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

Sodium chloride has face centred cubic structure. Therefore, the number of formula units or molecules per unit cell, Z = 4
Let Avogadro number = `N_A`
Molar mass of `NaCl = 23 + 35.5 = 58.5 g mol^(-1)`
Since distance between `Na^(+) and Cl^(-)` ions is 281 pm, the length of edge is double the distance between `Na^(+) and Cl^(-)` ions .
Edge of unit cell = `2 xx 281 p m = 562 p m`
or `" " = 562 xx 10^(-12) m = 562 xx 10^(-10) cm`
Density , `rho = (Z xx M)/(a^3 xx N_A)`
`2.165 g cm^(-3) = (4 xx (58.5 g mol^(-1)))/((562 xx 10^(-10)cm)^(3) xx N_A)`
or `" " N_A = (4 xx (58.5 g mol^(-1)))/((2.165 g cm^(-3)) xx (562 xx 10^(-10)cm)^(3))`
`= 6.09 xx 10^(23) mol^(-1)`.