Question

An ionic solid $FeO$ crystallizes into a cubic structure and has edge length equal to 5.0 A. If the density of crystal is 4 g/cm${}^3$, then the relation between formula mass $\left(X\right)$ and mass of a unit cell $\left(Y\right)$ is:

• A. $X=Y$
• B. $X=4Y$
• C. $Y=2X$
• D. $Y=4X$

Answer 1

The correct option is D $Y=4X$

Density $=\rho =\frac{Z\times M_A}{N_A\times a^3}$

Mass of $FeO=56+16=72$

Given,

$Z=?$
$a=5.0\mathring{A}$

$M_A=72$

$\rho =4$ $g/c{m}^3$

$N_A=6.023\times {10}^{2}3$

$4=\frac{Z\times 72}{6.023\times 125\times {10}^{-24}}$

$Z=4$

Therefore, appoximately $4$ molecules of $FeO$ are present in a unit cell.

$Y=4X$