Problem 125 - Chemistry An Atoms First Approach

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?

Step-by-Step Solution

Answer

The charge on the manganese ions in pyrolusite is +6, making them Mn^6+ ions.

Step 1: Analyze the structure of pyrolusite

According to the problem, pyrolusite has a body-centered cubic (BCC) structure of manganese ions surrounded by two oxide ions inside the unit cell and two oxide ions each on two faces of the cubic unit cell. This means there are 1 ion in the center, and 8 corner ions which are shared by 8 surrounding cells, resulting in an equivalent of one complete manganese ion per unit cell. (1/8 * 8)

Step 2: Determine the number of oxide ions inside the unit cell

The problem states that there are two oxide ions inside the unit cell, so there are exactly two O^2- ions.

Step 3: Determine the number of oxide ions on the faces of the unit cell

There are two oxide ions on each of two faces of the cubic unit cell. As each face-sharing ion is shared between two adjacent cells, we have two half ions per face. In total, we get a contribution of one complete oxide ion coming from the faces. Thus, there are 2 interior oxide ions + 1 face oxide ion = 3 complete oxide ions.

Step 4: Calculate the charge balance

To maintain the charge balance in the mineral, the total charge of manganese ions must equal the negative charge from the oxide ions. Let's denote the charge of manganese ion as Mn^x+. So, 1 Mn^x+ ion should balance the charge with 3 O^2- ions: Mn^x+ = 3 O^2-

Step 5: Determine the charge on manganese ions

From the charge balance equation in Step 4, we get: Mn^x+ = 3 * (-2) = -6 Since the charge on the manganese ions is positive, we can write: x = 6 So the charge on the manganese ions in pyrolusite is +6. The manganese ions in pyrolusite are Mn^6+ ions.