Gold (Au) has a face-centered cubic structure with a unit cell edge length of 407.8 pm. What is the calculated value of the density of gold based on this information? A) 15.78 g/cm³ B) 19.28 g/cm³ C) 9.64 g/cm³ D) 4.82 g/cm³ E) 11.6 g/cm³

Question

Quizplus · Accepted Answer

To calculate the density of gold, we need to know its atomic mass, which is 196.97 g/mol. The number of atoms in a face-centered cubic unit cell is 4 (one at each corner) plus 4 more at the center of each face (each counted as 1/2 of an atom). Therefore, the mass of a unit cell is:

(4 atoms x 196.97 g/mol) + (4 x 1/2 x 196.97 g/mol) = 787.88 g/mol

The volume of the unit cell can be calculated as follows:

V = a^3 = (407.8 pm)^3 = 6.717 x 10^-23 cm^3

So, the density can be calculated by dividing the mass by the volume:

Density = mass/volume = (787.88 g/mol)/(6.717 x 10^-23 cm^3) = 1.172 x 10^4 g/cm^3 = 19.28 g/cm^3

Therefore, the correct answer is B, 19.28 g/cm^3.

Gold (Au) Has a Face-Centered Cubic Structure with a Unit