/*! 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 36 A non-SI unit of mass used in ph... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

A non-SI unit of mass used in pharmaceutical work is the grain (gr) \((15 \mathrm{gr}=1.0 \mathrm{g}) .\) An aspirin tablet contains 5.0 gr of aspirin. A 155 lb arthritic individual takes two aspirin tablets per day. (a) What is the quantity of aspirin in two tablets, expressed in milligrams? (b) What is the dosage rate of aspirin, expressed in milligrams of aspirin per kilogram of body mass? (c) At the given rate of consumption of aspirin tablets, how many days would it take to consume 1.0 kg of aspirin?

Short Answer

Expert verified
The amount of aspirin in two tablets is 670 milligrams. The dosage rate is 9.52 milligrams of aspirin per kilogram of body mass. It would take 1493 days to consume 1.0 kg of aspirin at the current consumption rate.

Step by step solution

01

Calculate Quantity of Aspirin in Two Tablets

Firstly, convert the amount of aspirin in two tablets from grains to milligrams. Given that one tablet contains 5 gr of aspirin, two tablets contain \(10 gr\). Since \(15 gr = 1.0 g\), this means \(10 gr = \frac{10}{15} g = 0.67 g\). To convert grams to milligrams, multiply by 1000, so \(0.67 g = 0.67 * 1000 mg = 670 mg\).
02

Calculate Dosage Rate of Aspirin

The dosage rate is the amount of aspirin per kilogram of body mass. Convert the person's weight from pounds to kilograms, knowing that \(1 lb = 0.453592 kg\), hence \(155 lb = 155 * 0.453592 kg = 70.31 kg\). The dosage rate then equals the total amount of aspirin consumed per day (in mg) divided by the body mass (in kg), which is \(670 mg / 70.31 kg = 9.52 mg/kg\).
03

Calculate Total Consumption Days

To find out how many days it takes to consume 1.0 kg of aspirin, convert this weight into milligrams: \(1.0 kg = 1.0 * 1,000,000 mg = 1,000,000 mg\). Then, divide this weight by the daily consumption of aspirin: \(1,000,000 mg / 670 mg/day = 1492.54 days\). Since the quantity of pills cannot be a fraction, it would take 1493 days to consume the 1.0 kg of aspirin.

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 91Ó°ÊÓ!

Key Concepts

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

Non-SI Units
In many fields, including pharmaceuticals, non-SI units are occasionally used alongside the International System of Units (SI). The grain (gr) is a non-SI unit of mass frequently encountered in pharmaceutical calculations. One grain is equivalent to approximately 64.8 milligrams. It is important to be familiar with converting grains to more routinely used units like grams (g) and milligrams (mg) because they are the standard units used in most medical dosages. For example, when dealing with aspirin dosages, understanding this conversion is crucial. Knowing that 15 grains equal 1 gram, you can convert any quantity from grains to grams and further into milligrams for more precise dosage calculations. Such conversions ensure safe and accurate medication administration, which is critical in maintaining effective therapeutic outcomes.
Dosage Calculations
Dosage calculations are critical in determining the correct amount of medication for an individual based on their body weight. Ideal dosages ensure that the medication is effective and safe, minimizing the risk of overdose or insufficient treatment. In the exercise, we determined the dosage rate by calculating the body weight in kilograms, since medical dosages are commonly expressed per kilogram of body mass. Here, the individual's weight is given in pounds (lb), which first needs to be converted to kilograms using the conversion factor:
  • 1 lb = 0.453592 kg
Afterward, the daily dosage of aspirin in milligrams was divided by the body weight in kilograms. This provides a clear dosage rate in milligrams per kilogram (mg/kg), which is a standardized measure for drug administration, ensuring consistent and safe dosing across individuals who may vary significantly in size.
Unit Conversion
Unit conversion is a foundational skill in pharmaceutical calculations, ensuring that quantities are expressed in the most appropriate units for a given context. It involves using standardized relationships between units to transform one unit of measure into another. For instance, converting grains to milligrams allows healthcare providers to calculate dosages in a more widely accepted unit. Conversion factors, such as knowing that 15 grains are equivalent to 1 gram, or that 1 kilogram is 1,000,000 milligrams, are fundamental. When performing these conversions, it’s important to use precise arithmetic for accuracy in your calculations. Miscalculations could lead to incorrect dosages, which can potentially harm patients. Thus, mastering unit conversions is an essential competence for anyone involved in pharmaceutical or medical-related fields. Utilizing these skills can effectively translate weight and dosage measures into actionable prescription information for proper healthcare delivery.

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

An American press release describing the 1986 nonstop, round-the-world trip by the ultra-lightweight aircraft Voyager included the following data: flight distance: \(25,012 \mathrm{mi}\) flight time: 9 days, 3 minutes, 44 seconds fuel capacity: nearly 9000 lb fuel remaining at end of flight: \(14 \mathrm{gal}\) To the maximum number of significant figures permitted, calculate (a) the average speed of the aircraft in kilometers per hour (b) the fuel consumption in kilometers per kilogram of fuel (assume a density of \(0.70 \mathrm{g} / \mathrm{mL}\) for the fuel)

According to the rules on significant figures, the product of the measured quantities \(99.9 \mathrm{m}\) and \(1.008 \mathrm{m}\) should be expressed to three significant figures-\(101 \mathrm{m}^{2} .\) Yet, in this case, it would be more appropriate to express the result to four significant figures-\(100.7 \mathrm{m}^{2} .\) Explain why.

A vinegar sample is found to have a density of \(1.006 \mathrm{g} / \mathrm{mL}\) and to contain \(5.4 \%\) acetic acid by mass. How many grams of acetic acid are present in \(1.00 \mathrm{L}\) of this vinegar?

Express each number in exponential notation. (a) \(8950 .;\)(b) \(10,700 . ;(\text { c) } 0.0240 ; \text { (d) } 0.0047 ; \text { (e) } 938.3 ; \text { (f) } 275,482\).

The diameter of metal wire is often referred to by its American wire-gauge number. A 16-gauge wire has a diameter of 0.05082 in. What length of wire, in meters, is found in a 1.00 lb spool of 16 -gauge copper wire? The density of copper is \(8.92 \mathrm{g} / \mathrm{cm}^{3}\).

See all solutions

Recommended explanations on Chemistry Textbooks

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.