A compound forms bcc unit cell with edge length 400 pm. Determine the molar mass of the compound if the density of compound is 3.5 g cm ⁻³ [ N_A = 6.022 10²³ ]

Step-by-step solution

The formula for the density of a unit cell is given by: d = Z M N_A a^3 For a bcc unit cell, the number of atoms per unit cell is Z = 2 . Given: d = 3.5 g cm ⁻³ a = 400 pm = 4 10⁻⁸ cm N_A = 6.022 10²³ mol ⁻¹ Rearranging the formula to solve for molar mass M : M = d N_A a^3 Z Substituting the given values: M = 3.5 6.022 10²³ (4 10⁻⁸)^3 2 M = 3.5 6.022 10²³ 64 10⁻²⁴ 2 M = 3.5 6.022 6.4 2 M = 67.4464 g mol ⁻¹ Rounding to one decimal place, M 67.4 g mol ⁻¹ . Answer: 67.4 g mol ⁻¹