Final answer:
To calculate the number of moles in 1.02 x 10²⁵ atoms of aluminum (Al), use Avogadro's number concept and conversion factors. The number of moles is approximately 1.69 x 10².
Step-by-step explanation:
To calculate the number of moles in 1.02 x 10²⁵ atoms of aluminum (Al), we can use the Avogadro's number concept. Avogadro's number states that 1 mole of any substance contains 6.022 x 10²³ atoms.
First, we need to determine the number of moles in 1 mole of aluminum. From the given information, we know that there are 1.8069 x 10²⁴ aluminum atoms in a sample of 81 grams.
Therefore, we can write the proportion: 1.8069 x 10²⁴ atoms / 81 grams = 6.022 x 10²³ atoms / x moles, where x represents the number of moles in 1 mole of aluminum.
Solving this proportion, we find that x is equal to 26.98 grams/mol.
Now, we can use this conversion factor to calculate the number of moles in 1.02 x 10²⁵ atoms of aluminum.
First, we convert the given number of atoms to moles using the conversion factor: 1.02 x 10²⁵ atoms * (1 mole/6.022 x 10²³ atoms) = 1.69 x 10² moles.