Question

How many unit cells are present in a cube-shaped ideal crystal of NaCl of mass 1.00 g? [Atomic masses: Na = 23, Cl = 35.5]

Options

• 5.14 × 10²¹ unit cells

• 1.28 × 10²¹ unit cells

• 1.71 × 10²¹ unit cells

• 2.57 × 10²¹ unit cells

Answer 1

2.57 × 10²¹ unit cells

Explanation:

Since in the NaCl type of structure, 4 formula units are for a cell.

Molar mass of NaCl = 23 + 35.5

= 58.5

No. of unit cells present in a cubic crystal = `"Mass of all unit cells"/"Mass of one unit cell"`

= `(d xx a^3)/(M/N_A xx Z)`

d = `(m xx N_A)/(M xx Z)`

∴ Units cells = `(1.00 xx 6.022 xx 10^23)/(58.5 xx 4)`

= `(6.022 xx 10^23)/(234)`

= 2.57 × 10²¹ unit cells