A unit call of NaCl has four formula units. In NaCl crystal, radius ratio `(r_(+)//r_(-))` is 0.69 and edge-length of the unit cell is twice the sum of the radii of `Na^(+)andCl^(-)` ions. If the radius of `Na^(+)` is 116 pm then find the density of NaCl crystal. Formula mass of NaCl = `58.5g*mol^(-1)`.

Explanation

The unit cell of NaCl has 4 formula units. Hence, Z = 4.
Given, `r_(+)/r_(-)=0.69`, edge-length of the unit cell (a) = `2(r_(+)+r_(-))` and `r_(+)=116`pm
`therefore" "r_(-)=116/0.69=168.11`pm
`therefore" "a=2(r_(+)+r_(-))=2(116+168.11)`pm = 568.22pm
`=568.22xx10^(-10)cm`
We know, `rho=(ZxxM)/(Nxxa^(3))=(4xx58.5)/(6.022xx10^(23)xx(568.22xx10^(-10))^(3))`
`=2.117g*cm^(-3)`
`therefore" "`Density of NaCl = `2.117g*cm^(-3)`