Question

Apothecaries (druggists) use the following set of measures in the English system: $$\begin{aligned} 20 \text { grains ap } &=1 \text { scruple (exact) } \\ 3 \text { scruples } &=1 \text { dram ap (exact) } \\ 8 \operatorname{dram} a p &=1 \text { oz ap (exact) } \\ 1 \operatorname{dram} a p &=3.888 g \end{aligned}$$ a. Is an apothecary grain the same as a troy grain? (See Exercise 49.) b. 1 oz ap 5 ________ oz troy. c. An aspirin tablet contains \(5.00 \times 10^{2} \mathrm{mg}\) of active ingre- dient. 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. No, 1 apothecary grain is not the same as 1 troy grain. 1 apothecary grain is approximately 0.0648 g, while 1 troy grain is approximately 0.06479891 g. b. 1 oz ap is approximately 1.09714 oz troy. c. The aspirin tablet contains 500 mg or 0.5 g of active ingredient, which is approximately 7.717 grains ap or approximately 0.38585 scruples. d. The mass of 1 scruple is approximately 1.296 g.

Step-by-step solution

Calculate the mass of 1 apothecary grain in grams

According to the given information, 1 dram ap = 3.888 g, and 1 scruple = 1/3 dram ap, and 1 grain ap = 1/20 scruple. We need to find the mass of 1 grain ap in grams. 1 grain ap = (1/20) * (1/3) * 3.888 g Calculate this value.

Compare with troy grain mass

The mass of 1 troy grain, as given in Exercise 49, is approximately 0.06479891 g. Compare the mass of 1 apothecary grain with the mass of 1 troy grain and determine whether they are the same. #b. Convert 1 oz ap to oz troy#

Calculate the mass of 1 oz ap in grams

From the given information, 1 oz ap = 8 drams ap. Calculate the mass of 1 oz ap in grams by multiplying with the conversion factor. 1 oz ap = 8 * 3.888 g Calculate this mass in grams.

Convert grams to oz troy

To convert the mass in grams to oz troy, use the conversion factor from Exercise 49 which states that 1 g = 0.0321507 oz troy. Calculate the mass in oz troy. #c. Convert aspirin tablet mass to grains ap and scruples#

Convert mg to grains ap

The mass of the active ingredient in the aspirin tablet is 500 mg. First, convert this mass to grams. 500 mg = 0.5 g Now, convert the mass in grams to grains ap using the conversion factor. Calculate the mass in grains ap.

Convert grains ap to scruples

Now, convert the mass in grains ap to scruples using the given conversion factor. Calculate the mass in scruples. #d. Mass of 1 scruple in grams#

Calculate the mass of 1 scruple in grams

Since we know that 1 scruple = 1/3 dram ap, and 1 dram ap = 3.888 g, we can easily find the mass of 1 scruple in grams. 1 scruple = (1/3) * 3.888 g Calculate the mass in grams.

Key concepts

Mass Conversion

Mass conversion is a fundamental concept in apothecary measurement, especially when dealing with different units of mass such as grains, scruples, and drams. Understanding these conversions is crucial for precise measurement in pharmacy practices.
In the apothecary system, there are specific conversion rates used for mass.
Here is how they work:

• 1 dram ap is equivalent to 3.888 grams.
• 1 scruple equals one-third of a dram ap.
• 1 grain ap is equal to the twentieth of a scruple.

To convert from one unit to another, we rely on multiplying or dividing by these set conversion rates. For example, to find out how many grams are in one grain ap, we use:\[1 ext{ grain ap} = \left( \frac{1}{20} \right) \times \left( \frac{1}{3} \right) \times 3.888 ext{ g}\]Mastering these simple calculations allows for seamless switching between units, an essential skill for anyone working with historic or specialized measurement systems.

Troy Grain Comparison

The troy grain is slightly different from the apothecary grain, even though their names sound similar.
Understanding their difference is key in pharmaceutical contexts where precision is vital.
The troy system is another traditional system often used in weighing precious metals and gems.
Here's how the systems compare:

• 1 troy grain is approximately equal to 0.06479891 grams.
• 1 apothecary grain, after conversion, is less than this value.

Thus, when comparing these two grains: - If a task requires utmost precision with metals or jewels, the troy system is used. - For pharmaceuticals, apothecary grain is more common.
Both systems appear similar on the surface, but knowing the exact differences prevents measuring errors.

Dram Ap Measurement

In the apothecaries' system, the dram is a larger unit of measure, and is frequently used for larger quantities of substances. This measurement plays a pivotal role in pharmaceutical formulations.
Understanding the dram measurement involves knowing its place within the hierarchy of weights.

• 1 dram ap contains 3 scruples.
• Since 1 scruple equals 1/3 of a dram, it follows that multiplying that by the weight of a dram gives the weight of a scruple.

In modern weight systems, 1 dram ap is equivalent to:\[1 ext{ dram ap} = 3.888 ext{ grams}\]This widespread use in medicinal compounding makes the dram an invaluable measure for pharmacists who need precision in preparing medications.

Scruple to Grams Conversion

Converting between scruples and grams is straightforward when you know the correct conversion factors. In the apothecaries' system, the scruple is a smaller unit compared to the dram.
Here’s how you can convert a scruple to grams.

• Since 1 scruple is 1/3 of a dram ap, and 1 dram ap is 3.888 g, you multiply:\[1 ext{ scruple} = \frac{1}{3} \times 3.888 ext{ grams}\]

This calculation provides the mass of 1 scruple in grams, which is crucial for those needing exact measurements of ingredients in medical prescriptions.
By performing this simple multiplication, pharmacists can seamlessly switch between traditional and metric systems, ensuring accuracy.