Question

Gold has a face-centered cubic arrangement with a unit cell edge length of 4.08 Å . How many moles of gold fit in a gold nanoparticle sheet with a length of 57.3 nm , a width of 20.1 nm , and a thickness of 10.2 nm ?

Answer 1

volume of gold sheet = V = l x b x h

                                           = 57.3 x 20.1 x 10.2

                                           = 11747.65 nm^3

volume of gold sheet = 1.175 x 10^-23 m^3

unit cell edge length = 4.08 Å = 4.08 x 10^-10 m

volume of unit cell = a^3 = (4.08 x 10^-10)^3

                              = 6.79 x 10^-29 m^3

number of unit cells in the gold sheet = 1.175 x 10^-23 / 6.79 x 10^-29

                                                               = 1.73 x 10^5

The face centred cubic cell contains = 4 atoms of gold.

So No. of atoms in the sheet = 4 x1.73 x 10^5 = 6.92 x 10^5 gold atoms

No. of moles of atoms in the sheet = 6.92 x 10^5 / 6.02 x 10^23

                                                          = 1.149 x 10^-18 moles of gold atoms