Questions: An aluminum atom has a mass of 4.48 x 10^-23 g and a small airplane has a mass of 5000 kg. Use this information to answer the questions below. Be sure your answers have the correct number of significant digits. What is the mass of 1 mole of aluminum atoms? Round your answer to 3 significant digits. How many moles of aluminum atoms have a mass equal to the mass of a small airplane? Round your answer to 3 significant digits.

An aluminum atom has a mass of 4.48 x 10^-23 g and a small airplane has a mass of 5000 kg. Use this information to answer the questions below. Be sure your answers have the correct number of significant digits. What is the mass of 1 mole of aluminum atoms? Round your answer to 3 significant digits. How many moles of aluminum atoms have a mass equal to the mass of a small airplane? Round your answer to 3 significant digits.
Transcript text: An aluminum atom has a mass of $4.48 \times 10^{-23} \mathrm{~g}$ and a small airplane has a mass of 5000 kg . Use this information to answer the questions below. Be sure your answers have the correct number of significant digits. \begin{tabular}{|l|l|} \hline What is the mass of 1 mole of aluminum atoms? \\ Round your answer to 3 significant digits. & \\ \hline \begin{tabular}{l} How many moles of aluminum atoms have a mass equal to \\ the mass of a small airplane? \\ Round your answer to 3 significant digits. \end{tabular} \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Calculate the Mass of 1 Mole of Aluminum Atoms

The mass of one aluminum atom is given as \(4.48 \times 10^{-23} \, \text{g}\). To find the mass of 1 mole of aluminum atoms, we use Avogadro's number, \(6.022 \times 10^{23}\) atoms/mole.

\[ \text{Mass of 1 mole} = 4.48 \times 10^{-23} \, \text{g/atom} \times 6.022 \times 10^{23} \, \text{atoms/mole} \]

\[ = 27.0 \, \text{g/mole} \]

Step 2: Calculate the Number of Moles in a Small Airplane

The mass of the small airplane is given as 5000 kg, which is \(5.000 \times 10^6\) g. We need to find how many moles of aluminum atoms have this mass.

\[ \text{Number of moles} = \frac{5.000 \times 10^6 \, \text{g}}{27.0 \, \text{g/mole}} \]

\[ = 1.85 \times 10^5 \, \text{moles} \]

Final Answer

  • The mass of 1 mole of aluminum atoms is \(\boxed{27.0 \, \text{g/mole}}\).
  • The number of moles of aluminum atoms with a mass equal to the mass of a small airplane is \(\boxed{1.85 \times 10^5 \, \text{moles}}\).
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