Calculate the value of Avogadro's number from the following data:
Density of `NaCl = 2.165 g cm^(-3)`
Distance between `Na^(o+)` and `Cl^(Θ)` in `NaCl = 281` pm

Explanation

A unit cell of NaCl contains 4 NaCl units, therefore , Z=4 , M=23+35.5=`58.5 g mol^(-1), rho =2.165 g cm^(-3)`
As distance between `Na^+` and `Cl^-` =281 pm `therefore` Edge of the unit cell =`2xx281`=562 pm
(Edge is the distance from `Na^+` to `Na^+` ion or `Cl^-` to `Cl^-` ion.
Substituting these values in the expression , `rho=(ZxxM)/(a^3xxN_0)`
`2.165 g cm^(-3)=(4xx58.5 g mol^(-1))/((562xx10^(-10) cm)^3 xxN_0)` or `N_0=6.09xx10^23 mol^(-1)`