Question

I have a unit cube question to which the answer is given that I'm trying to figure out. The question is:

If under conditions of high pressure & temperature, the crystalline structure rearranges to form a face-centered cubic unit cell, what is the new density of the substance?

Answer: 11.20 g/cm^3

Obviously this is a multi-part problem; I have solved the other parts and here is the releveant info:

As a body centered cubic unit cell:

side length= 3.14 Angstroms (3.14*10^-8 cm)

density: 10.28 g/cm^3

radius 1.36 Angstroms (1.36*10^-8 cm)
molar mass= 95.94 g/mol

And of course for body centered cells:

4r=3^(1/2)s
AND
2 atoms/1 cell

face centered cubic unit cells have 4 atoms/cell

I tried [mass(element in g/mol)*(# elements/cell)(1/Avogadro's #)]/(s(cm)^3)
in the sense that this would (I thought) give me:
mass of cell(grams)/volume cell (cm^3)

but I get an answer of over 700 so I obviously went wrong somewhere.

Answer 1

mass unit cell = 95.94*4/6.022E23 = ??
volume = a^3
a = 4r/sqrt 2.
I get 11.19