Concentration Calculations - Pharmacy Technician Certification Exam Ptce

1. A pharmacy technician needs to prepare a 15% zinc oxide ointment. The pharmacy has 40% and 10% zinc oxide ointments available. In what proportion should the 40% and 10% ointments be mixed?
   Answer: 1 part 40% to 5 parts 10% Use the alligation method to determine the correct ratio. 1. Set up the alligation square with higher concentration (40%) at top left, lower concentration (10%) at bottom left, and desired concentration (15%) in the center. 2. Calculate differences diagonally: - |15 - 10| = 5 parts of the 40% ointment needed - |40 - 15| = 25 parts of the 10% ointment needed 3. The ratio is 5 parts of 40% to 25 parts of 10%. 4. Simplify by dividing both by 5: 1 part of 40% to 5 parts of 10%. Verification: (1 × 40% + 5 × 10%) ÷ 6 = (40 + 50) ÷ 6 = 90 ÷ 6 = 15% ✓
2. How many grams of hydrocortisone are present in a 60 g tube of 2.5% (w/w) hydrocortisone cream?
   Answer: 1.5 g A 2.5% w/w concentration means there are 2.5 grams of hydrocortisone for every 100 grams of cream. To find the amount in a 60 g tube, set up a proportion or multiply the total weight by the decimal equivalent of the percentage: $\text{Amount} = 60 \text{ g} \times 0.025 = 1.5 \text{ g}$ Alternatively, using a proportion: $\frac{2.5 \text{ g}}{100 \text{ g}} = \frac{X \text{ g}}{60 \text{ g}}$ $X = \frac{2.5 \times 60}{100} = 1.5 \text{ g}$ The other answers represent decimal placement errors.
3. How many milliliters of sterile water must be added to 100 mL of 90% ethanol to prepare a 45% ethanol solution?
   Answer: 100 mL 1. Use the dilution formula $C_1V_1 = C_2V_2$ to find the final volume ($V_2$). $(90\%) \times (100 \text{ mL}) = (45\%) \times V_2$ $9000 = 45 \times V_2$ $V_2 = \frac{9000}{45} = 200 \text{ mL}$ 2. This 200 mL is the final volume. The question asks for the volume of diluent to be added. $\text{Volume to add} = \text{Final Volume} - \text{Initial Volume} = 200 \text{ mL} - 100 \text{ mL} = 100 \text{ mL}$ Distractor D represents the final total volume, not the amount of diluent added.
4. Based on the instructions, how many milliliters of the reconstituted solution are required to administer a 450 mg dose?
   Answer: 4.5 mL The problem provides the final concentration after reconstitution (100 mg/mL) and the desired dose (450 mg). The volume of diluent added (9.6 mL) is extra information not needed for this specific calculation. Use the formula: Volume = Dose / Concentration. $\text{Volume} = \frac{450 \text{ mg}}{100 \text{ mg/mL}} = 4.5 \text{ mL}$ Therefore, 4.5 mL of the reconstituted solution is needed.
5. A 500 mg vial of vancomycin is reconstituted with 10 mL of sterile water to yield a final concentration of 50 mg/mL. How many milliliters should be drawn up to administer a 375 mg dose?
   Answer: 7.5 mL To find the volume needed for a specific dose, use the formula: Volume = Dose / Concentration. $\text{Volume} = \frac{\text{Desired Dose}}{\text{Concentration}}$ $\text{Volume} = \frac{375 \text{ mg}}{50 \text{ mg/mL}} = 7.5 \text{ mL}$ Therefore, 7.5 mL of the reconstituted solution is required for a 375 mg dose.
6. A technician needs to dilute 50 mL of a 23.4% NaCl solution to a final concentration of 0.9% NaCl. What is the total volume of the final solution?
   Answer: 1300 mL This is a dilution calculation that can be solved using the formula $C_1V_1 = C_2V_2$. Let $C_1 = 23.4\%$, $V_1 = 50$ mL, $C_2 = 0.9\%$, and $V_2 = ?$. $(23.4\%) \times (50 \text{ mL}) = (0.9\%) \times V_2$ $1170 = 0.9 \times V_2$ $V_2 = \frac{1170}{0.9} = 1300 \text{ mL}$ The total volume of the final solution will be 1300 mL.
7. A vial contains 2,000,000 units of penicillin G potassium. How much diluent must be added to the vial to make a solution with a concentration of 250,000 units/mL? (Assume powder volume is negligible).
   Answer: 8 mL To find the required volume of the final solution, use the formula: Volume = Total Amount / Desired Concentration. $\text{Volume} = \frac{2,000,000 \text{ units}}{250,000 \text{ units/mL}} = 8 \text{ mL}$ Since the powder volume is considered negligible, the volume of the final solution is equal to the volume of diluent that must be added.
8. A pharmacy technician needs to prepare 500 mL of a 2% (w/v) solution using a 10% (w/v) stock solution. How many milliliters of the stock solution are required?
   Answer: 100 mL This is a dilution calculation that can be solved using the formula $C_1V_1 = C_2V_2$, where $C$ is concentration and $V$ is volume. Let $C_1 = 10\%$, $V_1 = ?$, $C_2 = 2\%$, and $V_2 = 500$ mL. $(10\%) \times V_1 = (2\%) \times (500 \text{ mL})$ $10V_1 = 1000$ $V_1 = \frac{1000}{10} = 100 \text{ mL}$ Therefore, 100 mL of the 10% stock solution is required. Distractor D represents the amount of diluent needed, not the stock solution.
9. A 2 g vial of a drug is reconstituted to a final volume of 10 mL. A 2.5 mL dose of this reconstituted solution is then added to a 100 mL IV bag of Normal Saline. What is the final concentration in mg/mL in the IV bag?
   Answer: 4.9 mg/mL This is a multi-step problem. 1. Calculate the concentration of the reconstituted vial: $2 \text{ g} = 2000 \text{ mg}$. Concentration = $2000 \text{ mg} / 10 \text{ mL} = 200 \text{ mg/mL}$. 2. Calculate the amount of drug (in mg) being added to the IV bag: Dose = Concentration × Volume = $200 \text{ mg/mL} \times 2.5 \text{ mL} = 500 \text{ mg}$. 3. Calculate the final volume of the IV bag: Final Volume = Volume of IV fluid + Volume of drug added = $100 \text{ mL} + 2.5 \text{ mL} = 102.5 \text{ mL}$. 4. Calculate the final concentration in the IV bag: Final Concentration = Total Drug / Final Volume = $500 \text{ mg} / 102.5 \text{ mL} \approx 4.88 \text{ mg/mL}$. Rounded to one decimal place, this is 4.9 mg/mL. Distractor B is incorrect as it fails to account for the added drug volume.
10. A prescription requires a 75 mg dose of ranitidine. The pharmacy stocks ranitidine oral solution with a concentration of 15 mg/mL. How many milliliters are needed for one dose?
    Answer: 5 mL To calculate the volume required for a specific dose, use the formula: $\text{Volume} = \frac{\text{Desired Dose}}{\text{Concentration on Hand}}$ $\text{Volume} = \frac{75 \text{ mg}}{15 \text{ mg/mL}} = 5 \text{ mL}$ 5 mL of the solution should be administered.
11. A physician orders an IV admixture of dopamine at a concentration of 800 mcg/mL in 250 mL of D5W. The pharmacy stocks dopamine in vials of 40 mg/mL. How many milliliters of the stock dopamine solution must be added to the D5W bag?
    Answer: 5 mL 1. Calculate the total dose of dopamine needed in the bag: $\text{Total Dose} = 800 \text{ mcg/mL} \times 250 \text{ mL} = 200,000 \text{ mcg}$ 2. Convert the total dose from mcg to mg (since the stock is in mg/mL): $1 \text{ mg} = 1000 \text{ mcg}$ $200,000 \text{ mcg} \div 1000 = 200 \text{ mg}$ 3. Calculate the volume of stock solution needed using the formula Volume = Dose / Concentration: $\text{Volume needed} = \frac{200 \text{ mg}}{40 \text{ mg/mL}} = 5 \text{ mL}$
12. A pharmacy needs to make 1 liter of 0.9% Normal Saline solution. How many grams of sodium chloride (NaCl) are required?
    Answer: 9 g A 0.9% w/v solution means there are 0.9 grams of solute per 100 mL of solution. The desired final volume is 1 liter, which is 1000 mL. Set up a proportion to find the required amount of NaCl: $\frac{0.9 \text{ g}}{100 \text{ mL}} = \frac{X \text{ g}}{1000 \text{ mL}}$ $X = \frac{0.9 \times 1000}{100} = \frac{900}{100} = 9 \text{ g}$ Therefore, 9 grams of NaCl are needed.
13. How many milliliters of 70% alcohol and 20% alcohol are needed to prepare 1000 mL of 50% alcohol?
    Answer: 600 mL of 70% and 400 mL of 20% This problem can be solved using alligation. 1. Set up the tic-tac-toe grid. Place the higher concentration (70) at the top left, the lower concentration (20) at the bottom left, and the desired concentration (50) in the middle. 2. Subtract diagonally: $|50 - 20| = 30$ parts of the 70% solution. $|50 - 70| = 20$ parts of the 20% solution. 3. The ratio is 30 parts of 70% to 20 parts of 20%. Total parts = 30 + 20 = 50. 4. Calculate the volume for each: - Volume of 70% = $\frac{30}{50} \times 1000 \text{ mL} = 600 \text{ mL}$ - Volume of 20% = $\frac{20}{50} \times 1000 \text{ mL} = 400 \text{ mL}$
14. A 1 g vial of cefazolin powder for injection is reconstituted with 2.5 mL of sterile water. The resulting solution has a total volume of 3.0 mL. What is the final concentration in mg/mL?
    Answer: 333 mg/mL First, convert the total amount of drug from grams to milligrams: $1 \text{ g} = 1000 \text{ mg}$. The final volume after reconstitution is given as 3.0 mL. To find the concentration, divide the total amount of drug by the total volume: $\text{Concentration} = \frac{\text{Total Drug}}{\text{Total Volume}} = \frac{1000 \text{ mg}}{3.0 \text{ mL}} \approx 333.3 \text{ mg/mL}$ Rounding to the nearest whole number gives 333 mg/mL. Distractor C is incorrect because it divides by the volume of diluent added (2.5 mL) instead of the final volume.
15. How many milligrams of epinephrine are in 30 mL of a 1:1000 solution?
    Answer: 30 mg A ratio strength of 1:1000 means 1 gram of solute per 1000 mL of solution. First, convert this to mg/mL: $\frac{1 \text{ g}}{1000 \text{ mL}} = \frac{1000 \text{ mg}}{1000 \text{ mL}} = 1 \text{ mg/mL}$ Now, calculate the amount of drug in 30 mL: $\text{Amount} = \text{Concentration} \times \text{Volume} = 1 \text{ mg/mL} \times 30 \text{ mL} = 30 \text{ mg}$
16. A technician takes 10 mL of a 20% stock solution and dilutes it to 100 mL. Then, 10 mL of this new solution is taken and further diluted to a final volume of 50 mL. What is the final concentration of the solution?
    Answer: 0.4% This is a serial dilution problem. Solve it in two steps using $C_1V_1 = C_2V_2$. Step 1: First dilution. $(20\%) \times (10 \text{ mL}) = C_2 \times (100 \text{ mL})$ $C_2 = \frac{200}{100} = 2\%$ Step 2: Second dilution, using the 2% solution as the new stock. $(2\%) \times (10 \text{ mL}) = C_3 \times (50 \text{ mL})$ $C_3 = \frac{20}{50} = 0.4\%$ The final concentration is 0.4%.
17. A 50 mL vial containing 2 g of magnesium sulfate is added to a 1000 mL IV bag of Lactated Ringer's. What is the final concentration of magnesium sulfate in mg/mL?
    Answer: 1.9 mg/mL 1. Convert the amount of drug to mg: $2 \text{ g} = 2000 \text{ mg}$. 2. Calculate the total final volume: $1000 \text{ mL} \text{ (bag)} + 50 \text{ mL} \text{ (vial)} = 1050 \text{ mL}$. 3. Divide the total amount of drug by the total volume to find the concentration: $\text{Concentration} = \frac{2000 \text{ mg}}{1050 \text{ mL}} \approx 1.90 \text{ mg/mL}$ Distractor B is a common error made by ignoring the volume added from the vial.
18. A technician takes 10 mL of a 20% stock solution and dilutes it to 100 mL. Then, 10 mL of this new solution is taken and further diluted to a final volume of 50 mL. What is the final concentration of the solution?
    Answer: 0.40% This is a serial dilution problem. Solve it in two steps using $C_1V_1 = C_2V_2$. Step 1: First dilution. $(20\%) \times (10 \text{ mL}) = C_2 \times (100 \text{ mL})$ $C_2 = \frac{200}{100} = 2\%$ Step 2: Second dilution, using the 2% solution as the new stock. $(2\%) \times (10 \text{ mL}) = C_3 \times (50 \text{ mL})$ $C_3 = \frac{20}{50} = 0.4\%$ The final concentration is 0.4%.
19. A pharmacy has a 1 L bag of D20W (20% dextrose in water). How many milliliters of sterile water must be added to create a D5W solution?
    Answer: 3000 mL 1. Use the dilution formula $C_1V_1 = C_2V_2$ to find the final volume ($V_2$). The initial volume is 1 L = 1000 mL. $(20\%) \times (1000 \text{ mL}) = (5\%) \times V_2$ $20000 = 5 \times V_2$ $V_2 = \frac{20000}{5} = 4000 \text{ mL}$ 2. This is the final volume. The question asks how much sterile water to add. $\text{Volume to add} = \text{Final Volume} - \text{Initial Volume} = 4000 \text{ mL} - 1000 \text{ mL} = 3000 \text{ mL}$ Distractor D is the final volume, not the volume added.
20. What is the concentration in mg/mL of a 0.9% sodium chloride solution?
    Answer: 9 mg/mL A 0.9% (w/v) solution contains 0.9 grams of solute per 100 mL of solution. 1. Convert grams to milligrams: $0.9 \text{ g} = 900 \text{ mg}$. 2. So, the concentration is 900 mg per 100 mL. 3. To find the concentration in mg/mL, divide both values by 100: $\frac{900 \text{ mg}}{100 \text{ mL}} = 9 \text{ mg/mL}$ This is a common conversion that is useful to memorize.

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