The mineral manganosite, manganese(II)oxide, crystallizes in the rock salt structure (the face-centered structure adopted by NaCl)with a density of 5.365 g/cm³. Find the unit cell edge length of manganosite.

Question

Quizplus · Accepted Answer

The density of a crystal is given by:$$ho = \frac{ZM}{a^3N_A}$$where $ho$ is the density, $Z$ is the number of formula units per unit cell, $M$ is the molar mass, $a$ is the unit cell edge length, and $N_A$ is Avogadro's number.For manganosite, $Z = 4$, $M = 86.94 g/mol$, and $ho = 5.365 g/cm^3$. Substituting these values into the equation, we get:$$5.365 g/cm^3 = \frac{4 	imes 86.94 g/mol}{a^3 	imes 6.022 	imes 10^{23} mol^{-1}}$$Solving for $a$, we get:$$a = 444.5 pm$$

The Mineral Manganosite, Manganese(II)oxide, Crystallizes in the Rock Salt Structure