Question

A compound formed by elements X & Y. Crystallizes in a cubic structure, where X is the at corners of the cube and Y is at six face centers. What is the formula of the compound? If side length is $5\mathring{A}$, estimate the density of the solid assuming atomic weight of X and Y as 60 and 90 respectively.

Answer 1

$x\Rightarrow \frac{1}{8}\times 8=1\left(\text{corners}\right)$

$y\Rightarrow \frac{1}{2}\times 6=3\left(\text{face}\text{center}\right)$

$x{y}_3\Rightarrow \text{formula}\Rightarrow m=60+90\times 3$

60 + 270 = 330

$p=\frac{Z\times M}{N_A\times a^3}\Rightarrow \frac{4\times 330}{6.023\times {10}^{23}\times \left(5\times {10}^{-8}\right)3}5\times {10}^{-10}m$

$5\times {10}^{-8}cm$

$=\frac{330\times 4}{752.875\times {10}^{-24+23}}$

$=1.7532\times {10}^1=17.5g/c{m}^3$