Question

The toxic, highly unstable element derium (chemical symbol De) is discovered and is found to have a body-centered cubic unit cell. The radius of a derium atom is 86.906pm and the density of solid derium is 133.8g/cm3 at 25.0°C. a) Calculate the length (in pm) of an edge of the bcc unit cell for derium. 1) b) Calculate the molar mass (in g/mol) of derium. c) As for any cubic unit cell, part of the derium unit cell is empty space. What is the density (in g/cm2) of the empty space within the derium unit cell? d) As noted in part"c", part of the derium unit cell is empty space. What is the density (in 4. g/cm2) of the portion of the derium unit cell that is occupied by atoms?3 Under pressure, derium collapses to a face-centered structure. Assuming no change in the derium atom itself, calculate the length of an edge (in pm) for the fec unit cell of this new form of derium. e)

Answer 1

Given radius of De = 86.406 pm Density = 133.8 g/cm^3 In BCC relation b/w a sr squareroot 3a = 4r a = 4r/squareroot 3 = 4/squareroot 3 times 86.906 = 200.9 pm Density of white cell = rho = n times Atomic mass (gm)/N_A times a^3 n = 2, Atomic mass = ? N_A = 6.022 times 10^23 times 200.9 times 10^-10 cm Atomic mass (g) = rho times N_A times a^3/n = 133.8 times 6.022 times 10^23 times (200.9 times 10^-10)^3/2 = 3.62 times 10^7 times 10^23 times 10^-30 Molar mass = 362 gm/mol Packing efficiency = volume occupied by atoms times 100/Total volume = 2 times 4/3 pi r^3/a^3 times 100 = 2 times 4/3 times 3.14 times (86.906)^3/(200.9)^3 times 100 = 0.67.7 times 100 = 67.7 % % volume occupied by = 67.7 % or 67.7 parts Volume (empty space) = 100 - 67.7 % = 32.3% or 32.3 parts Edge