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Chapter 9: Problem 41

Consider bicycles where each wheel has 24 spokes. (a) How many bicycles are there in 1 mole of bicycles? (b) How many tires are there in 1 mole of bicycles? (c) How many spokes are there in 1 mole of bicycles? (d) How many bicycles would you need to have a total of 1 mole of spokes.

Short Answer

Expert verified
(a) 1 mole of bicycles = \(6.022 \times 10^{23}\) bicycles (b) Number of tires = \(1.204 \times 10^{24}\) tires (c) Number of spokes = \(2.891 \times 10^{25}\) spokes (d) Number of bicycles for 1 mole of spokes = \(1.255 \times 10^{22}\) bicycles

Step by step solution

01

(a) Find the number of bicycles in 1 mole of bicycles

Using Avogadro's number, we can find out how many bicycles are there in 1 mole of bicycles: 1 mole of bicycles = 6.022 x 10^23 bicycles
02

(b) Find the number of tires in 1 mole of bicycles

Each bicycle has 2 tires. So, to find the number of tires in 1 mole of bicycles, we can simply multiply the number of bicycles by 2: Number of tires = (6.022 x 10^23 bicycles) × 2 = 1.204 x 10^24 tires
03

(c) Find the number of spokes in 1 mole of bicycles

Each bicycle has 2 wheels, and each wheel has 24 spokes. Thus, the number of spokes in one bicycle is: Spokes in one bicycle = 2 wheels x 24 spokes = 48 spokes Now, to find the number of spokes in 1 mole of bicycles, we can multiply the number of bicycles by the number of spokes in one bicycle: Number of spokes = (6.022 x 10^23 bicycles) × 48 spokes = 2.891 x 10^25 spokes
04

(d) Find the number of bicycles needed to have a total of 1 mole of spokes

We're given that each bicycle has 48 spokes. We need to find the number of bicycles required to have a total of 1 mole, which is 6.022 x 10^23, of spokes. To do this, we can divide the mole of spokes by the number of spokes in one bicycle: Number of bicycles for 1 mole of spokes = (6.022 x 10^23 spokes) / 48 spokes = 1.255 x 10^22 bicycles

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Most popular questions from this chapter

Chrome yellow, a pigment used in paints, is \(64.11 \%\) by mass \(\mathrm{Pb}, 16.09 \%\) by mass \(\mathrm{Cr}\), and \(19.80 \%\) by mass O. What is the empirical formula of this compound?

Consider the unbalanced chemical equation \(\mathrm{As}_{4} \mathrm{~S}_{6}+\mathrm{O}_{2} \rightarrow \mathrm{As}_{4} \mathrm{O}_{6}+\mathrm{SO}_{2}\) (a) How many grams of \(\mathrm{O}_{2}\) are needed to react completely with \(58.9 \mathrm{~g}\) of \(\mathrm{As}_{4} \mathrm{~S}_{6}\) ? (b) If \(41.2 \mathrm{~g}\) of \(\mathrm{SO}_{2}\) is produced, what is the percent yield for the reaction?

Ethylene gas \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)\) reacts with fluorine gas \(\left(\mathrm{F}_{2}\right)\) to form carbon tetrafluoride gas and hydrogen fluoride gas. If \(2.78 \mathrm{~g}\) of ethylene reacted with an excess of fluorine, how many grams of each product could theoretically be produced?

Copper(I) oxide reacts with solid carbon to form copper metal. Carbon dioxide gas is the other product of this reaction. (a) Write the balanced chemical equation for this reaction. (b) Coke is a cheap, impure form of solid carbon that is often used industrially. If a sample of coke is \(95 \%\) C by mass, determine the mass in kilograms of coke needed to react completely with \(1.000\) ton of copper(I) oxide. \([1\) ton \(=2000 \mathrm{lb} ; 1 \mathrm{~kg}=2.205 \mathrm{lb}]\)

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