An atomic element crystallizes in a BCC (Body Centered Cubic) lattice, with a = 1 A. If the element has a density of 3 g cm-3. Calculate the molar mass (g/mol) of this element.

Answer 1

In BCC lattice, a = (4R)/√3 and the number atoms in BCC is n = 2.

From here, we can look at this equation for density: ρ = (nA)/(V_CN_A)

Where n is the number of atoms, A is the atomic weight (molar mass), V_C is the volume of the unit cell, and N_A is Avogadro's number

We can replace V_C with a³ and rearrange the equation to get A by itself: A = (ρa³N_A)/n.

When using this equation, we have to be careful with units, so to be consistent, I am converting A to cm and we get the following equation:

A = ((3 g/cm³)(1 * 10^-8 cm)³(6.022 * 10²³ atoms/mol))/(2 atoms) = 0.903 g/mol