The density of a particular crystal of LiF is 2.65 g/cc. X-ray analysis shows that Li+ and `F^(-)` ions are arranged in a cubic array at a spacing of 2.01 A. From these data calculate the apparent Avogadro constant. [Li = 6.939, F = 18.998 (1 A = `10^(-8)`cm.)]

Explanation

In this problem, we have to calculate Av. const., i.e., the number of LiF molecules present in 1 mole. As 1 mole of LiF weighs 25.937 g (LiF= 6.939+18.998)
volume of 1 mole = `("wt. of 1 mole")/("wt. per cc density") = (25.937)/(2.65)`
Since this volume is supposed to be of a cube the length of each edge of the cube = `root(3)(9.78)`
`=2.138 cm`
No. of ions present m one edge = `(2.138)/(2.01 xx 10^(-8))`
`=1.063 xx 10^(8)`
No. of ions (`Li^(+), F^(-)`) present in the cube = `(1.603 xx 10^(8))^(3)`
`=1.201 xx 10^(24)`
No. of LiF molecules per mole (i.e., Avogadro constant) = `(1.201 xx 10^(24))/2`
`=6.01 xx 10^(23)`