a. Determine the density of a cube of copper with a length of 5.00 cm and a mass of 1,112.50 g.

b. Calculate the number of atoms in the cube

since density = mass/volume, we have

1112.50g/(5.00cm)^3
= 1112.50/125.00 g/cm^3

# atoms is

g * moles/g * 6.02*10^23 atoms/mole

So, just look up the atomic weight of copper and plug it in.

a. To determine the density of the cube, we need to use the formula:

Density (ρ) = Mass (m) / Volume (V)

Given that the length of the cube is 5.00 cm and the mass is 1,112.50 g, we need to calculate the volume first.

The volume of a cube can be found using the formula:

Volume (V) = Length³

So, substitute the values:

Volume (V) = (5.00 cm)³ = 125.00 cm³

Now, plug in the values for mass and volume into the density formula:

Density (ρ) = 1,112.50 g / 125.00 cm³

Divide the mass by the volume to get the density:

Density (ρ) = 8.90 g/cm³

Therefore, the density of the cube of copper is 8.90 g/cm³.

b. To calculate the number of atoms in the cube, we need to use Avogadro's number (6.022 × 10²³ atoms/mol) and the molar mass of copper (63.55 g/mol).

First, let's calculate the number of moles of copper using the molar mass and mass of the cube:

Number of moles (n) = Mass (m) / Molar mass (M)

Number of moles (n) = 1,112.50 g / 63.55 g/mol

Next, we can use the relationship between moles and atoms to find the number of atoms in the cube:

Number of atoms = Number of moles (n) × Avogadro's number

Number of atoms = (1,112.50 g / 63.55 g/mol) × (6.022 × 10²³ atoms/mol)

Calculate the value to find the number of atoms in the cube.