Tip:
Highlight text to annotate it
X
Iron oxide has the rock salt structure
and we are given a density. The questions is what's the length
of its unit cell
So first we need to understand
what their rock salt structure means because
we're gonna have oxygen ions in a
face centered cubic structure so that means
we look at it cube and we put
oxygen atom on all the corners
and then we put oxygen atoms on all
faces. A little harder to draw that. This is a front
face. This is a side face and then we stick
the iron ion in the interstitial spaces
so that the iron to oxygen ratio is one because of the
iron oxide stoichiometry and then the
in this structure each iron
has 6 nearest neighbors meaning
iron is it in the octahedral site. So keep in mind iron ion
is smaller than the oxygen ion.
therefor can fit in interstitial space
so we want to calculate from the density value the unit cell value
so density is equel to mass
or volume so density is 5.70
grams per centimeter cubed. The
volume is "a" is the unit cell
dimension cubic so "a" cubed
would be the volume since we're looking at the density
for not just a few molecules but
for a mole we need Avogadros number
so we can work in moles and then for the mass so we have in unit cell
we have an oxygen on each corner so that's 8
oxygen but they are shared
with eight other unit cell surrounding
so that mean one oxygen ion
from there corners and we have six faces
6 oxygen atoms there and they are shared
with the adjoining unit cell so that's three ions
So that means we have four oxygen ions
in the unit cell each has
atomic mass 16 so
16 grams per mole and then we
have to and number iron ions as well
since the stoichiomety of iron oxide there must be also
four iron and again looking up
atomic weight from a periodic table
so this is the mass grams per mole. We now have in its cell
dimension it's gonna be centimeters
make in the units consists and Avogadros number
is a number per mole. If we rearrange this
we can solve for "a" cubed. This number on top is
multiplied out. 5.70
and then 6.023 times
ten to the 23rd. So we we can calculate
"a" cubed which means we can calculate "a"
so taking the cubic root we have the dimensions in centimeters we can
convert just to nanometers as the more normal
dimension. And ten squared centimeters is a meter
10 to the ninth nanometers is a meter. So the
unit cell dimension becomes 0.437
nanometers. So this is the unit cell dimension
for iron oxide which we got from the density
and from the structure