Question

Pyrolusite is a mineral containing manganese ions and oxide ions. Its structure can best be described as a body-centered cubic array of manganese ions with two oxide ions inside the unit cell and two oxide ions each on two faces of the cubic unit cell. What is the charge on the manganese ions in pyrolusite?

Short answer

In pyrolusite, the unit cell contains 1 manganese ion and 3 oxide ions. The total charge contributed by the oxide ions is -6. For the unit cell to be electrically neutral, the charge on the manganese ions must balance the negative charge from the oxide ions. Solving for the charge on the manganese ions, we find that the charge is +6.

Step-by-step solution

Identify the number of ions in the unit cell

We are given that pyrolusite has a body-centered cubic (BCC) array of manganese ions, with two oxide ions inside the unit cell and two oxide ions on each of two faces of the cubic unit cell. A BCC unit cell has one ion at the center and one-eighth of an ion at each of the eight corners. Thus, there is one manganese ion per unit cell in total. For the oxide ions, there are two inside the unit cell and two on each of two faces. Since a face-centered ion contributes half to the unit cell, there are in total: 2 (inside the unit cell) + 2 * 1/2 (on faces) = 3 oxide ions per unit cell.

Determine the total charge contributed by the oxide ions

Oxide ions (O^ 2-) have a charge of -2. Therefore, the total charge contributed by the 3 oxide ions is: Total charge of oxide ions = 3 * (-2) = -6

Find the charge on the manganese ions for charge balance

For the unit cell to be electrically neutral, the positive charge contributed by the manganese ions must balance the negative charge contributed by the oxide ions. Let x be the charge on the manganese ion: Manganese charge + Oxide charge = 0 x * (number of manganese ions) + (-6) * (number of oxide ions) = 0 x * 1 + (-6) * 3 = 0

Solve for the charge on the manganese ions

Now we can solve this equation for x: x - 6 = 0 x = +6 Therefore, the charge on the manganese ions in pyrolusite is +6.