A copper complex crystallising in a CCP lattice with a cell edge of 0.4518 nm has been revealed by employing X-ray diffraction studies. The density of a copper complex is found to be 7.62 g \(\mathrm{cm^{-3}}\). The molar mass of copper complex is ____________ g \(\mathrm{mol^{-1}}\). (Nearest integer)
[Given : \(N_A = 6.022\times 10^{23}\ \mathrm{mol^{-1}}\)]
[Given : \(N_A = 6.022\times 10^{23}\ \mathrm{mol^{-1}}\)]
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Correct Answer: 106
Solution and Explanation
\(a = 0.4518\ \mathrm{nm} = 4.518\times 10^{-8}\) cm, so \(a^3 = 9.222\times 10^{-23}\ \mathrm{cm^3}\).
\(\rho = \dfrac{ZM}{a^3 N_A}\Rightarrow M = \dfrac{\rho\,a^3 N_A}{Z}\)
\(M = \dfrac{7.62\times 9.222\times 10^{-23}\times 6.022\times 10^{23}}{4} = \dfrac{423.2}{4} = 105.8\)
Nearest integer = 106 g \(\mathrm{mol^{-1}}\)
Answer: 106
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