Question

The compound CuCl has ZnS structure and edge length of unit cell is 500 pm.Calculate its density.(Atomic mass of Cu=63,Cl=35.5)

Answer 1

since,ZnS has a cubic structure it contains 1 sphere so Z=1. density of CuCl is as follows [{(63+35.4)×1}÷{(6.023×10^23)×(500×10^-10)}] g/cc

Answer 2

Solution:

Since CuCl has a ZnS structure, it means that it has 4 atoms per unit cell. ZnS is cubic closest structure wherein each cell contains 4 atoms.  

The molar mass of CuCl:

Atomic mass of Cu=63 and Cl= 35.5

So, molecular mass of CuCl = M = 63 + 35.5 = 98.5

We use the formula for density as:

$\text{Density} =\frac{\text {Mass}}{\text {Volume}}$

$\text{Density} =\frac{Z \times M}{6.023 \times 10^{23} \times a^{3}}$

Where,

Z is atoms per unit cell

M is the molecular mass

a is the length per unit cell given to be 500pm

Now substituting the given values in the density formula, we get,

$Density =\frac{4 \times 98.5}{6.023 \times 10^{23} \times\left(50 \times 10^{-8}\right)^{3}}$

$Density =\frac{394}{75.28}$

$\Rightarrow \text { Density }=5.23 \ \mathrm{gm.cm}^{-3}$