Question

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

Answer 1

a=3.21

Step-by-step explanation:

Answer 2

The answer to your question is: a = 3.21 cm

Step-by-step 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 =
`\sqrt[3]{33.2}`

a = 3.21 cm