The density of aluminum is 2.70 g/cm3. how large a cube, in cm3, would contain 2.00 x 10^24 atoms of aluminum? use dimensional analysis to solve and show all work including units on every number

The answer to your question is:     a = 3.21 cm                            

Explanation:

Data

density = 2.7 g/cm³

# of atoms = 2.00 x 10²⁴

atomic number Al = 27g/mol

Formula

density = mass / volume

Process

1.- Calculate the mass of Al

                            6.023 x 10²³ atoms ---------------  27 g

                            2.00 x 10²⁴ atoms ----------------   x

                            x = (2.00 x 10²⁴ x 27) / 6 .023 x 10²³

                            x = 89.66 g

2.- Calculate volume

                            volume = mass / density

                            volume = 89.66 g / 2.7 g/cm³      

                            volume = 33.2 cm³

3.- Calculate the length of each side

                            volume = a³

                             a³ = 33.2 cm³

                             a =

                             a = 3.21 cm