Final answer:
To find the mass of the aluminum foil containing 8.60 × 10^{23} atoms, we use Avogadro's number and a ratio from a known quantity (1.8069 × 10^{24} atoms to 81 g), which results in a mass of approximately 38.6 grams for the foil sample.
Step-by-step explanation:
To calculate the mass of the aluminum foil with 8.60 × 10^{23} atoms, we first need to use Avogadro's number, which states there are 6.022 × 10^{23} atoms in one mole of any substance. Given that there are 1.8069 × 10^{24} aluminium atoms in a sample of 81 g, we can set up a proportion to find the mass of the given number of atoms.
The ratio of atoms to grams for aluminum is 1.8069 × 10^{24} atoms for 81 g. We can set up our equation as follows:
8.60 × 10^{23} atoms / x g = 1.8069 × 10^{24} atoms / 81 g
Solving for x (the mass of the aluminum foil), we get:
x g = (8.60 × 10^{23} atoms * 81 g) / 1.8069 × 10^{24} atoms
After calculating, x is found to be approximately 38.6 g. Therefore, the mass of the aluminum foil sample is about 38.6 grams.