Aluminum foil costs $3.88 for a 3.48 m² sheet that has a thickness of 0.013 mm.If the density of aluminum is 2700 kg/m³,what is the cost of one atom of aluminum? The atomic mass number for aluminum is 26.98.

Question

Quizplus · Accepted Answer

First, calculate the volume of aluminum foil: $3.48 \, \text{m}^2 \times 0.013 \times 10^{-3} \, \text{m} = 4.524 \times 10^{-2} \, \text{m}^3$. Then, find the mass: $2700 \, \text{kg/m}^3 \times 4.524 \times 10^{-2} \, \text{m}^3 = 122.148 \, \text{kg}$. The number of moles is $122.148 \, \text{kg} / (26.98 \times 10^{-3} \, \text{kg/mol}) = 4524.5 \, \text{moles}$. Since 1 mole contains $6.022 \times 10^{23}$ atoms, the total number of atoms is $4524.5 \times 6.022 \times 10^{23} = 2.724 \times 10^{27}$ atoms. Finally, the cost per atom is $\$3.88 / 2.724 \times 10^{27} = 1.4 \times 10^{-24}$.

Aluminum Foil Costs $3