Be sure to answer all parts. A cube made of platinum (Pt) has an edge length of
ID: 1082321 • Letter: B
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] pmExplanation / 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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