Measurement of Weight and Volume

Pharmacy is a field that regularly performs precise measurements, most often volumes and weights.

Common instruments for measuring weight and volume exist. To maintain a level of precision, these tools are calibrated.

In deciding what tools to use, one must take into account the amount of precision required.

Measurement of Volume

The measurement of volume is typically reserved for liquids, and utilized the SI Unit liters ($\text{L}$).

When deciding on a tool for volumetric measurement, you should choose a calibrated device that is the closest to your desired volume.

For example: you wouldn’t and shouldn’t use a $100\text{mL}$ device to measure only $5\text{mL}$.

It is also important to note that the narrower the chamber, the lesser the error in reading becomes.

Measurement of Weight

The measurement of weights in pharmacy can be through powders, tablets, or other similar items.

When deciding on the tool for weight measuring, choose a calibrated device that has the closest sensitivity requirement to your desired measurement.

Sensitivity Requirement

This is defined as the smallest amount of weight to be detected by your device.

Aliquot Method

The aliquot method is a method of measuring small volumes that do not meet the sensitivity requirements of your scales or the minimum measurable volume of your graduates.

An aliquot is a fraction of a larger mixture that has the desired weight or volume of a substance.

When using the aliquot method for volume, your must first identify the minimum measurable volume, which is usually the lowest calibration line on the graduate.

When using the aliquot method in weight, one must first know the least weighable quantity of your device.

To calculate this the following formula can be used:

Least Weighable Quantity Formula

• Use case:
  • For calculating the least weighable quantity.
• Variables:
  • $\text{LWQ}$ - Least weighable quantity.
  • $\text{sens req}$ - Sensitivity requirement of weighing device.
  • $\text{err\%}$ - Acceptable percentage of errors.
• Formula: $\text{LWQ}=\frac{100\times \text{sens req}}{\text{err\%}}$

Link to original

After determining your $\text{LWQ}$ or minimum measurable volume, your must determine a number factor to multiply to your desired amount that is equal to or slightly greater than your $\text{LWQ}$ or minimum measurable volume.

Example, if your desired quantity is $0.25\text{g}$ and your $\text{LWQ}$ is equal to $4\text{g}$, then your factor should give you $4\text{g}$ or higher when multiplied to $0.25\text{g}$. (in this case, a factor may be $16$).

Aliquot Amount Formula

• Use case:
  • Calculating amount of aliquot.
• Variables:
  • ${\text{a}}_{\text{aliqot}}$ - amount of aliquot.
  • ${\text{a}}_{\text{desired}}$ - desired amount.
  • $\text{f}$ - aliquot factor
• Formula: ${\text{a}}_{\text{aliquot}}={\text{a}}_{\text{desired}}\times f$

Link to original

After calculating the amount of aliquot, you can then proceed to calculate the total amount in your mixture.

Total Aliquot Mixture Formula

• Use case:
  • Calculating amount of total aliquot mixture.
• Variables:
  • ${\text{a}}_{\text{total}}$ - Total amount of mixture.
  • ${\text{a}}_{\text{aliquot}}$ - amount of aliquot.
  • $\text{f}$ - aliquot factor
• Formula: ${\text{a}}_{\text{total}}={\text{a}}_{\text{aliquot}}\times f$

Link to original

Next, you can calculate the amount of diluent

Aliquot Diluent Formula

• Use case:
  • Calculating amount of total aliquot mixture.
• Variables:
  • ${\text{a}}_{\text{diluent}}$ - amount of diluent.
  • ${\text{a}}_{\text{total}}$ - total amount of mixture.
  • ${\text{a}}_{\text{aliquot}}$ - amount of aliquot
• Formula: ${\text{a}}_{\text{diluent}}={\text{a}}_{\text{total}}-{\text{a}}_{\text{aliquot}}$

Link to original

After that, you can use the ratio formula below to calculate the exact amount of the total mixture to be weighed in order to get your desired amount of substance.

Aliquot Ratio Formula

• Use case:
  • Calculating the fraction of the total mixture that contains the desired amount of substance.
• Variables:
  • $a_{\text{weighed}}$ - amount of total mixture to be weighed that contains desired amount of substance.
  • $a_{\text{desired}}$ - desired amount of substance
  • $a_{\text{total}}$ - total amount of mixture
  • $a_{\text{aliquot}}$ - amount of aliquot.
• Formula: $\frac{a_{\text{weighed}}}{a_{\text{desired}}}=\frac{a_{\text{total}}}{a_{\text{aliquot}}}$

Link to original

Percentage Error

Percentage error is an agreed upon amount of error that a measurement is permissible to have.

In pharmacy, a percentage of $\pm 5\%$ is tolerated for most formulas, though lower percentages of error do exist.

To calculate the percentage of error in a measurement, one can use this formula:

Percentage Error Formula

• Use case:
  • for calculating the percentage of error in a measurement.
• Variables:
  • $\text{err\%}$ - percentage of error.
  • ${\text{err}}_{\text{measurement}}$ - the amount of error in a measurement
  • $q_{\text{desired}}$ - desired or expected quantity.
• Formula: $\text{err\%}=\frac{{\text{err}}_{\text{measurement}}}{q_{\text{desired}}}\times 100\%$

Link to original