Question

An element crystallizes in a f.c.c. lattice with cell edge of 250 pm. Calculate the density if 300 g of this element contain `2 xx 10^(24)` atoms.

Answer 1

Calculation for the molar mass of element
Mass of `2 xx 10^(24)` atoms = 300g
Mass of `6.022 xx 10^(23)` atoms = `(300)/(2 xx 10^(24)) xx 6.022 xx 10^(23)`
`= 15 xx 6.022 g`
Density `rho = (Z xx M)/(a^(3) xx Na)` (Z = 4 for fcc)
`rho = (4 xx 15 xx 6.022)/((250 xx 10^(-10))^(3) xx 6.022 xx 10^(23)) = 38.4 g//cm^(3)`