Question

CsCl has cubic structure. Its density is 3.99 g cm-cube. What is the distance between Cs+ and Cl- ions? Atomic mass of Cs = 133​

Answer 1

Answer :

• Interionic distance (d) = 357 pm.

Step-by-step explanation :

Given that,

• Density of CsCl = $\bold{3.99\:g\:cm^{-3}}$

• Atomic mass of Cs = 133 u.

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CsCl has BBC structure. It has one formula unit in the unit cell. So, Z = 1.

Also, atomic mass of Cl = 35.5 u.

We know, $\bold{\rho=\dfrac{Z\times{}M}{a^3\times{}N_0}}$

$\implies\bold{a^3=\dfrac{Z\times{}M}{\rho\times{}N_0}}$

$\implies\bold{a^3=\dfrac{1\times{}(133+35.5)g\:mol^{-1}}{3.99\:g\:cm^{-3}\times{}6.02\times{}10^{23}\:mol^{-1}}}$

$\implies\bold{a^3=70.15\times{}10^{-24}\:cm^3}$

$\implies\bold{a=(70.15)^{\frac{1}{3}}\times{}10^{-8}\:cm}$

$\implies\bold{a=(70.15)^{\frac{1}{3}}\times{}10^{2}\:pm}$

$\implies\bold{a=4.124\times{}10^2\:pm=412.4\:pm}$

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We know, $\bold{d=\dfrac{\sqrt{3}}{2}a}$

Applying the value of edge length, we get,

$\implies\bold{d=\dfrac{1.732}{2}\times{}412.4}$

$\implies\bold{357\:pm}$

∴ Interionic distance = 357 pm.