Ch.1 - Introduction: Matter, Energy, and Measurement

Brown - Chemistry: The Central Science 14th Edition

Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook

Brown 14th Edition

Ch.1 - Introduction: Matter, Energy, and Measurement

Problem 75d

Chapter 1, Problem 75d

The U.S. quarter has a mass of 5.67 g and is approximately 1.55 mm thick.(d) The U.S. National Debt Clock showed the outstanding public debt to be \$16,213,166,914,811 on October 28, 2012. How many stacks like the one described would be necessary to pay off this debt?

Verified step by step guidance

First, determine the value of a single U.S. quarter. As of the problem's context, a quarter is worth \$0.25.

Next, calculate the total number of quarters needed to pay off the debt by dividing the total debt amount, \$16,213,166,914,811, by the value of one quarter, \$0.25.

Once you have the total number of quarters, calculate the total height of the stack of quarters. Since each quarter is 1.55 mm thick, multiply the total number of quarters by 1.55 mm to find the total height in millimeters.

Convert the total height from millimeters to a more manageable unit, such as meters or kilometers, by using the appropriate conversion factors (1 meter = 1000 mm, 1 kilometer = 1000 meters).

Finally, interpret the result to understand the practicality or implications of such a stack, considering its height in the context of real-world distances or structures.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Mass and Volume Calculations

Understanding mass and volume is essential for determining how many quarters would be needed to reach a specific weight. The mass of a single quarter is given, and knowing the total debt allows for calculations based on the mass of the quarters to find the total number required.

Unit Conversion

Unit conversion is crucial in this problem, as it may require converting the total debt amount into a weight that can be compared to the mass of the quarters. This involves converting dollars into a weight measurement, typically using the value of the quarter to establish how much debt can be represented by a certain number of quarters.

Stack Height and Volume

The thickness of a quarter is important for calculating the total height of a stack of quarters needed to represent the total debt. By multiplying the thickness of a single quarter by the number of quarters, one can determine the overall height of the stack, which provides a tangible sense of the scale of the debt.

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Which of the following would you characterize as pure or nearly pure substance? (a) stomach acid; (b) dry ice; (c) ice-cream; (d) stainless steel; (e) petroleum; (f) distilled water; (g) carbon monoxide gas; (h) compressed air in balloon.

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Textbook Question

The U.S. quarter has a mass of 5.67 g and is approximately 1.55 mm thick. (a) How many quarters would have to be stacked to reach 575 ft, the height of the Washington Monument?

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Textbook Question

The U.S. quarter has a mass of 5.67 g and is approximately 1.55 mm thick. (c) How much money would this stack contain?

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Textbook Question

In the United States, water used for irrigation is measured in acre-feet. An acre-foot of water covers an acre to a depth of exactly 1 ft. An acre is 4840 yd2. An acre-foot is enough water to supply two typical households for 1.00 yr. (a) If desalinated water costs \$1950 per acre-foot, how much does desalinated water cost per liter?

755

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