Final answer:
To find the number of platinum atoms in the cube, calculate the volume of the cube, use the density to find the mass, convert the mass to moles using the molar mass of platinum, and then use Avogadro's number to convert the moles to atoms. The cube contains approximately 3.252 × 10^22 platinum atoms.
Step-by-step explanation:
To calculate the number of platinum (Pt) atoms in a cube with an edge length of 1.70 cm, you'll need to use the density of platinum, which is 21.45 g/cm3, and the atomic mass of platinum. Here's how you would do it:
- First, calculate the volume of the cube using the formula for the volume of a cube, V = a3, where 'a' is the edge length. So, V = (1.70 cm)3 = 4.913 cm3.
- Then, use the density of platinum to find the mass of the cube by multiplying the volume by the density (Mass = Volume × Density). Mass = 4.913 cm3 × 21.45 g/cm3 = 105.35 g.
- Next, we need to find the number of moles of Pt in this mass using the molar mass of Pt, which is approximately 195.08 g/mol (Moles = Mass / Molar Mass). Moles = 105.35 g / 195.08 g/mol = 0.54 mol.
- Finally, to find the number of atoms, multiply the number of moles by Avogadro's number (6.022 × 1023 atoms/mol). Number of Pt atoms = 0.54 mol × 6.022 × 1023 atoms/mol = 3.252 × 1022 atoms.
Therefore, the cube contains approximately 3.252 × 1022 platinum atoms.