Hard NAPLEX Sensitivity Practice Questions

Concept Explanation

NAPLEX sensitivity refers to the minimum weighable quantity (MWQ) of a substance that can be accurately weighed on a class A prescription balance within a specific permissible margin of error, typically 5%.

To ensure patient safety and dosing accuracy, pharmacists must understand the limitations of their weighing equipment. The United States Pharmacopeia (USP) sets standards for prescription balances, requiring that the sensitivity requirement (SR) be known. The SR is defined as the weight that causes a deflection of one scale division on the balance index. The formula to calculate the Minimum Weighable Quantity (MWQ) is based on the SR and the acceptable percentage of error:

For most NAPLEX calculations, the acceptable error is 5% (0.05). If the required dose is less than the MWQ, a pharmacist must use the aliquot method of weighing. This involves weighing a larger, measurable amount of the drug, mixing it with an inert diluent (like lactose) to create a trituration, and then weighing a portion (aliquot) of that mixture that contains the exact dose needed. Mastering these concepts is a core component of NAPLEX Prep, as it integrates basic algebra with practical compounding safety.

Solved Examples

1. Calculating MWQ: A class A prescription balance has a sensitivity requirement of 6 mg. Calculate the minimum amount that can be weighed with an error no greater than 5%.
   1. Identify the variables: $\ \text{SR} = 6 \ \text{ mg}$ and $\ \text{Error} = 0.05$.
   2. Apply the formula: $\ \text{MWQ} = \ \frac{6 \ \text{ mg}}{0.05}$.
   3. Solve: $\ \text{MWQ} = 120 \ \text{ mg}$.
   4. Conclusion: Any amount less than 120 mg cannot be weighed directly on this balance.
2. Determining Aliquot Proportions: A pharmacist needs to weigh 15 mg of a drug on a balance with an MWQ of 120 mg. If the pharmacist decides to weigh 120 mg of the drug and mix it with diluent, how much diluent is needed to ensure a 200 mg aliquot contains the 15 mg dose?
   1. Set up a ratio: $\ \frac{15 \ \text{ mg (dose)}}{200 \ \text{ mg (aliquot)}} = \ \frac{120 \ \text{ mg (drug weighed)}}{X \ \text{ (total mixture weight)}}$.
   2. Solve for X: $15X = 24,000 \ \rightarrow X = 1,600 \ \text{ mg total mixture}$.
   3. Calculate diluent: $1,600 \ \text{ mg (total)} - 120 \ \text{ mg (drug)} = 1,480 \ \text{ mg of diluent}$.
3. Calculating Percentage Error: A pharmacist attempts to weigh 80 mg of a powder on a balance with a sensitivity requirement of 5 mg. What is the percentage of error for this measurement?
   1. Formula: $\ \text{Percentage Error} = \ \frac{\ \text{SR}}{\ \text{Quantity Weighed}} \ \times 100$.
   2. Substitute: $\ \frac{5 \ \text{ mg}}{80 \ \text{ mg}} \ \times 100$.
   3. Solve: $0.0625 \ \times 100 = 6.25\%$.
   4. Conclusion: Since 6.25% exceeds the standard 5% limit, this measurement is inaccurate.

Practice Questions

1. A prescription calls for 12 mg of a potent drug. The balance has a sensitivity requirement of 4 mg and the acceptable error is 5%. What is the MWQ of this balance?

2. Using the balance from Question 1, a pharmacist weighs 100 mg of the drug and needs to create a trituration with lactose such that a 150 mg aliquot provides the 12 mg dose. How many milligrams of lactose must be added to the 100 mg of drug?

3. A balance has a sensitivity requirement of 5 mg. If a pharmacist weighs 125 mg of a substance, what is the percentage error? Is this within the standard USP limit?

4. You need to weigh 5 mg of a drug. The balance has an SR of 6 mg. You choose to weigh 120 mg of the drug and use a 120 mg aliquot. How much diluent is required for the total mixture?

5. A pharmacist is preparing a compound that requires 0.75 mg of a substance. The MWQ of the balance is 150 mg. The pharmacist weighs 150 mg of the substance and mixes it with 9,850 mg of diluent. What weight of the final mixture (in mg) should be weighed to obtain the 0.75 mg dose?

6. If the sensitivity requirement of a balance is 0.002 g, what is the smallest quantity that can be weighed with a 4% error margin?

7. A technician weighs 200 mg of a drug on a balance with an SR of 10 mg. Calculate the percentage error. If this drug was intended for an oncology therapeutics preparation where precision is vital, would this error be acceptable?

8. You are asked to prepare 20 capsules, each containing 2 mg of drug X. The balance SR is 6 mg and error limit is 5%. You weigh out 120 mg of drug X. How much total diluent is needed if each capsule's final weight (drug + diluent) must be 300 mg?

Answers & Explanations

1. Answer: 80 mg. Explanation: $\ \text{MWQ} = \ \frac{4 \ \text{ mg}}{0.05} = 80 \ \text{ mg}$. Since 12 mg is less than 80 mg, an aliquot is required.
2. Answer: 1,150 mg. Explanation: Ratio: $\ \frac{12 \ \text{ mg (dose)}}{150 \ \text{ mg (aliquot)}} = \ \frac{100 \ \text{ mg (drug)}}{X \ \text{ (total)}}$. $12X = 15,000 \ \rightarrow X = 1,250 \ \text{ mg}$. Diluent = $1,250 - 100 = 1,150 \ \text{ mg}$.
3. Answer: 4%; Yes. Explanation: $\ \frac{5}{125} \ \times 100 = 4\%$. This is within the standard 5% limit.
4. Answer: 2,760 mg. Explanation: Ratio: $\ \frac{5}{120} = \ \frac{120}{X}$. $5X = 14,400 \ \rightarrow X = 2,880 \ \text{ mg}$. Diluent = $2,880 - 120 = 2,760 \ \text{ mg}$.
5. Answer: 50 mg. Explanation: Total mixture = $150 \ \text{ mg (drug)} + 9,850 \ \text{ mg (diluent)} = 10,000 \ \text{ mg}$. Ratio: $\ \frac{150 \ \text{ mg (drug)}}{10,000 \ \text{ mg (total)}} = \ \frac{0.75 \ \text{ mg (dose)}}{X \ \text{ (aliquot)}}$. $150X = 7,500 \ \rightarrow X = 50 \ \text{ mg}$.
6. Answer: 50 mg. Explanation: $0.002 \ \text{ g} = 2 \ \text{ mg}$. $\ \text{MWQ} = \ \frac{2 \ \text{ mg}}{0.04} = 50 \ \text{ mg}$.
7. Answer: 5%; Yes. Explanation: $\ \frac{10}{200} \ \times 100 = 5\%$. While 5% is the standard limit, high-precision fields like infectious disease or oncology often prefer even lower margins, though 5% technically passes general USP standards.
8. Answer: 5,880 mg. Explanation: Total drug needed = $20 \ \times 2 \ \text{ mg} = 40 \ \text{ mg}$. Weighed drug = 120 mg. Ratio: $\ \frac{40 \ \text{ mg}}{X \ \text{ (total aliquot weight)}} = \ \frac{120 \ \text{ mg}}{Y \ \text{ (total mixture weight)}}$. Since total capsules weight is $20 \ \times 300 = 6,000 \ \text{ mg}$, the total mixture weight (Y) must be 6,000 mg. Diluent = $6,000 - 120 = 5,880 \ \text{ mg}$.

Frequently Asked Questions

What is the Sensitivity Requirement (SR) of a balance?

The sensitivity requirement is the minimum weight needed to shift the balance's pointer or indicator by one full scale division. It represents the inherent precision limit of the mechanical or digital weighing system.

How do you calculate the Minimum Weighable Quantity (MWQ)?

To find the MWQ, divide the sensitivity requirement by the maximum allowable percentage of error, usually 0.05 for 5%. For example, an SR of 6 mg divided by 0.05 equals an MWQ of 120 mg.

Why is the aliquot method used in compounding?

The aliquot method is used when the required dose of a drug is smaller than the balance's minimum weighable quantity. It ensures dosing accuracy by weighing a larger, safe amount and diluting it proportionally.

Can I use a digital balance for small quantities?

Yes, many modern digital analytical balances have much lower sensitivity requirements than traditional Class A balances. However, you must still verify the balance's specific MWQ based on its manufacturer-validated SR before weighing potent substances.

Is 5% always the error limit on the NAPLEX?

Yes, unless a different percentage is explicitly stated in the problem, the standard USP acceptable error for pharmacy calculations is 5%. You can use the AI Question Generator to practice scenarios with different error thresholds.