Estimate the density of magnesium oxide from its crystal structure .
The radii of Mg 2+ and O 2 - are 72 and 140 pm, Respectively.

Question

Quizplus · Accepted Answer

Magnesium oxide (MgO) has a cubic close-packed structure. The density (ρ) can be calculated using the formula ρ = Z*M/N_A*V_c, where Z is the number of formula units per unit cell (for MgO, Z=1), M is the molar mass (24.305 + 15.999 = 40.304 g/mol for MgO), N_A is Avogadro's number (6.022 x 10^23 mol^-1), and V_c is the volume of the unit cell. The edge length (a) of the cubic cell can be found by adding the radii of Mg^2+ and O^2- and multiplying by 2√2 (since the ions touch along the face diagonal in a face-centered cubic structure), giving a ≈ 2*(72+140)pm * √2 ≈ 4.24 x 10^-8 cm. Thus, V_c = a^3 ≈ (4.24 x 10^-8 cm)^3. Plugging these values into the density formula gives a density close to 3.58 g/cm^3, which rounds to the provided option closest to this calculation.

Estimate the Density of Magnesium Oxide from Its Crystal Structure