Question

an aluminum atom has a mass of ( 4.48\times10^{-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.

Explanation:

Step1: Calculate the mass of 1 mole of aluminum atoms

Avogadro's number \(N_A = 6.022\times10^{23}\text{ mol}^{-1}\).
The mass of one aluminum atom \(m = 4.48\times 10^{-23}\text{ g}\).
The mass of 1 mole of aluminum atoms \(M= m\times N_A\).

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Step2: Calculate the number of moles of aluminum atoms with the mass of the airplane

The mass of the airplane \(m_{\text{plane}}=5000\text{ kg}=5000\times10^{3}\text{ g}\).
Let the number of moles be \(n\). We know \(n=\frac{m_{\text{plane}}}{M}\).
Substitute \(M = 27.0\text{ g/mol}\) and \(m_{\text{plane}}=5000\times 10^{3}\text{ g}\)

$$ n=\frac{5000\times 10^{3}\text{ g}}{27.0\text{ g/mol}}\approx1.85\times 10^{5}\text{ mol} $$

Answer:

The mass of 1 mole of aluminum atoms is \(27.0\text{ g}\).
The number of moles of aluminum atoms with the mass of the airplane is \(1.85\times 10^{5}\text{ mol}\).