The unit cell of is FCC with . If density , the value of '' is — Solid State Chemistry Question
Question
The unit cell of $\text{TlAl(SO}_4\text{)}_2 \cdot x\text{H}_2\text{O}$ is FCC with $a = 1.26 \text{ nm}$. If density $= 2.14 \text{ g/ml}$, the value of '$x$' is $[\text{Tl} = 207, \text{Al} = 27, (1.26)^3 = 2]$
Answer: 0012
💡 Solution & Explanation
Edge length $a = 1.26 \times 10^{-7} \text{ cm}$. Volume $V = 2 \times 10^{-21} \text{ cm}^3$. Molar mass $M = \frac{d \times N_A \times V}{Z} = \frac{2.14 \times 6.0 \times 10^{23} \times 2 \times 10^{-21}}{4} = 642 \text{ g/mol}$. The formula mass is $207 + 27 + 2(96) + 18x = 426 + 18x$. Equating the two: $426 + 18x = 642 \implies 18x = 216 \implies x = 12$. Therefore, correct answer is 0012.
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