An element with density `2.8 g cm^(-3)` forms a fcc unit cell with edge length `4 xx 10^(-8) cm`. Calculate the molar mass of the element.
(Given : `N_A = 6.022 xx 10^(23) mol^(-3)` )

Explanation

Given, Density of solid, `d = 2.8 g cm^(-3)`
For foc unit cell, `Z=4`
Edge length, `a = 4 xx 10^(-8) cm`,
Molar mass, M=?
`N_A = 6.022 xx10^(23) mol^(-1)` Using formula, `d =(Zxx M)/(N_Axxa^3)or M= (dxxN_A xx a^3)/Z`
Substituting these values, we get
`M = (2.8 g cm^(-3) xx 6.022 xx 10^(23) mol^(-3)xx(4xx10^(-8) cm)^3)/4`
or `M =(2.8 xx 6.022 xx 6.4)/4 = 26.98 gmol^(-1)`