A pure copper cube has an edge length of 2.00cm. How many copper atoms does it contain? (volume of a cube = (edge length)^3; density of copper = 8.96g/cm^3 )

Calculate the volume. Use density and volume to calculate mass, convert mass to moles. Then you know 1 mole Cu contains 6.022E23 atoms.

To determine the number of copper atoms in the given pure copper cube, we need to calculate its volume and then use Avogadro's number to convert it to the number of atoms.

Step 1: Calculate the volume of the copper cube.
The volume of a cube is given by the formula: volume = (edge length)^3.
Given that the edge length of the copper cube is 2.00 cm, the volume can be calculated as follows:
Volume = (2.00 cm)^3.

Step 2: Convert the volume to cm^3.
To obtain the volume in cm^3, we square the value calculated in step 1:
Volume = (2.00 cm)^3
= 8.00 cm^3.

Step 3: Convert the volume from cm^3 to grams.
Since the density of copper is given as 8.96 g/cm^3, we can multiply the volume by the density to obtain the mass:
Mass = Volume x Density
= 8.00 cm^3 x 8.96 g/cm^3.

Step 4: Calculate the mass of the copper cube.
Multiply the volume and density values calculated from steps 2 and 3 to find the mass:
Mass = 8.00 cm^3 x 8.96 g/cm^3
= 71.68 g.

Step 5: Determine the number of atoms in the copper cube.
Using the atomic weight of copper (63.55 g/mole) and Avogadro's number (6.022 x 10^23 atoms/mole), we can calculate the number of atoms in the copper cube.
Number of moles = Mass / Atomic weight of copper
= 71.68 g / 63.55 g/mole.

Step 6: Convert moles to atoms.
To convert moles to atoms, we multiply the number of moles by Avogadro's number:
Number of atoms = Number of moles x Avogadro's number
= (71.68 g / 63.55 g/mole) x (6.022 x 10^23 atoms/mole).

By performing the calculations, you will find the number of copper atoms in the given pure copper cube.

To determine the number of copper atoms in the pure copper cube, we need to follow these steps:

1. Calculate the volume of the copper cube. The volume of a cube is given by the formula: volume = (edge length)^3. In this case, the edge length is 2.00 cm, so the volume would be (2.00 cm)^3 = 8.00 cm^3.

2. Convert the volume of the copper cube from cubic centimeters (cm^3) to grams (g). To do this, we need to use the density of copper, which is provided as 8.96 g/cm^3. Multiply the volume by the density: 8.00 cm^3 x 8.96 g/cm^3 = 71.68 g.

3. Calculate the molar mass of copper. The molar mass of an element is the mass of one mole of atoms of that element. The molar mass of copper (Cu) can be found on the periodic table and is approximately 63.55 grams/mole.

4. Use the molar mass of copper to convert the mass of copper (in grams) to the number of moles of copper atoms. Divide the mass of copper by the molar mass: 71.68 g / 63.55 g/mol = 1.128 mol.

5. Finally, calculate the number of copper atoms in 1.128 moles using Avogadro's number, which is approximately 6.022 x 10^23 atoms/mole. Multiply the number of moles by Avogadro's number: 1.128 mol x 6.022 x 10^23 atoms/mol ≈ 6.804 x 10^23 copper atoms.

Therefore, a pure copper cube with an edge length of 2.00 cm contains approximately 6.804 x 10^23 copper atoms.