Using the given information about the aluminum crystal's density and the size of the theoretical cube, we can calculate the experimental value of Avogadro's number. The experimental value is approximately 1.03 × 10^23 atoms/mol, based on the mass and molar mass of aluminum.
To find the experimental value of Avogadro's number, we can use the given information about the aluminum crystal and its density.
1. Calculate the volume of the theoretical cube occupied by each aluminum atom:
The volume of a cube is given by V = s^3, where s is the length of a side.
V = (0.255 nm)^3 = 0.0165 nm^3
2. Convert the volume to cm^3:
1 nm^3 = 1 × 10^(-21) cm^3
Therefore, 0.0165 nm^3 = 0.0165 × 10^(-21) cm^3 = 1.65 × 10^(-23) cm^3
3. Calculate the mass of each aluminum atom:
The density of the aluminum crystal is given as 2.70 g/cm³.
The density is defined as mass/volume, so mass = density × volume.
Mass = 2.70 g/cm³ × 1.65 × 10^(-23) cm^3 = 4.455 × 10^(-23) g
4. Find the molar mass of aluminum:
The molar mass of aluminum is 26.98 g/mol.
5. Determine the number of atoms in 1 mole of aluminum:
The number of atoms in 1 mole is equal to Avogadro's number, which is approximately 6.022 × 10^23 atoms/mol.
6. Calculate the experimental value of Avogadro's number:
Avogadro's number = (4.455 × 10^(-23) g) / (26.98 g/mol) × (6.022 × 10^23 atoms/mol)
Avogadro's number ≈ 1.03 × 10^23 atoms/mol
Therefore, the experimental value of Avogadro's number is approximately 1.03 × 10^23 atoms/mol.