = 0.1 / 0.1 = 1 \text{ mL} .

    Quick Quiz

    Interactive Quiz 5 questions

    1. A pharmacist adds 200 mL of water to 300 mL of a 50% solution. What is the new concentration?

    • A 20%
    • B 30%
    • C 33.3%
    • D 40%
    Check answer

    Answer: B. 30%

    2. What is the ratio strength of a solution prepared by diluting 20 mL of a 5% solution to 500 mL?

    • A 1:200
    • B 1:500
    • C 1:1000
    • D 1:250
    Check answer

    Answer: B. 1:500

    3. How many mL of 95% alcohol are needed to make 1 liter of 70% alcohol?

    • A 736.8 mL
    • B 665.2 mL
    • C 700 mL
    • D 525 mL
    Check answer

    Answer: A. 736.8 mL

    4. If a 10% solution is diluted 1:10 (1 part solution to 9 parts diluent), what is the final percentage?

    • A 0.1%
    • B 1%
    • C 0.01%
    • D 5%
    Check answer

    Answer: B. 1%

    5. A patient needs 500 mL of 0.45% NaCl. You have 23.4% NaCl (4 mEq/mL) and sterile water. How much 23.4% NaCl is needed?

    • A 8.4 mL
    • B 9.6 mL
    • C 12.2 mL
    • D 15.4 mL
    Check answer

    Answer: B. 9.6 mL

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    Frequently Asked Questions

    What is the C1V1 = C2V2 formula used for in NAPLEX?

    This formula is the primary tool for calculating dilutions where the amount of solute remains constant while the volume changes. It allows candidates to determine the required volume of a stock solution or the final concentration after adding a diluent.

    How do I convert ratio strength to percentage strength?

    To convert a ratio strength like 1:2500 to a percentage, divide the first number by the second and multiply by 100 (e.g., 1 / 2500 × 100 = 0.04 % 1 / 2500 \times 100 = 0.04\% ). This conversion is a vital first step in most NAPLEX dilution problems to ensure unit consistency.

    What is the difference between w/v and v/v in dilution?

    Weight/Volume (w/v) refers to grams of a solid solute in 100 mL of liquid, while Volume/Volume (v/v) refers to milliliters of a liquid solute in 100 mL of total solution. The math for dilution remains the same regardless of the units, provided they are consistent throughout the calculation.

    When should I use the alligation method instead of C1V1?

    Alligation is best used when you are mixing two different concentrations of the same active ingredient to obtain a third, intermediate concentration. While C 1 V 1 C_1V_1 works for single dilutions with a pure diluent (0%), alligation simplifies math when both components contain the drug.

    Does the NAPLEX provide a calculator for these questions?

    Yes, the NAPLEX provides an on-screen calculator, but your ability to set up the equation correctly is the most important skill. Practicing with tools like the AI Exam Simulator can help you get used to the interface and timing of the actual exam.

    How should I round my answers on the NAPLEX math section?

    Always follow the specific instructions provided in the question stem, such as "round to the nearest tenth" or "round to the nearest whole number." If no instructions are given, standard pharmacy practice is to round to the nearest tenth or hundredth depending on the measurement's precision.

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