Calculate the number of unit cells in 8.1 g of aluminum if it crystallizes in a face-centred cubic (f.c.c.) structure. (Atomic mass of Al = 27 g mol^–1)

Given:

Weight of Al (m) = 8.1 g

Atomic mass (M) = 27 g mol^-1

The crystallization is taking place in face-centered cubic (f.c.c) structure. F.c.c. structure contains 4 atoms in one unt cell.

First, we will calculate the no. of moles (n). To calculate the no. of moles of Al, we use the formula given below:

n=

⇒ n=

⇒ n = 0.3 mole

As we know that 1 mole contains 6.022 × 10²³ atoms

∴ No. of atoms of aluminum = 6.022 × 10²³ × 0.3

Now, the no. of atoms present in one unit cell (fcc) = 4 (given)

∴ no. of unit cells =

⇒ no. of unit cells = 4.5× 10²²

Thus, the number of unit cells in 8.1 g of aluminum = 4.5 × 10²²