Question

What is the volume of 1 mole of a crystalline solid having unit cell edge length 16 \(\times\) 10\(^{-10}\) cm, if its unit cell contains 24 molecules?

• A. 102.7 cm\(^3\)mol\(^{-1}\)
• B. 404.0 cm\(^3\)mol\(^{-1}\)
• C. 159.3 cm\(^3\)mol\(^{-1}\)
• D. 142.1 cm\(^3\)mol\(^{-1}\)

Hint:

To calculate the volume of 1 mole of crystalline solid, use the unit cell edge length and Avogadro’s number, considering the number of molecules per unit cell.

Answer 1

The Correct Option is A

Step 1: Formula for the volume of 1 mole of solid.
The volume of 1 mole of a crystalline solid can be calculated using the formula: \[ V = \frac{N \times a^3}{\text{number of molecules per unit cell}} \] Where: - \(N = 6.022 \times 10^{23}\) molecules/mol (Avogadro’s number) - \(a = 16 \times 10^{-10}\) cm (unit cell edge length) - The number of molecules per unit cell is 24. Step 2: Substituting the values.
The volume of 1 mole of the solid is: \[ V = \frac{6.022 \times 10^{23} \times (16 \times 10^{-10})^3}{24} = 102.7 \, \text{cm}^3\text{mol}^{-1} \] Step 3: Conclusion.
The correct answer is (A) 102.7 cm\(^3\)mol\(^{-1}\).