Medium NAPLEX Alligation Practice Questions

Concept Explanation

Alligation is a mathematical method used in pharmacy to calculate the proportions of two or more substances of known concentrations required to produce a mixture of a desired final concentration. This technique relies on the principle of mass balance, ensuring that the total amount of active ingredient from each component equals the amount in the final product. Mastery of this skill is essential for pharmaceutical calculations, as it allows pharmacists to accurately compound creams, ointments, and liquid solutions when specific strengths are not commercially available.

To perform an alligation calculation, you arrange the known concentrations in a grid (the alligation cross). The desired target concentration is placed in the center. By calculating the absolute difference between the target and each starting concentration, you determine the parts of each component needed. You can use the Bevinzey calculation tool to streamline your practice sessions and improve your speed.

Solved Examples

1. Problem: How many grams of 5% ointment and 20% ointment are needed to prepare 100g of a 10% ointment?
   • Step 1: Set up the alligation cross. Place 5 and 20 on the left, and 10 in the center.
   • Step 2: Calculate the differences. $|20 - 10| = 10$ parts of the 5% ointment. $|5 - 10| = 5$ parts of the 20% ointment.
   • Step 3: Total parts = $10 + 5 = 15$.
   • Step 4: Calculate grams: $\frac{10}{15} \times 100g = 66.67g$ of 5% ointment; $\frac{5}{15} \times 100g = 33.33g$ of 20% ointment.
2. Problem: You need 500mL of a 30% alcohol solution. You have 50% and 10% alcohol solutions. How much of each is required?
   • Step 1: Differences: $|10 - 30| = 20$ parts of 50%; $|50 - 30| = 20$ parts of 10%.
   • Step 2: Total parts = $20 + 20 = 40$.
   • Step 3: Calculate volume: $\frac{20}{40} \times 500mL = 250mL$ of each solution.
3. Problem: Prepare 60g of a 2.5% hydrocortisone cream using 1% and 5% creams.
   • Step 1: Differences: $|5 - 2.5| = 2.5$ parts of 1%; $|1 - 2.5| = 1.5$ parts of 5%.
   • Step 2: Total parts = $2.5 + 1.5 = 4$.
   • Step 3: Calculate grams: $\frac{2.5}{4} \times 60g = 37.5g$ of 1% cream; $\frac{1.5}{4} \times 60g = 22.5g$ of 5% cream.

Practice Questions

1. How many milliliters of 70% alcohol and 20% alcohol are needed to prepare 500mL of a 40% alcohol solution?
2. Prepare 150g of 15% zinc oxide ointment using 25% and 5% ointments. How many grams of each are required?
3. You need 1L of a 5% dextrose solution. You have 10% and 2.5% dextrose solutions available. How many milliliters of each are needed?

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Practice Calculations
4. How many grams of white petrolatum (0%) should be mixed with 50g of 10% salicylic acid ointment to make a 2% ointment?
5. You have a 40% potassium chloride solution and sterile water (0%). How much of each is needed to make 250mL of a 10% solution?
6. A pharmacist needs 200g of a 12% coal tar ointment. If they have 20% and 4% ointments, how many grams of each are required?
7. How many milliliters of a 1:1000 solution and a 1:10,000 solution are needed to prepare 500mL of a 1:2000 solution?
8. Calculate the amount of 80% alcohol and 30% alcohol needed to make 600mL of a 50% alcohol solution.
9. How many grams of 3% hydrocortisone cream and 1% hydrocortisone cream are needed to make 30g of 2.5% cream?
10. You require 500mL of 0.9% sodium chloride. You have 10% NaCl and sterile water. How many milliliters of the 10% solution are needed?

Answers & Explanations

1. 200mL of 70%, 300mL of 20%. Calculation: 20 parts of 70%, 30 parts of 20%. Total 50 parts. (20/50)*500=200mL.
2. 75g of 25%, 75g of 5%. Calculation: 10 parts of 25%, 10 parts of 5%. Equal amounts.
3. 666.7mL of 10%, 333.3mL of 2.5%. Calculation: 2.5 parts of 10%, 5 parts of 2.5%. Total 7.5 parts.
4. 200g of white petrolatum. Calculation: 2 parts of 10% (50g), 8 parts of 0% (x). x = (8/2)*50 = 200g.
5. 62.5mL of 40%, 187.5mL of water. Calculation: 10 parts of 40%, 30 parts of 0%. Total 40 parts. (10/40)*250=62.5mL.
6. 100g of 20%, 100g of 4%. Calculation: 8 parts of 20%, 16 parts of 4%. Ratio 1:2. Sum 3 parts. 200/3 = 66.67g (20%), 133.33g (4%).
7. 277.8mL of 1:1000, 222.2mL of 1:10,000. Express as percentages: 0.1% and 0.01%, target 0.05%. Parts: 0.04 and 0.05. Total 0.09. (0.04/0.09)*500=222.2, (0.05/0.09)*500=277.8.
8. 240mL of 80%, 360mL of 30%. Calculation: 20 parts of 80%, 30 parts of 30%. Total 50. (20/50)*600=240, (30/50)*600=360.
9. 22.5g of 3%, 7.5g of 1%. Calculation: 1.5 parts of 3%, 0.5 parts of 1%. Total 2. 30/2=15. 1.5*15=22.5, 0.5*15=7.5.
10. 45mL of 10% NaCl. Calculation: 0.9 parts of 10%, 9.1 parts of 0%. Total 10 parts. (0.9/10)*500=45mL.

Quick Quiz

Frequently Asked Questions

Can alligation be used for more than two components?

Yes, alligation alternate can be used for more than two components, though it requires grouping them into pairs or using algebraic equations if the ratios are not fixed. It is most commonly applied to two-component systems in standard pharmacy practice.

What should I do if the target concentration is outside the range of my stock concentrations?

Alligation will not work if the desired concentration is higher than your strongest stock or lower than your weakest stock. In such cases, you must acquire a different stock concentration to perform the compounding.

Is alligation applicable to percentage strengths and ratios?

Yes, alligation works with any concentration expression, including percentages, ratios, or mg/mL, provided all values are converted to the same units before starting the grid.

Does alligation account for volume contraction when mixing liquids?

Standard alligation assumes additive volumes, which is usually sufficient for pharmaceutical compounding. However, for highly precise laboratory work, one should consider potential volume changes due to intermolecular forces.

How do I verify my alligation results?

You can verify your results by calculating the total amount of active ingredient in each component and ensuring it equals the amount of active ingredient in the final desired volume or weight.

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