Referring to Figure 11.26, determine the number of each type of ion within the unit cells.

Name: Problem 126, Chapter 11: Chemistry
Uploaded: 2020-07-20T05:20:52-08:00
Duration: 3 min 12 s
Channel: Jake Rempel
Description: Referring to Figure 11.26, determine the number of each type of ion within the unit cells.

Referring to Figure 11.26, determine the number of each type...

Key Concepts

Ionic Crystal Structure

An ionic crystal structure describes the ordered arrangement of cations and anions in a lattice. In such structures, the positions and numbers of different types of ions are critical to maintaining charge neutrality and determining the overall properties of the material. Analyzing the unit cell in an ionic crystal involves accounting for the differing contributions of each ion based on their positions.

Lattice Positions

Lattice positions denote specific locations within the unit cell such as corners, edges, faces, and the center. Each position has a characteristic contribution to the unit cell based on how many neighboring cells share that position. Understanding these positions is key to accurately counting the number of ions in a unit cell.

Fractional Occupancy

Fractional occupancy refers to the fact that atoms or ions located at the corners, edges, or faces of a unit cell are shared among adjacent cells. For example, an atom at the corner contributes 1/8th of its volume to a single unit cell, while one on a face contributes 1/2. This concept is used to determine the effective number of ions present within one complete unit cell.

Unit Cell

The unit cell is the smallest repeating structural unit of a crystal lattice that, when repeated in three dimensions, recreates the entire crystal. It serves as the basic building block for understanding the crystal structure and determining the arrangement and number of atoms or ions within the solid.

Transcript

00:01 So here i've gone ahead and i've drawn out what each of these different cells we're working with looks like.

00:07 So starting with a, let's take a look at what we have.

00:11 We know that in the center you have the smallest ion, which is going to be our positive ion.

00:17 So that means that our blue ion is going to be one c as positive ion.

00:24 And the black we're working with here, in each corner is going to be our chlorine ions.

00:30 So let's go ahead and count up how many chlorines we have.

00:33 We have one eighth of a chlorine in each corner, and we know we have one, two, three, four, five, six, seven, eight corners on our cube, which eight times one eighth is going to give us one cl minus on this part a.

00:52 Moving on to part b, we see that we're working with four small ions sitting inside, and those ions are going to be our zinc 2 positive.

01:05 So right away, we have 4 zn2 plus, and we know that the zinc we're working with is complete because it's entirely inside the unit cell.

01:18 It's not on one of the edges or a corner, so we know it's going to be a complete atom.

01:23 Now let's go ahead and sum up the rest of the sulfur that we have.

01:30 We know from before that we're going to have eight of these one -eighths sitting on the corners.

01:37 That'll get us one sulfur totaled out of that.

01:42 Then each of these right on the edge is going to be one -half...

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