Measurement Accuracy and the Aliquot Method

Why accuracy matters

Every balance and every measure can be slightly wrong. This unavoidable error matters a great deal when the quantity being measured is small, because the error is a bigger share of what you are trying to measure.

Percentage error

percentage error = (error ÷ quantity measured) × 100

Example 1: weighing. A balance may be wrong by up to 5 mg.

The same balance is ten times worse at 50 mg than at 500 mg.

Example 2: measuring a liquid. You need to measure 10 mL.

Choosing a measure

• Use the smallest measure that can hold the volume, because it has the smallest error.
• As a rule of thumb, the volume you measure should be at least 20% (one fifth) of the capacity of the measure. To measure 10 mL, do not use anything larger than a 50 mL measure.
• Read the bottom of the curve (the meniscus) with your eye level with the liquid.

Minimum weighable quantity

The minimum weighable quantity is the smallest amount that can be weighed on a balance without exceeding the error you are willing to accept.

minimum quantity = balance error ÷ (acceptable error as a fraction)

Example 1. A balance may be wrong by ±5 mg. You accept an error of 5% (0.05).

• Minimum quantity = 5 ÷ 0.05 = 100 mg

Example 2. A balance may be wrong by ±2 mg. You accept an error of 2% (0.02).

• Minimum quantity = 2 ÷ 0.02 = 100 mg

If the amount you need is less than this, weighing it directly gives too much error. You use the aliquot method.

The aliquot method

An aliquot is a measured fraction of a larger quantity. The idea is to weigh a larger amount that the balance can handle accurately, dissolve it in a measured volume, and then measure out just the part that holds the quantity you need.

For solids

1. Weigh at least the minimum weighable quantity of the drug.
2. Dissolve it in a suitable liquid and make it up to a measured volume.
3. Work out the strength (mg per mL).
4. Measure the aliquot that contains the amount you need.
5. Use the aliquot in the preparation, and discard the rest.

Example 1. You need 15 mg of a drug. The minimum weighable quantity is 100 mg.

1. Weigh 120 mg of the drug. This is more than 100 mg, so the error is acceptable.
2. Dissolve it in water and make up to 40 mL.
3. Strength = 120 ÷ 40 = 3 mg per mL.
4. Volume needed = 15 ÷ 3 = 5 mL. Measure 5 mL, which contains 15 mg.

You could also weigh 100 mg and make it up to 50 mL (2 mg per mL), then measure 15 ÷ 2 = 7.5 mL. Both routes give the same amount of drug. Choose numbers that make the aliquot easy to measure.

Example 2. A prescription needs 12 mg of drug in 100 mL of mixture. The minimum weighable quantity is 100 mg.

1. Weigh 120 mg and dissolve it in water to make 100 mL of stock solution.
2. Strength = 120 ÷ 100 = 1.2 mg per mL.
3. Volume needed = 12 ÷ 1.2 = 10 mL.
4. Measure 10 mL of the stock solution and add it to the mixture. It is part of the final 100 mL, so account for it when you make up to volume.

For liquids

The same idea works for a small volume of liquid that is too little to measure accurately.

Example. You need 0.2 mL of a liquid.

1. Measure 1 mL of the liquid and dilute it with a suitable diluent to 10 mL. Now 1 mL of the dilution contains 0.1 mL of the liquid.
2. You need 0.2 mL, so measure 2 mL of the dilution.

Good practice

• Use a diluent that is compatible with the drug and the final preparation.
• Make up to a measured volume accurately, so the strength is known.
• Mix well before taking the aliquot.
• Discard the unused stock solution unless the pharmacist says otherwise.
• Keep the working written down so it can be checked.

For solid powders, the same principle is used with a powder diluent. That method, called trituration, is covered in the lesson on dilution and concentration.