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Chapter 3: Problem 34

If Avogadro's number of pennies is divided equally among the 321 million men, women, and children in the United States, how many dollars would each receive? How does this compare with the gross domestic product (GDP) of the United States, which was \(\$ 17.419\) trillion in 2015\(?\) (The GDP is the total market value of the nation's goods and services.)

Short Answer

Expert verified
Each person would receive approximately \(1.875 \times 10^{15}\) dollars if Avogadro's number of pennies were divided equally among the 321 million people in the United States. This is approximately 107.69 times the GDP of the United States in 2015, which was \(\$17.419\) trillion.

Step by step solution

01

Use Avogadro's Number

Avogadro's number is a scientific constant representing the number of units (atoms, ions, molecules, etc.) in one mole of a substance. Avogadro's number is approximately \(6.022 \times 10^{23}\). In this exercise, we'll use this number to represent the total number of pennies.
02

Divide Pennies Among the Population

We need to divide the Avogadro's number of pennies equally among the 321 million people in the United States. To accomplish this, we will divide Avogadro's number (total number of pennies) by the population size. \[ \frac{6.022 \times 10^{23} \mathrm{\,pennies}}{321 \times 10^6 \mathrm{\,people}} \]
03

Calculate Number of Pennies per Person

Perform the division to find out how many pennies each person would receive: \[ \frac{6.022 \times 10^{23}}{321 \times 10^6} = 1.875 \times 10^{17} \mathrm{\,pennies\,per\,person} \]
04

Convert Pennies to Dollars

Now, we will convert the number of pennies each person receives to dollars, using the conversion factor that 100 pennies is equal to 1 dollar. \[ 1.875 \times 10^{17} \mathrm{\,pennies\,per\,person} \times \frac{1\mathrm{\,dollar}}{100 \mathrm{\,pennies}} = 1.875 \times 10^{15} \mathrm{\,dollars\,per\,person} \]
05

Compare to Gross Domestic Product (GDP) of the United States

The GDP of the United States in 2015 was \(\$17.419\) trillion which is equal to \(\$17.419 \times 10^{12}\). To compare this with the amount each person would receive, we can divide the dollars per person by the US GDP: \[ \frac{1.875 \times 10^{15}}{17.419 \times 10^{12}} \approx 107.69 \] This means that each person would receive approximately 107.69 times the GDP of the United States in 2015 if Avogadro's number of pennies were divided equally among the population.

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Most popular questions from this chapter

An iron ore sample contains \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) together with other substances. Reaction of the ore with CO produces iron metal: $$ \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{CO}(g) \longrightarrow \mathrm{Fe}(s)+\mathrm{CO}_{2}(g) $$ (a) Balance this equation. (b) Calculate the number of grams of CO that can react with 0.350 \(\mathrm{kg}\) of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) . (c) Calculate the number of grams of Fe and the number of grams of \(\mathrm{CO}_{2}\) formed when 0.350 \(\mathrm{kg}\) of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) reacts. (d) Show that your calculations in parts (b) and (c) are consistent with the law of conservation of mass.

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