Be sure to answer all parts. A cube made of platinum (Pt) has an edge length of

Question

Be sure to answer all parts. A cube made of platinum (Pt) has an edge length of 3.00 cm The density of Pt is 21.45 g/cm3 (a) Calculate the number of Pt atoms in the cube. 1.788 atoms (b)Atoms are spherical in shape. Therefore, the Pt atoms in the cube cannot fill all the available space. If only 74.0 percent of the space inside the cube is taken up by Pt atoms, calculate the radius in picometers of a Pt atom. The mass of a single Pt atom is 3.240 x 1022 g. [The volume of a sphere of radius r is (4/3) r^. The volume of a cube is 3, where l is the length of a side. Avogadro's number is 6.022 x 1023] pm

Explanation / Answer

First part is correct

atoms = 1.788 x 1024

b) total volume is 27 cm3, only 74% is occupied so

0.74 * 27 = 19.98 cm3

Volume of a single atom is

volume occupied / number of atoms

Volume of a single atom = 19.98 / 1.788 x 1024 = 1.1177 x 10-23 cm3

volume of a sphere = (4/3) * 3.1416 * r3

1.1177 x 10-23 = 4/3 * 3.1416 * r3

2.668 x 10-24 = r3

r = 1.387x10-8 cm

1 cm is 1 x 1010 pm

r = 139 pm

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