The sublimation temperature of a substance is . It exist as cubic packed structure with unit cell ed — Solid State Chemistry Question
Question
The sublimation temperature of a substance is $-83^\circ\text{C}$. It exist as cubic packed structure with unit cell edge length $5.0$ Å and density $\frac{8}{3} \text{ g/cm}^3$, at $-100^\circ\text{C}$. What should be density of substance at $0^\circ\text{C}$ and 1 atm? ($N_A = 6 \times 10^{23}$)
Answer: C
💡 Solution & Explanation
Molar mass $M = \frac{d \times N_A \times a^3}{Z} = \frac{(8/3) \times 6 \times 10^{23} \times (5 \times 10^{-8})^3}{4} = 50 \text{ g/mol}$. At $0^\circ\text{C}$ (273 K), it is a gas since it sublimes at $-83^\circ\text{C}$. Gas density = $\frac{PM}{RT} = \frac{1 \times 50}{0.0821 \times 273} \approx 2.23 \text{ g/L}$. Therefore, correct answer is C.
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