Question

A typical sugar cube has an edge length of 1 cm. If you had a cubical box that contained a mole of sugar cubes, what would its edge length be? (One mole = 6.02 × 10^23 units.)

Answer 1

The answer is 8 × 10² km.

Volume of the cube with edge a is: V = a³
1 mole = V = a³
1 mole = 6.02 × 10²³ cm³
a = ?

a = ∛6.02 × 10²³ cm³ = 84 436 877 cm 
1 km = 1 000 000 cm
1 cm = 0.000001 km
a = 84 436 877 cm = 844 km = 8.44 × 100 km = 8.44 × 10² km ≈ 8 × 10² km