BuyFindarrow_forward

Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Solutions

Chapter
Section
BuyFindarrow_forward

Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

Consider the three types of cubic units cells.

  1. (a) Assuming that the spherical atoms or ions in a primitive cubic unit cell just touch along the cube’s edges, calculate the percentage of occupied space within the unit cell. (Recall that the volume of a sphere is (4/3)πr3, where r is the radius of the sphere.)
  2. (b) Compare the percentage of occupied space in the primitive cell (pc) with the bcc and fcc unit cells. Based on this, will a metal in these three forms have the same or different densities? If different, in which is it most dense? In which is it least dense?

(a)

Interpretation Introduction

Interpretation:

Percentage of occupied space within the unit cell has to be calculated.

Concept introduction:

The packing efficiency can be calculated by the percent of space occupied by spheres present in a unit cell.packing efficiency=volumeoccupiedbythespherespresentinunitcellTotalvolumeoftheunitcell×100

Volume of the cube = a3

Explanation

Calculate the packing efficiency of primitive cell

volumeofthesphere=43Πr3Volume of the cube =(2r)3One unit cell of the simple cubic contains only one atom therefore,volumeoffouratoms=1×43Πr3The packing efficiency can be calculated by the percent of space occupied by spheres present in a unit cell.Packing efficiency=volumeoccupiedbythespherespresentinunitcellTotalvolumeoftheunitcellPacking efficiency=43Πr3(2r)3×100Packing efficiencyofFCC=52.4%

Calculate the packing efficiency of FCC

One unit cell of the fcc contains four atoms therefore,

volumeofthesphere=43Πr3Volume of the cube =(2r2)3One unit cell of the fcc contains four atoms therefore,volumeoffouratoms=43Πr3The packing efficiency can be calculated by the percent of space occupied by spheres present in a unit cell

(b)

Interpretation Introduction

Interpretation:

On comparing the percentage of occupied space in PC with BCC and FCC, most dense and least dense has to be identified.

Concept introduction:

The packing efficiency can be calculated by the percent of space occupied by spheres present in a unit cell.packing efficiency=volumeoccupiedbythespherespresentinunitcellTotalvolumeoftheunitcell×100

Volume of the cube = a3

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Additional Science Solutions

Find more solutions based on key concepts

Show solutions add

Whether from the tap or from a bottle, all water comes from the same sources. T F

Nutrition: Concepts and Controversies - Standalone book (MindTap Course List)

How do eating disorders affect health?

Understanding Nutrition (MindTap Course List)

Define the following terms: a. chromosome b. chromatin

Human Heredity: Principles and Issues (MindTap Course List)

What is ketosis?

Organic And Biological Chemistry