The molar volume of a certain form of solid lead is 18 cm 3 /mol.Assuming cubic closest packed structure,determine the following:
-The number of Pb atoms per unit cell.
A)1
B)2
C)4
D)6
E)10

Question

Quizplus · Accepted Answer

In a cubic closest packed structure, each unit cell contains: - 4 atoms located at the corners of the unit cell - 4 atoms located at the center of each face of the unit cell - 1 atom located at the center of the unit cell The total number of atoms per unit cell is therefore: 4 + 4 x 1/2 + 1 = 4 + 2 + 1 = 7 However, the problem states that the molar volume is 18 cm³/mol. This means that one unit cell contains one mole of lead atoms. Therefore, the number of Pb atoms per unit cell is: 6.022 x 10²³ atoms/mol / 1 unit cell = 6.022 x 10²³ / 1.8 x 10²⁴ cm³ = 0.334 Since the number of atoms must be a whole number, the closest integer to 0.334 is 0, which means that there are 4 atoms per unit cell. Therefore, the answer is choice C) 4.

The Molar Volume of a Certain Form of Solid Lead