MHT CET · Chemistry · Solid State

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?

A \(102 \cdot 7 \mathrm{~cm}^{3} \mathrm{~mol}^{-1}\)
B \(404 \cdot 0 \mathrm{~cm}^{3} \mathrm{~mol}^{-1}\)
C \(159 \cdot 3 \mathrm{~cm}^{3} \mathrm{~mol}^{-1}\)
D \(142 \cdot 1 \mathrm{~cm}^{3} \mathrm{~mol}^{-1}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(102 \cdot 7 \mathrm{~cm}^{3} \mathrm{~mol}^{-1}\)

Step-by-step Solution

Detailed explanation

\(16 \times 10^{-8} \mathrm{~cm}\)
\(a=16 \times 10^{-8}\) 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 \(=\frac{4096 \times 10^{-24}}{24}=170.67 \times 10^{-24} \mathrm{~cm}^{3}\)
\(\therefore\) Volume of 1 mole of a crystalline solid \(=170.67 \times 10^{-24} \times 6.022 \times 10^{23}\)
\(=1027.77 \times 10^{-1}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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