Question

A titanium cube contains 3.15 ×1023 atoms. The density of titanium is 4.50 g/cm3. What is the edge length of the cube?

Answer 1

Answer: Given a titanum cube contains 3.15x10²³ atoms, which will allow you to determine how many moles you actually have

3.15x10²³ atoms⋅(1 mole Ti/6.023x10²³atoms)=0.523 moles (Since 1mole=6.023x10²³ atoms)

From here, use Ti's molar mass to find out how many grams you have.

0.523 molesx(47.9 grams/1 mole Ti)=25.05 grams (Molar mass of Ti=47.9 g/mol)

Use the given density to determine the volume you have

ρ=m/V⇒V=m/ρ=25.05 g/4.50 g/cm3=5.567 cm3 (Given density=4.50 g/cm³)

Since you're dealing with a cube, which has a volume of Vcube=edge³, your edge length will be

Edge=V^1/3=(5.567)^1/3=1.77 cm.

The edge length of the cube=1.77 cm