/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 46 Apothecaries (druggists) use the... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 46

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

Expert verified
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

01

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.
02

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: $$ 102 \text{ grains ap} = 102 \text{ grains troy} = 0.2125 \text{ oz troy} $$
03

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.
04

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Classify the following as physical or chemical changes. a. Moth balls gradually vaporize in a closet. b. Hydrofluoric acid attacks glass and is used to etch calibration marks on glass laboratory utensils. c. A French chef making a sauce with brandy is able to boil off the alcohol from the brandy, leaving just the brandy flavoring. d. Chemistry majors sometimes get holes in the cotton jeans they wear to lab because of acid spills.

Make molecular-level (microscopic) drawings for each of the following. a. Show the differences between a gaseous mixture that is a homogeneous mixture of two different compounds, and a gaseous mixture that is a homogeneous mixture of a compound and an element. b. Show the differences among a gaseous element, a liquid element, and a solid element.

The properties of a mixture are typically averages of the properties of its components. The properties of a compound may differ dramatically from the properties of the elements that combine to produce the compound. For each process described below, state whether the material being discussed is most likely a mixture or a compound, and state whether the process is a chemical change or a physical change. a. An orange liquid is distilled, resulting in the collection of a yellow liquid and a red solid. b. A colorless, crystalline solid is decomposed, yielding a pale yellow-green gas and a soft, shiny metal. c. A cup of tea becomes sweeter as sugar is added to it.

You are in Paris, and you want to buy some peaches for lunch. The sign in the fruit stand indicates that peaches cost \(2.45\) euros per kilogram. Given that 1 euro is equivalent to approximately \(\$ 1.32\), calculate what a pound of peaches will cost in dollars.

Which of the following statements is(are) true? a. A spoonful of sugar is a mixture. b. Only elements are pure substances. c. Air is a mixture of gases. d. Gasoline is a pure substance. e. Compounds can be broken down only by chemical means.
See all solutions

Recommended explanations on Chemistry Textbooks

Kinetics

Read Explanation

Chemical Analysis

Read Explanation

The Earths Atmosphere

Read Explanation

Chemistry Branches

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Chemical Reactions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.