Q22 / 160 · AP EAMCET 2022 (07 Jul Shift 2) · Chemistry

Ag crystallises in fcc lattice. What is the total number of tetrahedral voids present in $540 \mathrm{~g}$ of Ag metal? $\left(N_A=\right.$ Avagadro number; $\mathrm{Ag}$ atomic weight $=108 \mathrm{~g} \mathrm{~mol}^{-1}$ )

  • Correct answer
    A
    $10 N_A$
  • B
    $20 N_A$
  • C
    $40 N_A$
  • D
    $60 N_A$

Solution

Ag crystallises in fcc lattice. Each unit cell contains 4 atoms and 8 tetrahedral voids. The mass of one $\mathrm{Ag}$-atom $$ =\frac{\text { Atomic mass }}{N_A}=\frac{108 \mathrm{~g} \mathrm{~mol}^{-1}}{N_A} $$ The mass of one unit cell will be $=4 \times \frac{108 \mathrm{~g} \mathrm{~mol}^{-1}}{N_A}$ Number of unit cells in $540 \mathrm{~g}$ of crystal $$ =\frac{540 \mathrm{~g} \times N_A}{4 \times 108}=1.25 N_A $$ Number of tetrahedral voids in 1.25 unit cell $$ =N_A \times 8 \times 1.25=10 N_A $$

Hence, the correct answer is option: 'A'.

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