Question

Calculate the value of Avogadro's number from the following data :
Density of NaCl = 2.165 g cm-3. Distance between Na+ and Cl- in NaCl = 281 pm.​

Answer 1

Answer :

• Avogadro's number = $\rm{6.09\times{}10^{23}\:mol^{-1}}$

Step-by-step explanation :

Given that,

• Density, ρ = $\rm{2.165\:g\:cm^{-3}}$
• Edge length of unit cell = 562 (2 × 281) pm.

Also,

• A unit cell of NaCl contains 4 NaCl units, ∴ Z = 4.
• Molar mass of NaCl, M = 23 + 35.5 = 58.5 g/mol.

$\hrulefill$

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

$\bold{OR}$

$\rm{N_0=\dfrac{Z\times{}M}{a^3\times{}N_0}}$

Putting the given values, we get,

$\implies\rm{N_0=\dfrac{4\times{}58.5\:g\:mol^{-1}}{(562\times{}10^{-10}\:cm)^3\times{}2.165\:g\:cm^{-3}}}$

$\implies\rm{N_0=}\bold{6.09\times{}10^{23}\:mol^{-1}}$