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.

Question

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.