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AUTHORS’ NOTE:
It is important for the student to recognize that answers to aliquot calculations may vary, but still be correct, depending upon the multiple factors arbitrarily chosen for use.
Measuring Volume by the Aliquot Method
The aliquot method of measuring volume, which is identical in principle to the aliquot method of weighing, may be used when relatively small volumes must be measured with great precision:
STEP 1. Multiply the desired volume by a factor that will produce a
quantity that can be measured with the required precision.
STEP 2. Select an aliquot amount that can be measured with the required
precision.
STEP 3. Determine the final volume to which to dilute the active
ingredient. When measuring by volume, the exact amount of diluent to add cannot be easily determined because volumes may not be additive. The diluent is usually a solvent for the liquid to be measured and must be compatible with the liquid.
STEP 4. Clearly convey the quantities calculated and check for accuracy.
Example Problems
1. A formula calls for 0.5 mL of hydrochloric acid. Using a 10-mL
graduate that can accurately measure 2 mL or greater, explain how you would obtain the desired quantity of hydrochloric acid by the aliquot method.
STEP 1. Choosing 4 as the multiplier, the amount of hydrochloric acid to measure would be:
0.5 mL hydrochloric acid × 4 = 2 mL hydrochloric acid to measure STEP 2. 2 mL can be chosen as the aliquot. STEP 3. The final volume to which to dilute the hydrochloric acid can be determined as follows:
STEP 4. The directions for measuring utilizing the amounts calculated earlier are shown here: Measure 2 mL of hydrochloric acid. Dilute the hydrochloric acid to 8 mL with water. Mix thoroughly. Measure a 2-mL aliquot from the mixture to obtain 0.5 mL hydrochloric acid.
Proof:
2. A prescription calls for 0.2 mL of clove oil. Using a 5-mL graduate
with a minimum accurate volume of 1 mL, how would you obtain the required amount of clove oil using the aliquot method and alcohol as the diluent?
STEP 1. Choosing 5 as the multiplier, the amount of clove oil to measure would be:
STEP 2. 1 mL can be chosen as the aliquot. STEP 3. The final volume to which to dilute the clove oil can be determined as follows:
STEP 4. The directions for measuring utilizing the amounts calculated earlier are shown here: Measure 1 mL of clove oil. Dilute the clove oil to 5 mL with alcohol. Mix thoroughly. Measure a 1-mL aliquot from the mixture to obtain 0.2 mL clove oil.
Proof:
Least Weighable Quantity Method of Weighing
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This method may be used as an alternative to the aliquot method of weighing to obtain small quantities of a drug substance.
After determining the quantity of drug substance that is desired and the smallest quantity that can be weighed on the balance with the desired degree of accuracy, the procedure is as follows:
STEP 1. Weigh an amount of the drug substance that is equal to or
greater than the least weighable quantity.
STEP 2. Dilute the drug substance with a calculated quantity of inert
diluent such that a predetermined quantity of the drug–diluent mixture will contain the desired quantity of the drug.
If 20 mg of a drug substance is needed to fill a prescription, explain how you would obtain this amount of drug with an accuracy of ±5% using a balance with an SR of 6 mg. Use lactose as the diluent.
In this problem, 20 mg is the amount of drug substance needed. The least weighable quantity would be 120 mg. The amount of drug substance to be weighed, therefore, must be ≥120 mg. In solving the problem, 120 mg of drug substance is weighed. In calculating the amount of diluent to use, a predetermined quantity of drug–diluent mixture must be selected to contain the desired 20 mg of drug substance. The quantity selected must be >120 mg because the drug–diluent mixture must be obtained accurately through weighing on the balance. An amount of 150 mg may be arbitrarily selected. The total amount of diluent to use may then be determined through the calculation of the following proportion:
x = 900 mg of the drug–diluent mixture to prepare
Hence, 900 mg − 120 mg = 780 mg of diluent (lactose) to use
It should be noted that in this procedure, each weighing, including that of the drug substance, the diluent, and the drug–diluent mixture, must be determined to be equal to or greater than the least weighable quantity as determined for the balance used and accuracy desired.
CALCULATIONS CAPSULE
Weighing Accuracy
The sensitivity requirement (SR) of a balance must be known or determined. An SR of 6 mg is usual for torsion balances, and the SR is usually lower for electronic balances. An error in weighing of ±5% or less is acceptable.
The smallest quantity that should be weighed on a prescription balance is determined by the equation:
To weigh smaller quantities, the aliquot method of weighing should be used.
Percentage of Error
Because measurements in the community pharmacy are never absolutely accurate, it is important for the pharmacist to recognize the limitations of the instruments used and the magnitude of the errors that may be incurred. When a pharmacist measures a volume of liquid or weighs a material, two quantities become important: (1) the apparent weight or volume measured and (2) the possible excess or deficiency in the actual quantity obtained.
Percentage of error may be defined as the maximum potential error multiplied by 100 and divided by the correct quantity or quantity desired.
The calculation may be formulated as follows:
Calculating Percentage of Error in Volumetric Measurement
The percentage of error in a measurement of volume may be calculated from the preceding equation, relating the volume in error (determined through devices of greater precision) to the volume desired (or apparently measured).
Using a graduated cylinder, a pharmacist measured 30 mL of a liquid. On subsequent examination, using a narrow-gauge burette, it was determined that the pharmacist had actually measured 32 mL. What was the percentage of error in the original measurement?
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Calculating Percentage of Error in Weighing
The various scales and balances used in pharmaceutical weighing have ascribed to them different degrees of precision. As described previously in this chapter, knowledge of the sensitivity requirement of the balance being used is critical in weighing to a specified degree of accuracy. The sensitivity requirement of a balance may be used to determine the percentage of error in a given weighing. The percentage of error can also be used to determine an acceptable weight range when weighing ingredients in preparing dosage forms in compounding or manufacturing.
1. When the maximum potential error is ±4 mg in a total of 100 mg, what
is the percentage of error?
2. A pharmacist needs to compound capsules, and the total weight of the
ingredients in each capsule is 470 mg. What is the weight range for the capsules to fall within ±5% error?
3. A prescription calls for 800 mg of a substance. After weighing this
amount on a balance, the pharmacist decides to check by weighing it again on a more sensitive balance, which registers only 750 mg. Because the first weighing was 50 mg short of the desired amount, what was the percentage of error?
Examples of Measurement Applications in Pharmaceutical Compounding
The following are examples of the calculations applied in weighing and measuring in the compounding of pharmaceutical formulas or medication orders. Many additional problems are found in Chapter 17, Selected
Calculations in Contemporary Compounding.
Compounding instructions:
1. Accurately weigh each of the ingredients.
2. Place the misoprostol in a mixing vessel, and add the polyethylene oxide in equal portions until thoroughly blended.
3. Add the hydroxypropyl methylcellulose in portions until all ingredients are thoroughly blended.
4. Label and dispense.
a. Would a torsion prescription balance with a sensitivity of 6 mg allow
the accurate direct weighing of each ingredient? Explain.
b. Explain how the misoprostol might be accurately obtained using a
torsion prescription balance and the aliquot method of weighing.
c. How many misoprostol tablets, each containing 0.2 mg, could be
used in compounding this order? How would they be combined?
Answers:
a. The least weighable quantity using a torsion balance is 120 mg (with
an SR of 6 mg and an acceptable error of ±5%), as shown in previous example problems. The amount of misoprostol required is 400 μg or 0.4 mg, which is significantly less than the least weighable quantity.
b. STEP 1. Choosing 300 as the multiplier, the amount of misoprostol to
weigh would be:
0.4 mg misoprostol × 300 = 120 mg misoprostol STEP 2. 120 mg can be chosen as the aliquot. STEP 3. Polyethylene oxide can be used as the diluent, and the amount can be determined as follows: 120 mg aliquot × 300 = 36,000 mg dilution 36,000 mg dilution – 120 mg misoprostol = 35,880 mg or 35.88 g of polyethylene oxide Note: 120 mg of the mixture would contain 0.4 mg of misoprostol
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and 119.6 mg of polyethylene oxide. To complete the formula, the pharmacist must add 80.4 mg (200 mg – 119.6 mg) of polyethylene oxide, which is lower than the least weighable quantity. Therefore, the better option is provided by (c).
c. Two misoprostol tablets each containing 0.2 mg (200 μg) would
provide the 400 μg required. The tablets would be pulverized using a mortar and pestle and the other ingredients combined in portions as described in the compounding instructions as stated previously.
Compounding instructions:
1. Accurately weigh and measure each of the ingredients.
2. Dissolve the methylparaben and the propylparaben in the propylene glycol.
3. Dissolve the fentanyl citrate in the normal saline solution.
4. Slowly add the solution of the parabens to the fentanyl citrate solution and mix well.
5. Sterilize by filtering through a sterile 0.2-μm filter into a sterile metered spray bottle.
6. Label and dispense.
a. What type of balance should be used to weigh the fentanyl citrate
and the parabens?
b. What are the best options for measuring the propylene glycol?
Answers:
a. The smallest quantity to be weighed is 2.5 mg (fentanyl citrate), so
an analytical balance with a minimum weighable amount of 2.5 mg must be used. The sensitivity requirement for the balance can be calculated as follows:
b. A graduated pipette or a 1-mL syringe.
CASE IN POINT 3.1
A pharmacist is asked to compound the following formula for the preparation of 100 capsules3:
Using a balance that has an SR of 6 mg, the aliquot method of weighing, lactose as the diluent, and an error in weighing of 4%, show, by calculations, how the correct quantity of estrone can be obtained to accurately compound the formula.
CASE IN POINT 3.2
A physician prescribed 25 4-mg capsules of a drug for a special needs patient, knowing that the dose prescribed was considered “subtherapeutic.” The lowest strength commercially available tablets contain 25 mg.
The pharmacist decided to select the minimum required number of 25-mg tablets (4 tablets), reduce them to a powder with a mortar and pestle, weigh the powder (280 mg), and continue the process using the aliquot method. She called upon her pharmacy student intern to calculate (a) the minimum quantity of lactose (diluent) to use in preparing the crushed tablet–diluent mixture and (b) the quantity of the mixture to use to fill each capsule.
The prescription balance had an SR of 6 mg, and a weighing error of 5% was acceptable.
Show your calculations for (a) and (b), and (c) prove that your answer to (b) is correct by demonstrating that each capsule would
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indeed contain 4 mg of drug.
PRACTICE PROBLEMS
Calculations of Aliquot Parts by Weighing
A prescription calls for 50 mg of chlorpheniramine maleate. Using a prescription balance with a sensitivity requirement of 6 mg, explain how you would obtain the required amount of chlorpheniramine maleate with an error not >5%.
An electronic balance has a sensitivity requirement of 2 mg. Explain how you would weigh 15 mg of capsaicin with an error not >5%, using starch as the diluent.
A torsion prescription balance has a sensitivity requirement of 4 mg. Explain how you would weigh 5 mg of hydromorphone hydrochloride with an error not >5%. Use lactose as the diluent.
An electronic balance has a sensitivity requirement of 3.2 mg. Using lactose as the diluent, explain how you would weigh 8 mg of digoxin with an error not >5%.
A prescription balance has a sensitivity requirement of 6.5 mg. Explain how you would weigh 20 mg of a substance with an error not >2%.
Calculations of Aliquot Parts by Measuring Volume
A formula calls for 0.6 mL of a coloring solution. Using a 10-mL graduate that can accurately measure 2 mL or greater, how could you obtain the desired quantity of the coloring solution by the aliquot method? Use water as the diluent.
Using a 10-mL graduate with a minimum accurate volume of 2 mL, explain how you would measure 1.25 mL of a dye solution by the aliquot method. Use water as the diluent.
The formula for 100 mL of pentobarbital sodium elixir calls for 0.75 mL of orange oil. Using alcohol as a diluent and a 10-mL graduate accurate for 2 mL or greater, how could you obtain the desired quantity of orange oil?
Calculations of Percentage of Error
In compounding a prescription, a pharmacist weighed 50 mg of a substance on a balance with a sensitivity requirement of 4 mg. What was the maximum potential error in terms of percentage?
A pharmacist weighed 475 mg of a substance on a balance of dubious accuracy. When checked on a balance of high accuracy, the
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weight was found to be 445 mg. Calculate the percentage of error in the first weighing.
A 10-mL graduate weighs 42.745 g. When 5 mL of distilled water is measured in it, the combined weight of the graduate and water is
47.675 g. By definition, 5 mL of water should weigh 5 g. Calculate the weight of the measured water and express any deviation from 5 g as percentage of error.
A pharmacy student attempts to measure 40 mL of water in a 2-fl.oz. bottle, then double-checks his measurement with a 50-mL graduated cylinder. The volume of water when measured in the graduated cylinder is 37 mL. What is the percent error in his measurement?
A pharmacist attempts to weigh 0.375 g of morphine sulfate on a balance of dubious accuracy. When checked on a highly accurate balance, the weight is found to be 0.4 g. Calculate the percentage of error in the first weighing.
A student pharmacist prepares capsules in the compounding lab, and the contents of each capsule should weigh 330 mg. What would be the weight range for each capsule to fall within a ±5% error range?
Measurement Applications in Compounding
15.
Using a balance with a sensitivity of 4 mg, an acceptable weighing error of 5%, and cherry syrup as the solvent for tartar emetic, how could you obtain the correct quantity of tartar emetic to fill the prescription?
16.
Compounding instructions:
1. Weigh carvedilol.
2. Grind carvedilol powder in a mortar with the purified water until a smooth paste results.
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