An ionic compound MX crystallizes in a rock-salt lattice. The molar mass of the compound is 48 g mol ⁻¹ and its density is 5.0 g cm ⁻³ . The shortest distance between two M ^+ ions in the lattice is x 2 10⁻¹⁰ m. The value of x is _________. (Given : N_A = 6.0 10²³ mol ⁻¹ )

Step-by-step solution

For a rock-salt (NaCl type) lattice, the effective number of formula units per unit cell is Z = 4 . Using the density formula: d = Z M N_A a^3 Substitute the given values to find the volume of the unit cell, a^3 : 5.0 = 4 48 6.0 10²³ a^3 a^3 = 192 30 10²³ = 6.4 10⁻²³ cm ^3 = 64 10⁻²⁴ cm ^3 Taking the cube root gives the edge length a : a = 4 10⁻⁸ cm = 4 10⁻¹⁰ m In a rock-salt lattice, the cations ( M ^+ ) form a face-centered cubic (FCC) sub-lattice. The shortest distance between two identical ions (next-nearest ne