Question

A pure titanium cube has an edge length of 2.66 in. How many titanium atoms does it contain? Titanium has a density of 4.50g/cm^3.

Answer 1

A pure Titanium cube has edge length = 2.66 inches

density = 4.50 g/cm3

All sides of cube will have length = 2.66 inches

Then volume of length = 2.66 in x 2.66 in x 2.66 in = 18.8210 inches³

1 inch = 2.54 cm

So 1 inch³ = 2.54³ cm³ = 16.39 cm³

Then

Volume = 18.8210 inches³ x 16.39cm³ / inch³

= 308.42 cm³

Now we can convert to mass by using density as both are having same units now

308.42 cm³ x 4.5 g/cm³ = 1387.89 g of titanium

And molar mass of titanium = 47.88 g/mole

Then moles of titanium = 1387.89 g / 47.88 g/mol

= 28.98 moles

Now by using Avagadros number we can find number of atoms

So

Number of atoms of titanium = 28.98 moles x (6.022 x 10²³ atoms/mol)

= 1.745 x 10²⁵ atoms