A molecule `A_(2)B (Mw = 166.4)` occupies triclinic lattice with `a = 5 Å, b = 8 Å`, and `c = 4 Å`,. If the density of `AB_(2)` is `5.2 g cm^(-3)`, the number of molecules present in one unit cell is

Options

A. `2`
B. `3`
C. `4`
D. `5`

Answer

B

Explanation

Volume of unit cell ` = a xx b xx c = 5 xx 10^(-8) xx 8`
` xx 10^(8) xx 4 xx 10^(-8)`
`= 1.6 xx 10^(-22) cm^(3)`
Mass of unit cell `= 1.6 xx 10^(-22) cm^(3)`
Mass of unit cell `= 1.6 xx 10^(-22) xx 5.2 = 8.32 xx 10^(-22)g`
Number of molecules in one unit cell `= (8.32 xx 10^(-22)g)/(166.4 g mol^(-1))`
`= 3`