An ionic compound crystallizes in a rock salt type structure. The sum of the ionic radii of the cation and the anion is 250 pm . If the density of the crystal is 3.2 g cm ⁻³ , the molar mass of the ionic compound is ________ g mol ⁻¹ . (Given: N_A = 6.0 10²³ mol ⁻¹ )

Step-by-step solution

For a rock salt (FCC) structure, the edge length a is related to the sum of the cationic and anionic radii by: a = 2(r_+ + r_-) Given that (r_+ + r_-) = 250 pm : a = 2 250 pm = 500 pm = 5 10⁻⁸ cm The number of formula units per unit cell for a rock salt structure is Z = 4 . The density is given by: d = Z M N_A a^3 Rearranging for molar mass M : M = d N_A a^3 Z Substituting the given values: M = 3.2 6.0 10²³ (5 10⁻⁸)^3 4 M = 3.2 6.0 10²³ 125 10⁻²⁴ 4 M = 3.2 6.0 12.5 4 M = 0.8 75 = 60 g mol ⁻¹ The molar mass of the i