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Chapter 1: Problem 83

For a pharmacist dispensing pills or capsules, it is often easier to weigh the medication to be dispensed than to count the individual pills. If a single antibiotic capsule weighs \(0.65 \mathrm{~g}\), and a pharmacist weighs out \(15.6 \mathrm{~g}\) of capsules, how many capsules have been dispensed?

Short Answer

Expert verified
The pharmacist has dispensed approximately 24 antibiotic capsules, rounding to the nearest capsule since we cannot have a fraction of a capsule.

Step by step solution

01

Write down the given information

We are given the following information: - Weight of a single antibiotic capsule: \(0.65 \mathrm{~g}\) - Total weight of capsules: \(15.6 \mathrm{~g}\)
02

Set up the equation to find the number of capsules

Let x be the number of capsules dispensed. We can set up the equation as follows: \(0.65x = 15.6\)
03

Solve the equation for x

In order to solve for x, we will divide both sides by 0.65: \(x = \frac{15.6}{0.65}\)
04

Calculate the number of capsules

Now, we can calculate the value of x: \(x = \frac{15.6}{0.65} \approx 24\)
05

Conclude the answer

The pharmacist has dispensed approximately 24 antibiotic capsules, rounding to the nearest capsule since we cannot have a fraction of a capsule.

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Most popular questions from this chapter

The active ingredient of aspirin tablets is acetylsalicylic acid, which has a density of \(1.4 \mathrm{~g} / \mathrm{cm}^{3} .\) In a lab class, a student used paper chromatography to isolate another common ingredient of headache remedies. The isolated sample had a mass of \(0.384 \mathrm{~g}\) and a volume of \(0.32 \mathrm{~cm}^{3}\). Given the data in the following table, what was the other ingredient in the headache remedy? $$ \begin{array}{l} \text { Density Values for Potential } \\ \text { Headache Remedies } \\ \begin{array}{lc} \text { Compound } & \text { Density }\left(\mathrm{g} / \mathrm{cm}^{3}\right) \\ \hline \text { White table sugar } & 0.70 \\ \text { Caffeine } & 1.2 \\ \text { Acetylsalicylic acid } & 1.4 \\ \text { Sodium chloride } & 2.2 \\ \hline \end{array} \end{array} $$

Perform the following mathematical operations and express the result to the correct number of significant figures. a. \(\frac{2.526}{3.1}+\frac{0.470}{0.623}+\frac{80.705}{0.4326}\) b. \((6.404 \times 2.91) /(18.7-17.1)\) c. \(6.071 \times 10^{-5}-8.2 \times 10^{-6}-0.521 \times 10^{-4}\) d. \(\left(3.8 \times 10^{-12}+4.0 \times 10^{-13}\right) /\left(4 \times 10^{12}+6.3 \times 10^{13}\right)\) e. \(\frac{9.5+4.1+2.8+3.175}{4}\) (Assume that this operation is taking the average of four numbers. Thus 4 in the denominator is exact.) f. \(\frac{8.925-8.905}{8.925} \times 100\) (This type of calculation is done many times in calculating a percentage error. Assume that this example is such a calculation; thus 100 can be considered to be an exact number.)

A \(25.00-\mathrm{g}\) sample of a solid is placed in a graduated cylinder and then the cylinder is filled to the \(50.0-\mathrm{mL}\) mark with benzene. The mass of benzene and solid together is \(58.80 \mathrm{~g}\). Assuming that the solid is insoluble in benzene and that the density of benzene is \(0.880 \mathrm{~g} / \mathrm{cm}^{3}\), calculate the density of the solid.

Would a car traveling at a constant speed of \(65 \mathrm{~km} / \mathrm{h}\) violate a 40\. mi/h speed limit?

What is the difference between random error and systematic error?
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