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Chapter 1: Problem 36

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.

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