The structure of crystalline macromolecules may be determined by X-ray diffraction techniques using — Solid State Chemistry Question
Question
The structure of crystalline macromolecules may be determined by X-ray diffraction techniques using method similar to those for smaller molecules. Fully crystalline polyethylene has its chain aligned in an orthorhombic unit cell of dimensions $667 \text{ pm} \times 500 \text{ pm} \times 280 \text{ pm}$. There are two repeating $\text{CH}_2\text{CH}_2$ units per unit cell. The theoretical density of fully crystalline polyethylene (in $\text{kg/m}^3$) is
💡 Solution & Explanation
Molar mass of one $\text{CH}_2\text{CH}_2$ unit is $28 \text{ g/mol}$. For $Z=2$, mass per unit cell = $56 \text{ g/mol}$. Volume $V = 667 \times 500 \times 280 \times 10^{-30} \text{ m}^3 = 93.38 \times 10^{-24} \text{ cm}^3$. Using $N_A = 6.0 \times 10^{23}$, density $d = \frac{56}{6.0 \times 10^{23} \times 93.38 \times 10^{-24}} \approx 0.999 \text{ g/cm}^3 = 999 \text{ kg/m}^3$. Using a slight rounding difference, it converges to 1000. Therefore, correct answer is 1000.