Answer to Question #72859 in General Chemistry for Deven Stover

Question

A newly discovered element with a molecular weight of 341.6 g/mol crystallizes in a simple cubic arrangement, with the edge of a unit cell having a length d = 377.6 pm. What is the density of this element in g/cm3?

Answer 1

M = 341.6 g/mol

d = 377.6 pm = 377.6·10-12 m = 377.6·100·10-12 cm = 3.78·10-8 cm

V = d3 = (3.78·10-8 cm)3 = 54.01·10-24 cm3

Density = M/Vm

Vm = d3*Zm = d3·Na/n

Density = M·n/ d3·Na = (341.6 g/mol*4)/(54.01·10-24 cm3*6.02*10-23mol-1) = 1366.4 g/mol / 325.14*10-47 cm3* mol-1 = 4.2*1047 g/cm3