What is the volume of 1 mole of a crystalline solid having unit cell edge length $16 \times 10^{-8}…
What is the volume of 1 mole of a crystalline solid having unit cell edge length $16 \times 10^{-8} \mathrm{~cm}$, if it's unit cell contains 24 molecules?
$102 \cdot 7 \mathrm{~cm}^{3} \mathrm{~mol}^{-1}$
$404 \cdot 0 \mathrm{~cm}^{3} \mathrm{~mol}^{-1}$
$159 \cdot 3 \mathrm{~cm}^{3} \mathrm{~mol}^{-1}$
$142 \cdot 1 \mathrm{~cm}^{3} \mathrm{~mol}^{-1}$
Solution
$16 \times 10^{-8} \mathrm{~cm}$
$a=16 \times 10^{-8}$ cme unit cell $=a^{3}=\left(16 \times 10^{-8}\right)^{3}$
Volume of one unit cellat $=4096 \times 10^{-24} \mathrm{~cm}^{3}$
volume of 24 molecules $=4096 \times 10^{-24} \mathrm{~cm}^{3}$
$\therefore$ Volume of 1 molecule $=\frac{4096 \times 10^{-24}}{24}=170.67 \times 10^{-24} \mathrm{~cm}^{3}$
$\begin{aligned} \therefore \text { Volume of } 1 \text { mole of a crystalline solid } &=170.67 \times 10^{-24} \times 6.022 \times 10^{23} \\ &=1027.77 \times 10^{-1} \end{aligned}$