Question

Determine the density (in g/cm3) of an AX ionic compound in which the ionic radii and atomic weights of the cation and anion are given below: (answer fromt X.XX) cation: radius = 0.098 nm A = 44 g/mol anion: radius = 0.165 nm A = 53.4 g/mol Hint: Compute the cation to anion radius ratio to predict the coordination number of the ions. Remember that knowing the coordination number allows us to predict the crystal structure. Given the ratio of radii, I determined the coordination number to be 6 which means the unit cell is an octahedral. The problem is I don't know how to determine the number of atoms contained within the unit cell to calculate the mass for the density equation. Any help would be greatly appreciated.

Answer 1

Radius ratio = radius of cation/radius of anion = 0.098/0.165 = 0.59; which lies in the range 0.414 - 0.732, the range for rock salt(NaCl type) structure.

Hence each unit cell of the given compound contains 4 cations and 4 anions, i.e., No of formula units per unit cell(z) = 4.

Formula mass of the compound(M) = (44+53.4) g/mol = 97.4 g/mol.