Question

A titanium cube contains 3.10•10^23 atoms. The density of a titanium is 4.50g/cm^3. What is the edge length of the cube?

Answer 1

Answer:

1.76cm

Explanation:

We'll begin by calculating the mass of titanium that contain 3.10x10²³ atoms. This can be obtained as follow:

From Avogadro's hypothesis, we understood that 1 mole of any substance contains 6.02x10²³ atoms. This implies that 1 mole of titanium also contains 6.02x10²³ atoms.

1 mole of titanium = 48g

Now, if 48g of titanium contains 6.02x10²³ atoms,

Then Xg of titanium will contain 3.10x10²³ atoms i.e

Xg of titanium = (48x3.10x10²³)/6.02x10²³

Xg of titanium = 24.72g

Next, we shall determine the volume of the titanium. This is illustrated below:

Density of titanium = 4.50g/cm³

Mass of titanium = 24.72g

Volume of titanium =..?

Density = Mass /volume

Volume = Mass /Density

Volume of titanium = 24.72g/4.50g/cm³

Volume of titanium = 5.49cm³

Finally we shall determine the edge length of the titanium cube as follow:

Volume = L³

5.49cm³ = L³

Take the cube root of both side

L = 3√(5.49cm³)

L = 1.76cm

Therefore, the edge length is 1.76cm