A copper complex crystallising in a CCP lattice with a cell edge of $0.4518 n m$ has been revealed by employing X-ray diffraction studies. The density of a copper complex is found to be $7.62 g c m^{- 3} .$
The molar mass of copper complex is __________
$g m o l^{- 1} .$ (Nearest integer) [Given : $N_{A} = 6.022 \times 10^{23} m o l^{- 1}]$

106

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106.0

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106.00

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Solution

Given: the density of a copper complex = $7.62 g c m^{- 3}, N_{A} = 6.022 \times 10^{23} m o l^{- 1}, a = 0.4518 n m, Z = 4$
We know the $d = \frac{Z \times M}{a \times N_{A}}$
CCP lattice has a fcc structure:
For a fcc unit cell, atoms are present at corners as well as face centres :
$Number of atoms in unit cell = (8 \times \frac{1}{8}) + (6 \times \frac{1}{2}) = 4$
$7.62 = \frac{4 \times M}{(0.4518 \times 10^{- 7})^{3} \times 6.022 \times 10^{23}}$

$M = 105.8 g / m o l$

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