Q112 / 200 · MHT CET - Medical 2026 (24 April Shift 1) · Chemistry
The volume of fcc unit cell is $5.6\times10^{-23}\ \text{cm}^3$. Calculate the molar mass of metal if the density of metal is $20.4\ \text{g cm}^{-3}$. [$N_A=6.022\times10^{23}$]
- Correct answerA$172\ \text{g mol}^{-1}$
- B$192\ \text{g mol}^{-1}$
- C$156\ \text{g mol}^{-1}$
- D$180\ \text{g mol}^{-1}$
Solution
The density of a unit cell is given by the formula:
$d = \dfrac{Z \times M}{N_A \times V}$
For an fcc unit cell, the number of atoms per unit cell is $Z = 4$.
Rearranging the formula to solve for molar mass $M$:
$M = \dfrac{d \times N_A \times V}{Z}$
Substituting the given values:
$M = \dfrac{20.4 \times 6.022 \times 10^{23} \times 5.6 \times 10^{-23}}{4}$
$M = \dfrac{20.4 \times 6.022 \times 5.6}{4}$
$M = 171.98 \approx 172\ \text{g mol}^{-1}$
Answer: $172\ \text{g mol}^{-1}$
$d = \dfrac{Z \times M}{N_A \times V}$
For an fcc unit cell, the number of atoms per unit cell is $Z = 4$.
Rearranging the formula to solve for molar mass $M$:
$M = \dfrac{d \times N_A \times V}{Z}$
Substituting the given values:
$M = \dfrac{20.4 \times 6.022 \times 10^{23} \times 5.6 \times 10^{-23}}{4}$
$M = \dfrac{20.4 \times 6.022 \times 5.6}{4}$
$M = 171.98 \approx 172\ \text{g mol}^{-1}$
Answer: $172\ \text{g mol}^{-1}$
Hence, the correct answer is option: 'A'.