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A molecule A(2)B (Mw = 166.4) occupies t...

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 `A_(2)B` is `5.2 g cm^(-3)`, the number of molecules present in one unit cell is

A

`2`

B

`3`

C

`4`

D

`5`

Text Solution

Verified by Experts

The correct Answer is:
B
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`
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