Ptcb Quiz: Concentration Calculations
20 questions · exam conditions
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Concentration CalculationsQuestion 1 of 20

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?

285 mg/mL
333 mg/mL
400 mg/mL
1000 mg/mL
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Ptcb Quiz: Concentration Calculations

Practice Concentration Calculations in Ptcb with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

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This quiz focuses on Concentration Calculations, giving you a quick way to practice the rules, question types, and explanations that matter most for Ptcb.

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Question 1

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?

  1. 285 mg/mL
  2. 333 mg/mL (correct answer)
  3. 400 mg/mL
  4. 1000 mg/mL
Explanation: First, convert the total amount of drug from grams to milligrams: 1 g=1000 mg1 \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: Concentration=Total DrugTotal Volume=1000 mg3.0 mL≈333.3 mg/mL\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.

Question 2

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?

  1. 5 mL (correct answer)
  2. 8 mL
  3. 10 mL
  4. 20 mL
Explanation:
  1. Calculate the total dose of dopamine needed in the bag: Total Dose=800 mcg/mL×250 mL=200,000 mcg\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 mg=1000 mcg1 \text{ mg} = 1000 \text{ mcg} 200,000 mcg÷1000=200 mg200,000 \text{ mcg} \div 1000 = 200 \text{ mg}
  3. Calculate the volume of stock solution needed using the formula Volume = Dose / Concentration: Volume needed=200 mg40 mg/mL=5 mL\text{Volume needed} = \frac{200 \text{ mg}}{40 \text{ mg/mL}} = 5 \text{ mL}

Question 3

The instructions for a drug vial state: "Reconstitute with 9.6 mL of sterile water to provide a solution containing 100 mg/mL."

Based on the instructions, how many milliliters of the reconstituted solution are required to administer a 450 mg dose?

  1. 0.45 mL
  2. 4.5 mL (correct answer)
  3. 9.6 mL
  4. 45 mL
Explanation: 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. Volume=450 mg100 mg/mL=4.5 mL\text{Volume} = \frac{450 \text{ mg}}{100 \text{ mg/mL}} = 4.5 \text{ mL} Therefore, 4.5 mL of the reconstituted solution is needed.

Question 4

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?

  1. 0.2%
  2. 0.4% (correct answer)
  3. 2.0%
  4. 4.0%
Explanation: This is a serial dilution problem. Solve it in two steps using C1V1=C2V2C_1V_1 = C_2V_2. Step 1: First dilution. (20%)×(10 mL)=C2×(100 mL)(20\%) \times (10 \text{ mL}) = C_2 \times (100 \text{ mL}) C2=200100=2%C_2 = \frac{200}{100} = 2\% Step 2: Second dilution, using the 2% solution as the new stock. (2%)×(10 mL)=C3×(50 mL)(2\%) \times (10 \text{ mL}) = C_3 \times (50 \text{ mL}) C3=2050=0.4%C_3 = \frac{20}{50} = 0.4\% The final concentration is 0.4%.

Question 5

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?

  1. 0.2 mL
  2. 5 mL (correct answer)
  3. 15 mL
  4. 1125 mL
Explanation: To calculate the volume required for a specific dose, use the formula: Volume=Desired DoseConcentration on Hand\text{Volume} = \frac{\text{Desired Dose}}{\text{Concentration on Hand}} Volume=75 mg15 mg/mL=5 mL\text{Volume} = \frac{75 \text{ mg}}{15 \text{ mg/mL}} = 5 \text{ mL} 5 mL of the solution should be administered.

Question 6

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?

  1. 4.9 mg/mL (correct answer)
  2. 5.0 mg/mL
  3. 20.0 mg/mL
  4. 25.0 mg/mL
Explanation: This is a multi-step problem.
  1. Calculate the concentration of the reconstituted vial: 2 g=2000 mg2 \text{ g} = 2000 \text{ mg}. Concentration = 2000 mg/10 mL=200 mg/mL2000 \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 mg/mL×2.5 mL=500 mg200 \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 mL+2.5 mL=102.5 mL100 \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 mg/102.5 mL≈4.88 mg/mL500 \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.

Question 7

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?

  1. 5 mL (correct answer)
  2. 8 mL
  3. 10 mL
  4. 20 mL
Explanation:
  1. Calculate the total dose of dopamine needed in the bag: Total Dose=800 mcg/mL×250 mL=200,000 mcg\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 mg=1000 mcg1 \text{ mg} = 1000 \text{ mcg} 200,000 mcg÷1000=200 mg200,000 \text{ mcg} \div 1000 = 200 \text{ mg}
  3. Calculate the volume of stock solution needed using the formula Volume = Dose / Concentration: Volume needed=200 mg40 mg/mL=5 mL\text{Volume needed} = \frac{200 \text{ mg}}{40 \text{ mg/mL}} = 5 \text{ mL}

Question 8

The instructions for a drug vial state: "Reconstitute with 9.6 mL of sterile water to provide a solution containing 100 mg/mL."

Based on the instructions, how many milliliters of the reconstituted solution are required to administer a 450 mg dose?

  1. 0.45 mL
  2. 4.5 mL (correct answer)
  3. 9.6 mL
  4. 45 mL
Explanation: 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. Volume=450 mg100 mg/mL=4.5 mL\text{Volume} = \frac{450 \text{ mg}}{100 \text{ mg/mL}} = 4.5 \text{ mL} Therefore, 4.5 mL of the reconstituted solution is needed.

Question 9

What is the ratio strength (w/v) of a 0.5% solution?

  1. 1:2
  2. 1:20
  3. 4:20 (correct answer)
  4. 34:20:00
Explanation: A 0.5% solution means 0.5 g of solute in 100 mL of solution. Ratio strength is expressed as 1:X. To find X, set up a proportion: 0.5 g100 mL=1 gX mL\frac{0.5 \text{ g}}{100 \text{ mL}} = \frac{1 \text{ g}}{X \text{ mL}} Cross-multiply to solve for X: 0.5X=1000.5X = 100 X=1000.5=200X = \frac{100}{0.5} = 200 The ratio strength is 1:200.

Question 10

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?

  1. 4.9 mg/mL (correct answer)
  2. 5.0 mg/mL
  3. 20.0 mg/mL
  4. 25.0 mg/mL
Explanation: This is a multi-step problem.
  1. Calculate the concentration of the reconstituted vial: 2 g=2000 mg2 \text{ g} = 2000 \text{ mg}. Concentration = 2000 mg/10 mL=200 mg/mL2000 \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 mg/mL×2.5 mL=500 mg200 \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 mL+2.5 mL=102.5 mL100 \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 mg/102.5 mL≈4.88 mg/mL500 \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.

Question 11

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?

  1. 0.20%
  2. 0.40% (correct answer)
  3. 2.00%
  4. 4.00%
Explanation: This is a serial dilution problem. Solve it in two steps using C1V1=C2V2C_1V_1 = C_2V_2. Step 1: First dilution. (20%)×(10 mL)=C2×(100 mL)(20\%) \times (10 \text{ mL}) = C_2 \times (100 \text{ mL}) C2=200100=2%C_2 = \frac{200}{100} = 2\% Step 2: Second dilution, using the 2% solution as the new stock. (2%)×(10 mL)=C3×(50 mL)(2\%) \times (10 \text{ mL}) = C_3 \times (50 \text{ mL}) C3=2050=0.4%C_3 = \frac{20}{50} = 0.4\% The final concentration is 0.4%.

Question 12

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?

  1. 1 part 40% to 5 parts 10% (correct answer)
  2. 5 parts 40% to 1 part 10%
  3. 1 part 40% to 2 parts 10%
  4. 2 parts 40% to 1 part 10%
Explanation: 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% ✓

Question 13

How many milliliters of sterile water must be added to 100 mL of 90% ethanol to prepare a 45% ethanol solution?

  1. 50 mL
  2. 100 mL (correct answer)
  3. 150 mL
  4. 200 mL
Explanation:
  1. Use the dilution formula C1V1=C2V2C_1V_1 = C_2V_2 to find the final volume (V2V_2). (90%)×(100 mL)=(45%)×V2(90\%) \times (100 \text{ mL}) = (45\%) \times V_2 9000=45×V29000 = 45 \times V_2 V2=900045=200 mLV_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. Volume to add=Final Volume−Initial Volume=200 mL−100 mL=100 mL\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.

Question 14

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?

  1. 1000 mL
  2. 2000 mL
  3. 3000 mL (correct answer)
  4. 4000 mL
Explanation:
  1. Use the dilution formula C1V1=C2V2C_1V_1 = C_2V_2 to find the final volume (V2V_2). The initial volume is 1 L = 1000 mL. (20%)×(1000 mL)=(5%)×V2(20\%) \times (1000 \text{ mL}) = (5\%) \times V_2 20000=5×V220000 = 5 \times V_2 V2=200005=4000 mLV_2 = \frac{20000}{5} = 4000 \text{ mL}
  2. This is the final volume. The question asks how much sterile water to add. Volume to add=Final Volume−Initial Volume=4000 mL−1000 mL=3000 mL\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.

Question 15

A pharmacy needs to make 1 liter of 0.9% Normal Saline solution. How many grams of sodium chloride (NaCl) are required?

  1. 0.09 g
  2. 0.9 g
  3. 9 g (correct answer)
  4. 90 g
Explanation: 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: 0.9 g100 mL=X g1000 mL\frac{0.9 \text{ g}}{100 \text{ mL}} = \frac{X \text{ g}}{1000 \text{ mL}} X=0.9×1000100=900100=9 gX = \frac{0.9 \times 1000}{100} = \frac{900}{100} = 9 \text{ g} Therefore, 9 grams of NaCl are needed.

Question 16

How many milliliters of 70% alcohol and 20% alcohol are needed to prepare 1000 mL of 50% alcohol?

  1. 400 mL of 70% and 600 mL of 20%
  2. 500 mL of 70% and 500 mL of 20%
  3. 600 mL of 70% and 400 mL of 20% (correct answer)
  4. 700 mL of 70% and 300 mL of 20%
Explanation: 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|50 - 20| = 30 parts of the 70% solution. ∣50−70∣=20|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% = 3050×1000 mL=600 mL\frac{30}{50} \times 1000 \text{ mL} = 600 \text{ mL}
    • Volume of 20% = 2050×1000 mL=400 mL\frac{20}{50} \times 1000 \text{ mL} = 400 \text{ mL}

Question 17

If a pharmacy technician mixes 200 g of a 10% cream with 300 g of a 20% cream, what is the final percentage strength of the mixture?

  1. 15.0%
  2. 16.0% (correct answer)
  3. 16.7%
  4. 17.5%
Explanation:
  1. Calculate the amount of active ingredient in each cream:
    • In the 10% cream: 200 g×0.10=20 g200 \text{ g} \times 0.10 = 20 \text{ g} of active ingredient.
    • In the 20% cream: 300 g×0.20=60 g300 \text{ g} \times 0.20 = 60 \text{ g} of active ingredient.
  2. Find the total amount of active ingredient and the total weight of the mixture:
    • Total active ingredient = 20 g+60 g=80 g20 \text{ g} + 60 \text{ g} = 80 \text{ g}
    • Total weight = 200 g+300 g=500 g200 \text{ g} + 300 \text{ g} = 500 \text{ g}
  3. Calculate the final percentage strength: Final %=Total Active IngredientTotal Weight×100=80 g500 g×100=0.16×100=16.0%\text{Final \%} = \frac{\text{Total Active Ingredient}}{\text{Total Weight}} \times 100 = \frac{80 \text{ g}}{500 \text{ g}} \times 100 = 0.16 \times 100 = 16.0\%

Question 18

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?

  1. 1.9 mg/mL (correct answer)
  2. 2.0 mg/mL
  3. 38.1 mg/mL
  4. 40.0 mg/mL
Explanation:
  1. Convert the amount of drug to mg: 2 g=2000 mg2 \text{ g} = 2000 \text{ mg}.
  2. Calculate the total final volume: 1000 mL (bag)+50 mL (vial)=1050 mL1000 \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: Concentration=2000 mg1050 mL≈1.90 mg/mL\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.

Question 19

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?

  1. 25 mL
  2. 50 mL
  3. 100 mL (correct answer)
  4. 400 mL
Explanation: This is a dilution calculation that can be solved using the formula C1V1=C2V2C_1V_1 = C_2V_2, where CC is concentration and VV is volume. Let C1=10%C_1 = 10\%, V1=?V_1 = ?, C2=2%C_2 = 2\%, and V2=500V_2 = 500 mL. (10%)×V1=(2%)×(500 mL)(10\%) \times V_1 = (2\%) \times (500 \text{ mL}) 10V1=100010V_1 = 1000 V1=100010=100 mLV_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.

Question 20

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?

  1. 1000 mL
  2. 2000 mL
  3. 3000 mL (correct answer)
  4. 4000 mL
Explanation:
  1. Use the dilution formula C1V1=C2V2C_1V_1 = C_2V_2 to find the final volume (V2V_2). The initial volume is 1 L = 1000 mL. (20%)×(1000 mL)=(5%)×V2(20\%) \times (1000 \text{ mL}) = (5\%) \times V_2 20000=5×V220000 = 5 \times V_2 V2=200005=4000 mLV_2 = \frac{20000}{5} = 4000 \text{ mL}
  2. This is the final volume. The question asks how much sterile water to add. Volume to add=Final Volume−Initial Volume=4000 mL−1000 mL=3000 mL\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.