Question

Iron crystallizes in a body-centered cubic unit cell. The edge length of this cell is 287 pm. Calculate the density of iron in g/ml.

Answer 1

Answer:

Density = 7.87 grams per mL

Explanation:

Density is given by the formula:

$d=\frac{Z\times M}{a^{3}\times N_a}$

where

Z = effective number of atoms in one unit cell.

M = Molecular mass of the substance

a = edge length of unit cell

Na = Avogadro number = 6.022×10²³

In this case:

Z=2 as it is body-centered type unit cell

M = 56 g per mole for iron

a =  287 pm = $287\times10^{-10}\ cm$

Substituting the above values in the density formula we get:

$d=\frac{2\times56}{(287\times10^{-10})^{3}\times6.022\times10^{23}}=7.87\ g\ per\ ml$

Density of iron is 7.87 grams per mL.