QuestionJuly 17, 2025

If 1.4 mol of dust particles were laid end to end along the equator, how many times would they encircle the planet? The circumference of the Earth at the equator is 40,076 km. Express your answer using two significant figures.

If 1.4 mol of dust particles were laid end to end along the equator, how many times would they encircle the planet? The circumference of the Earth at the equator is 40,076 km. Express your answer using two significant figures.
If 1.4 mol of dust particles were laid end to end along the equator, how many times would they encircle the planet? The circumference of the Earth at the equator is 40,076 km. Express your answer using two significant figures.

Solution
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Answer

21 times Explanation 1. Calculate the total length of dust particles Assume each dust particle is approximately 1 \times 10^{-9} m in diameter. Total length = 1.4 \, \text{mol} \times 6.022 \times 10^{23} \, \text{particles/mol} \times 1 \times 10^{-9} \, \text{m/particle}. 2. Convert total length to kilometers Convert meters to kilometers: 1 \, \text{km} = 1000 \, \text{m}. 3. Calculate how many times they encircle the Earth Divide the total length in km by Earth's circumference: \frac{\text{Total length in km}}{40,076 \, \text{km}}.

Explanation

1. Calculate the total length of dust particles<br /> Assume each dust particle is approximately $1 \times 10^{-9}$ m in diameter. Total length = $1.4 \, \text{mol} \times 6.022 \times 10^{23} \, \text{particles/mol} \times 1 \times 10^{-9} \, \text{m/particle}$.<br />2. Convert total length to kilometers<br /> Convert meters to kilometers: $1 \, \text{km} = 1000 \, \text{m}$.<br />3. Calculate how many times they encircle the Earth<br /> Divide the total length in km by Earth's circumference: $\frac{\text{Total length in km}}{40,076 \, \text{km}}$.
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