Final answer:
To find the number of platinum atoms in a cube, calculate the cube's volume, use the density of platinum to find the mass, and then calculate the number of atoms using Avogadro's number and the molar mass of platinum.
Step-by-step explanation:
To calculate the number of platinum (Pt) atoms in the cube, we would first find the volume of the cube using the formula for the volume of a cube, which is V = edge length3. Then, use the known density of platinum to find the mass of the cube. Finally, we'd calculate the number of atoms by dividing the mass of the cube by the mass of a single Pt atom.
Step 1: Calculate the volume of the cube.
Volume (V) = edge length3 = (1.60 cm)3 = 4.096 cm3
Step 2: Find the mass of the cube using the density (density = mass/volume).
Mass = density × volume = 21.45 g/cm3 × 4.096 cm3 = 87.8616 g
Step 3: Calculate the number of Pt atoms.
Using the molar mass of Pt, which is approximately 195.08 g/mol, and Avogadro's number (6.022 x 1023 atoms/mol), we can find the number of atoms in 87.8616 g of Pt.
Number of Pt atoms = (87.8616 g) / (195.08 g/mol) × (6.022 x 1023 atoms/mol)
Using this method, we can find an accurate number of platinum atoms in the cube, maintaining the correct number of significant figures throughout the calculation.