an aluminum atom has a mass of 4.48×10⁻²³ g and a small airplane has a mass of 5000. kg. use this…

Explanation:

Step1: Recall Avogadro's number

Avogadro's number $N_A = 6.022\times 10^{23}\text{ atoms/mol}$.

Step2: Calculate mass of 1 - mole of aluminum atoms

Multiply mass of one aluminum atom by Avogadro's number. Given mass of one aluminum atom $m = 4.48\times 10^{-23}\text{ g/atom}$. So mass of 1 - mole $M_1=m\times N_A=(4.48\times 10^{-23}\text{ g/atom})\times(6.022\times 10^{23}\text{ atoms/mol})$. [ \begin{align*} M_1&=(4.48\times6.022)\text{ g/mol}\ &=4.48\times6.022\text{ g/mol}\ &\approx26.98\text{ g/mol} \end{align*} ]

Step3: Convert mass of airplane to grams

The mass of the small airplane $m_{plane}=5000\text{ kg}=5000\times10^{3}\text{ g} = 5\times 10^{6}\text{ g}$.

Step4: Calculate number of moles of aluminum atoms equal to mass of airplane

Let $n$ be the number of moles. We know $n=\frac{m_{plane}}{M_1}$. Substitute $m_{plane}=5\times 10^{6}\text{ g}$ and $M_1 = 26.98\text{ g/mol}$. [ n=\frac{5\times 10^{6}\text{ g}}{26.98\text{ g/mol}}\approx1.85\times 10^{5}\text{ mol} ]

Answer:

26.98 g 1.85×10⁵ mol