Final answer:
Avogadro's number is used to convert moles of a substance to the number of atoms or molecules. To find the number of atoms of aluminum in the entire roll, we convert the mass of aluminum to moles using its molar mass and then multiply by Avogadro's number.
Step-by-step explanation:
Avogadro's number is a constant that represents the number of atoms or molecules in one mole of a substance. It is equal to 6.022 x 10²³. To find the number of atoms of aluminum in the entire roll, we need to know the molar mass of aluminum and the amount of aluminum in the roll.
The molar mass of aluminum (Al) is 26.98 g/mol. The given information states that there are 1.8069 x 10²⁴ aluminum atoms in a sample of 81 g.
To find the number of atoms in the entire roll, we can use the molar mass of aluminum to convert the mass into moles and then use Avogadro's number to convert the moles into atoms.
Given:
- Molar mass of aluminum (Al) = 26.98 g/mol
- Number of aluminum atoms in 81 g = 1.8069 x 10²⁴ atoms
Step 1: Convert the mass of aluminum in the roll to moles:
Number of moles = mass / molar mass = 81 g / 26.98 g/mol = 3.0062 mol
Step 2: Convert the number of moles to atoms using Avogadro's number:
Number of atoms = number of moles x Avogadro's number = 3.0062 mol x (6.022 x 10²³ atoms/mol) = 1.809 x 10²⁴ atoms
Therefore, there are approximately 1.809 x 10²⁴ atoms of aluminum in the entire roll.