Question

Help fast please ! 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

33.2

Step-by-step explanation:

Answer 2

33.2 cm³

Step-by-step explanation:

We are given;

Density of Aluminium is 2.70 g/cm³

Number of atoms of Aluminium is 2.00 × 10^24 atoms

We are required to calculate the volume of the cube;

We know that 1 mole of a compound or an element contains a number of particles equivalent to the Avogadro's constant.

Therefore;

1 mole of Aluminium contains 6.022 × 10^23 atoms

But, 1 mole of Al = 27 g

Therefore;

27 g of Al contains 6.022 × 10^23 atoms

We need to calculate the mass that contains 2.00 × 10^24 atoms

Moles of Al = (2.00 × 10^24 atoms) ÷ (6.022 × 10^23 atoms)

= 3.32 moles

Mass of Al = 27 g/mol × 3.32 moles

= 89.64 g

We can then calculate volume of Aluminium

Density = Mass ÷ Volume

Rearranging the formula;

Volume = Mass ÷ Density

= 89.64 g ÷ 2.70 g/cm³

= 33.2 cm³