Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 2: Problem 103

A U.S. 1 -cent coin (a penny) has a diameter of \(19 \mathrm{~mm}\) and a thickness of \(1.5 \mathrm{~mm}\). Assume the coin is made of pure copper, whose density and approximate market price are \(8.9 \mathrm{~g} / \mathrm{cm}^{3}\) and \(\$ 2.40\) per pound, respectively. Calculate the value of the copper in the coin, assuming its thickness is uniform.

Short Answer

Expert verified
Based on the given information, we can find the value of the copper in the penny by following these steps: 1. Calculate the volume of the coin: \(V = π(9.5)^2(1.5)\) 2. Convert volume to mass: \(m = 8.9~g/cm^3 × V~cm^3\) 3. Convert mass to weight in pounds: \(mass~(lbs) = \frac{m~(g)}{453.592}\) 4. Calculate the value of the copper: \( Value = \$ 2.40/lb × mass~(lbs)\) By performing these calculations, we can determine the value of the copper in the penny.

Step by step solution

01

Calculate the volume of the coin

First, we need to find the volume of the copper used in the penny. Since the penny is assumed to be a flat cylinder in shape, we can use the formula for the volume of a cylinder: \(V = πr^2h\), where V is the volume, r is the radius, and h is the height (thickness) of the coin. Given the diameter of the penny is 19 mm, the radius is \(r = \frac{19}{2}\) mm = 9.5 mm. The thickness (height) of the coin is given as 1.5 mm. Now, calculate the volume: \(V = π(9.5)^2(1.5)\)
02

Convert volume to mass

We have the volume of the copper used in the penny measured in mm^3. Convert the volume from mm^3 to cm^3: \(1~cm^3 = 1000~mm^3\). In order to find the mass of copper used in the penny, we need the given density of copper which is 8.9 g/cm^3. The mass (m) of copper in the coin can be obtained by multiplying the density by volume: m = density × volume.
03

Convert mass to weight in pounds

To find the value of the copper in the penny, we need first to convert the mass of the copper (in grams) to pounds (lbs). Convert the mass of copper from grams to pounds, using the conversion factor: \(1 lb = 453.592 g\).
04

Calculate the value of the copper in the penny

Now that we have the mass of copper in pounds, we can use the given market price of copper, which is $2.40 per pound, to calculate the value of the copper in the penny: Value = Market price × Mass of copper in pounds. Once you find the value of the copper in the penny, you can compare it to the actual value of the coin (1 cent).

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Predict whether each of the following compounds is molecular or ionic: $(\mathbf{a}) \mathrm{HClO}_{4}(\mathbf{b}) \mathrm{CH}_{3} \mathrm{OCH}_{3}(\mathbf{c}) \mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}(\mathbf{d}) \mathrm{H}_{2} \mathrm{~S}\( (e) \)\mathrm{TiCl}_{4}(\mathbf{f}) \mathrm{K}_{2} \mathrm{O}_{2}(\mathbf{g}) \mathrm{PCl}_{5}(\mathbf{h}) \mathrm{P}(\mathrm{OH})_{3} .$

Discovering which of the three subatomic particles proved to be the most difficult-the proton, neutron, or electron? Why?

Give the name or chemical formula, as appropriate, for each of the following acids: $(\mathbf{a}) \mathrm{HBrO}_{3},(\mathbf{b}) \mathrm{HBr},(\mathbf{c}) \mathrm{H}_{3} \mathrm{PO}_{4},(\mathbf{d})$ hypochlorous acid, (e) iodic acid, (f) sulfurous acid.

Give the name or chemical formula, as appropriate, for each of the following binary molecular substances: (a) $\mathrm{SF}_{6},(\mathbf{b}) \mathrm{IF}_{5},\( (c) \)\mathrm{XeO}_{3}$, (d) dinitrogen tetroxide, (e) hydrogen cyanide, (f) tetraphosphorus hexasulfide.

Consider the following organic substances: ethylethanoate, ethylmethylether, hexanol, and propanone. (a) Which of these molecules contains three carbons? (b) Which of these molecules contain a \(\mathrm{C}=\) O group?
See all solutions

Recommended explanations on Chemistry Textbooks

Ionic and Molecular Compounds

Read Explanation

Nuclear Chemistry

Read Explanation

Chemistry Branches

Read Explanation

Chemical Analysis

Read Explanation

Kinetics

Read Explanation

Physical Chemistry

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.

Sign-up for free