Question

Apothecaries (druggists) use the following set of measures in the English system: $$ \begin{aligned} 20 \text { grains ap } &=1 \text { scruple (exact) } \\ 3 \text { scruples } &=1 \text { dram ap (exact) } \\ 8 \text { dram ap } &=1 \mathrm{oz} \text { ap (exact) } \\ 1 \text { dram ap } &=3.888 \mathrm{~g} \end{aligned} $$ a. Is an apothecary grain the same as a troy grain? (See Exercise 45.) b. \(102 \mathrm{ap}=\)_____oz troy. c. An aspirin tablet contains \(5.00 \times 10^{2} \mathrm{mg}\) of active ingredient. What mass in grains ap of active ingredient does it contain? What mass in scruples? d. What is the mass of 1 scruple in grams?

Short answer

a. Yes, 1 apothecary grain is the same as 1 troy grain. Both are equal to 0.0648 grams. b. \(102 \mathrm{ap} = 0.2125\) oz troy. c. The aspirin tablet contains approximately 7.72 grains ap and 0.386 scruples of the active ingredient. d. The mass of 1 scruple is 1.296 grams.

Step-by-step solution

a. Comparing the apothecary grain to the troy grain.

We shall compare both metrics with a widely accepted unit of mass such as grams. From Exercise 45, we have that 1 grain troy = 0.0648 g. Therefore, to compare the apothecary grain to the troy grain, we need to convert 1 apothecary grain to grams: $$ 20 \text{ grains ap} = 1 \text{ scruple} $$ $$ 3 \text{ scruples} = 1 \text{ dram ap} $$ $$ 1 \text{ dram ap} = 3.888 \text{~g} $$ Multiplying these equations, we have: $$ (20 \times 3) \text{ grains ap} = 1 \text{ scruple} \times 1 \text{ dram ap} = 3.888 \text{~g} $$ $$ 60 \text{ grains ap} = 3.888 \text{~g} $$ Thus, 1 grain ap is equal to \( \frac{3.888}{60} \) g: $$ 1 \text{ grain ap} = 0.0648 \text{~g} $$ Therefore, 1 apothecary grain is the same as 1 troy grain.

b. Converting 102 ap grains to troy ounces

We convert 102 grains ap to troy ounces using the given conversion relationships: $$ 102 \text{ grains ap} = \frac{102}{20} \text{ scruples} = 5.1 \text{ scruples} $$ $$ 5.1 \text{ scruples} = \frac{5.1}{3} \text{ drams ap} = 1.7 \text{ drams ap} $$ $$ 1.7 \text{ drams ap} = \frac{1.7}{8} \text{ oz ap} = 0.2125 \text{ oz ap} $$ Since 1 grain ap = 1 grain troy: $$ 102 \text{ grains ap} = 102 \text{ grains troy} = 0.2125 \text{ oz troy} $$

c. Calculating mass of aspirin tablet in grains ap and scruples

We first convert the given mass of the active ingredient from mg to g: $$ 5.00 \times 10^{2} \text{ mg} = 0.500 \text{~g} $$ Now we'll convert 0.500 g to grains ap. From our previous calculations, 1 grain ap = 0.0648 g. Thus: $$ 0.500 \text{~g} = \frac{0.500}{0.0648} \text{ grains ap} \approx 7.72 \text{ grains ap} $$ Finally, we convert grains ap to scruples: $$ 7.72 \text{ grains ap} = \frac{7.72}{20} \text{ scruples} \approx 0.386 \text{ scruples} $$ The aspirin tablet contains 7.72 grains ap and 0.386 scruples of the active ingredient.

d. Calculating the mass of 1 scruple in grams

From our initial calculations of conversion relationships, we have: $$ 1 \text{ scruple} = \frac{1}{3} \text{ dram ap} $$ and $$ 1 \text{ dram ap} = 3.888\text{~g} $$ To find the mass of 1 scruple in grams, we substitute the value of 1 dram ap in grams: $$ 1 \text{ scruple} = \frac{1}{3} \times 3.888 \text{~g} = 1.296 \text{~g} $$ Therefore, the mass of 1 scruple is 1.296 g.

Key concepts

Understanding the Scruple

In the apothecary system, a scruple is a unit of weight used for measuring medicinal ingredients. It is essential to grasp the concept of a scruple in order to effectively navigate this system.
To define it more precisely:

• 1 scruple = 20 grains ap
• 3 scruples = 1 dram ap
• 1 dram ap = 3.888 g

Each scruple represents a specific combination of grains and drams. Using these conversions, we can decode the scruple's importance in the measurement of substances used in pharmacy.
This unit plays a historical role since it allows druggists to maintain consistency in the formulation of medicines. Knowing that 1 scruple is approximately 1.296 grams becomes crucial in converting or comparing measurements in modern units.

Simplifying Gram Conversion

Conversion between apothecary measurements and modern metric units such as grams is crucial for clarity. For instance, many pharmacological formulas still require calculations with the know-how of transforming ancient measures into more universally recognized units.
When converting grains ap to grams, this relationship is important:

• 1 grain ap = 0.0648 g

Through this conversion, an apothecary grain directly equates to a troy grain. Applying direct proportionality, we can further convert other measurements, ensuring precision in dosage and mixtures in pharmacology.
This knowledge is particularly useful when you need to convert known drug dosages in mills or grams to the apothecary equivalents for precise formulation.

Clarifying the Troy Grain Comparison

The apothecary grain and the troy grain share the same weight, but understanding their context in use is important. Both were utilized historically in different systems of measurement, primarily for precious metals in the troy system and medicinal ingredients in the apothecary system.
The relationship is simple:

• 1 grain ap = 1 grain troy = 0.0648 g

Understanding this equivalence helps prevent errors in comparison and ensures accuracy in converting old recipes or formulas into modern contexts.
The clarity of this equivalence allows for seamless continuity between historic drug practices and contemporary metrics, thus helping old measurement systems stay relevant in today's pharmacological and trade practices.