Final answer:
To calculate the number of Pt atoms in a 1.50 cm cube of platinum, first compute the cube's volume, then the mass using the density of platinum, convert mass to moles using platinum's molar mass and finally multiply the moles by Avogadro's number to find the number of atoms.
Step-by-step explanation:
The question involves calculating the number of platinum (Pt) atoms in a cube with an edge length of 1.50 cm, given that the density of platinum is 21.45 g/cm³. First, we need to calculate the volume of the cube using the formula for the volume of a cube (V = edge length³). After that, we can find the mass of the cube using the density formula (mass = density x volume). Once we have the mass in grams, we convert it to moles of Pt using its molar mass (atomic weight of Pt is 195.08 g/mol). Finally, to get the number of atoms, we multiply the number of moles by Avogadro's number (6.022 x 10²³ atoms/mol).
- Calculate the volume of the cube: V = l³ = (1.50 cm)³ = 3.375 cm³.
- Calculate the mass of platinum in the cube: mass = density x volume = 21.45 g/cm³ x 3.375 cm³ = 72.39375 g.
- Convert the mass to moles of Pt: moles of Pt = mass / molar mass = 72.39375 g / 195.08 g/mol = 0.371 moles of Pt.
- Calculate the number of Pt atoms: number of atoms = moles x Avogadro's number = 0.371 moles x 6.022 x 10²³ atoms/mol = 2.233 x 10²² atoms.
The calculation results in approximately 2.233 x 10²² platinum atoms in the cube.