Question:
A copper complex crystallising in a CCP lattice with a cell edge of $0.4518 \mathrm{~nm}$ has been revealed by employing X-ray diffraction studies. The density of a copper complex is found to be $7.62 \mathrm{~g} \mathrm{~cm}^{-3}$. The molar mass of copper complex is ________ $g \mathrm{~mol}^{-1}$
(Nearest integer)
[Given : $\mathrm{N}_{\mathrm{A}}=6.022 \times 10^{23} \mathrm{~mol}^{-1}$ ]
Solution:
$\mathrm{d}\left(\frac{\mathrm{gm}}{\mathrm{cc}}\right)=\frac{4 \times \frac{\mathrm{M}}{\mathrm{N}_{\mathrm{A}}}}{(\mathrm{a} \mathrm{cm})^{3}}$
$7.62=\frac{4 \times \mathrm{M} / 6.022 \times 10^{23}}{\left(0.4518 \times 10^{-7} \mathrm{~cm}\right)^{3}} \Rightarrow \mathrm{M}=105.8 \mathrm{~g} / \mathrm{mol}$