Question

Crystalline $CsCl$ has density $3.988\, gcm ^{-3}$. The volume occupied by single CsCl pair in the crystal will be:
(Molar mass $CsCl =168.4\, g / mol$ )

• A. $7.014 \times 10^{-3} cm ^{3}$
• B. $7.014 \times 10^{-23} cm ^{3}$
• C. $1.014 \times 10^{-3} cm ^{3}$
• D. $1.542 \times 10^{-5} cm ^{3}$

Answer 1

Answer: (B)

$CsCl$ forms $SCC$ lattice ($BCC$ type), $Z=1$

Volume of unit cell $=$ volume of single $CsCl$ ion pair $= a ^{3}$

$d =\frac{ Z \times M }{ N _{ A } \times a ^{3}}$

$\Rightarrow a ^{3}=\frac{ Z \times M }{ d \times N _{ A }}$

$=\frac{1 \times 168.4}{3.988 \times 6.023 \times 10^{23}} $

$=7.014 \times 10^{-23}\, cm ^{3}$