Question

Argon crystallises in fcc arrangement and the density of solid and liquid $Ar$ is 1.59 $g/$ $c{m}^3$ and 1.42 $g/$ $c{m}^3$ , respectively . The percentage of empty space in liquid $Ar$ is:

• A. 34.84%
• B. 43.8%
• C. 23.4%
• D. 21.6%

Answer 1

The correct option is A 34.84%

Let the volume of solid $Ar=100$ mL

Mass of solid $Ar=V$ $\times \rho =100\times 1.59g/c{m}^3=159g$
Volume of liquid $Ar$

$=\frac{Mass}{\rho }=\frac{159g}{1.4gc{m}^{-3}}$
= 113.57 ml

$\because$ $Ar$ crystallises in fcc type lattice, the packing fraction = 0.74

Actual volume occupied by $Ar$

= Packing fraction $\times$ volume of solid $Ar$

= 0.74 x 100 = 74 mL

$\therefore$ % empty in liquid Ar $=\frac{(113.57-74)\times 100}{113.57}$

= 34.84%