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?

Question

Quizplus · Accepted Answer

The first step is to calculate the volume of the unit cell:

V = (edge length)^3 = (407.8 pm)^3 = 6.246 x 10^-23 cm^3

Next, we need to determine the mass of gold in the unit cell. The molar mass of gold is 196.97 g/mol, and there is one gold atom per unit cell. Therefore, the mass of gold in the unit cell is:

m = (1 atom) x (196.97 g/mol) / (6.022 x 10^23 atoms/mol) = 3.269 x 10^-22 g

Finally, we can calculate the density of gold based on its mass and volume:

density = mass / volume = (3.269 x 10^-22 g) / (6.246 x 10^-23 cm^3) = 19.30 g/cm^3

Therefore, the answer is B.

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