Question

An unknown metal is found to have a density of 19.300 g/cm^3 and to crystallize in a body-centered cubic lattice. The edge of the unit cell is found to be 0.31627 nm.

Calculate the atomic mass of the metal.

Im not sure how to approach this problem...when i tried doing it i got an answer of 3.1*10^-7..but it was hard...can someone please explain how to do this problem

thank you

Answer 1

Convert a in nm to cm.
Then volume of the unit cell is a^3.

mass of unit cell = volume x density
Calculate mass unit cell since you have volume and density. Substitute for mass of unit cell below.

Then mass of the unit cell =
#atoms in unit cell which is 2 x molar mass/6.022E23

a = (3.1627E-8 cm)^3 = about 3E-23 cc but you need to do it more exactly.
mass = volume x density = about 3E-23 cc x 19.3 g/cc = about 6E-22.
Then 6E-22 = 2*molar mass/6.022E-23 = and solve for molar mass. I get something like 180 but you need to do it more accurately. My guess is W.