Chemistry: The Science in Context (Fifth Edition)
Chemistry: The Science in Context (Fifth Edition)
5th Edition
ISBN: 9780393614046
Author: Thomas R. Gilbert, Rein V. Kirss, Natalie Foster, Stacey Lowery Bretz, Geoffrey Davies
Publisher: W. W. Norton & Company
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 12, Problem 12.30QP

(a)

Interpretation Introduction

Interpretation: The density and the radius of the simple cubic phase of Ca atom is to be calculated.

Concept introduction: In simple cubic crystal structure there is one lattice point on each corner of the cubic unit cell that is there are 8 corners and one lattice point is present at each of the eight corners.

Body centered cubic cell form consists of one lattice point at the center with eight corner lattice points.

Face centered cubic cell form consists of lattice point on all the six faces of the cubic unit cell with eight corner lattice points.

To determine: The density of Ca metal in simple cubic phase.

(a)

Expert Solution
Check Mark

Answer to Problem 12.30QP

Solution

The density of Ca metal in simple cubic phase is 0.809g/cm3_ .

Explanation of Solution

Explanation

The number of atom for simple cubic unit cell, Z is 1 .

The molar mass of Calcium metal, M is, 40.08g/mol .

The value of Avogadro’s number, NA is 6.022×1023atoms .

The standard value of radius of Calcium metal in FCC phase is 231pm .

As 1pm=1010cm

Therefore, the radius of Ca metal will be written as 231×1010cm .

The value of edge length of a simple cubic unit cell is Calculated by the expression,

a=2r

Where,

  • a is the edge of simple unit cell
  • r is the radius

The radius of Calcium atoms (r) is 231×1010cm .

Substitute this value of radius in the edge length expression.

a=2×231×1010cm=462×1010cm

The density of simple unit cell is calculated by the formula,

ρ=Z×Ma3×NA

Where,

  • ρ is the density of the unit cell.
  • Z is the number of atoms present per unit cell.
  • M is the molar mass of the element.
  • a is the edge length of the unit cell.

Substitute the values of Z , M , NA and a in the above formula and Calculate the density of Calcium metal in simple cubic phase.

ρ=Z×Ma3×NA

ρ=1×48.08g/mol9.86×10cm3×6.022×1023mol1=48.08g59.38cm3=0.809g/cm3_

Therefore, The density of Ca metal in simple cubic phase is 0.809g/cm3_ .

Conclusion

The density of Ca metal in simple cubic phase is 0.809g/cm3_ .

(b)

Interpretation Introduction

To determine: The radius of Ca metal in simple cubic phase.

(b)

Expert Solution
Check Mark

Answer to Problem 12.30QP

Solution

The radius of Ca metal in simple cubic phase is 1.86×10-8cm_ .

Explanation of Solution

Explanation

The values of Z , M , and NA will remain the same for Calcium metal in simple cubic phase as above.

The standard value of density of Ca metal in FCC is 1.55g/cm3

The value of edge length of a simple cubic unit cell is Calculated by the expression,

a=2r

Where,

  • a is the edge of simple unit cell.
  • r is the radius.

The density of simple unit cell is Calculated by the formula,

ρ=Z×Ma3×NA

Where,

  • ρ is the density of the unit cell.
  • Z is the number of atoms present per unit cell.
  • M is the molar mass of the element.
  • a is the edge length of the unit cell.

Substitute the values of Z , M , NA and a in the above formula and Calculate the radius of Calcium metal in simple cubic phase.

ρ=Z×Ma3×NA1.55g/cm3=1×48.08g/mol(2r)3×6.022×1023mol1r3=48.08g8×1.55g/cm3×6.022×1023r=1.86×10-8cm_

Therefore, the radius of Ca metal in simple cubic phase is 1.86×10-8cm_ .

Conclusion

The radius of Ca metal in simple cubic phase is 1.86×10-8cm_ .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 12 Solutions

Chemistry: The Science in Context (Fifth Edition)

Ch. 12 - Prob. 12.3VPCh. 12 - Prob. 12.4VPCh. 12 - Prob. 12.5VPCh. 12 - Prob. 12.6VPCh. 12 - Prob. 12.7VPCh. 12 - Prob. 12.8VPCh. 12 - Prob. 12.9VPCh. 12 - Prob. 12.10VPCh. 12 - Prob. 12.11VPCh. 12 - Prob. 12.12VPCh. 12 - Prob. 12.13VPCh. 12 - Prob. 12.14VPCh. 12 - Prob. 12.15VPCh. 12 - Prob. 12.16VPCh. 12 - Prob. 12.17QPCh. 12 - Prob. 12.18QPCh. 12 - Prob. 12.19QPCh. 12 - Prob. 12.20QPCh. 12 - Prob. 12.21QPCh. 12 - Prob. 12.22QPCh. 12 - Prob. 12.23QPCh. 12 - Prob. 12.24QPCh. 12 - Prob. 12.25QPCh. 12 - Prob. 12.26QPCh. 12 - Prob. 12.27QPCh. 12 - Prob. 12.28QPCh. 12 - Prob. 12.29QPCh. 12 - Prob. 12.30QPCh. 12 - Prob. 12.31QPCh. 12 - Prob. 12.32QPCh. 12 - Prob. 12.33QPCh. 12 - Prob. 12.34QPCh. 12 - Prob. 12.35QPCh. 12 - Prob. 12.36QPCh. 12 - Prob. 12.37QPCh. 12 - Prob. 12.38QPCh. 12 - Prob. 12.39QPCh. 12 - Prob. 12.40QPCh. 12 - Prob. 12.41QPCh. 12 - Prob. 12.42QPCh. 12 - Prob. 12.43QPCh. 12 - Prob. 12.44QPCh. 12 - Prob. 12.45QPCh. 12 - Prob. 12.46QPCh. 12 - Prob. 12.47QPCh. 12 - Prob. 12.48QPCh. 12 - Prob. 12.49QPCh. 12 - Prob. 12.50QPCh. 12 - Prob. 12.51QPCh. 12 - Prob. 12.52QPCh. 12 - Prob. 12.53QPCh. 12 - Prob. 12.54QPCh. 12 - Prob. 12.55QPCh. 12 - Prob. 12.56QPCh. 12 - Prob. 12.57QPCh. 12 - Prob. 12.58QPCh. 12 - Prob. 12.59QPCh. 12 - Prob. 12.60QPCh. 12 - Prob. 12.61QPCh. 12 - Prob. 12.62QPCh. 12 - Prob. 12.63QPCh. 12 - Prob. 12.64QPCh. 12 - Prob. 12.65QPCh. 12 - Prob. 12.66QPCh. 12 - Prob. 12.67QPCh. 12 - Prob. 12.68QPCh. 12 - Prob. 12.69QPCh. 12 - Prob. 12.70QPCh. 12 - Prob. 12.71QPCh. 12 - Prob. 12.72QPCh. 12 - Prob. 12.73QPCh. 12 - Prob. 12.74QPCh. 12 - Prob. 12.75QPCh. 12 - Prob. 12.76QPCh. 12 - Prob. 12.77QPCh. 12 - Prob. 12.78QPCh. 12 - Prob. 12.79QPCh. 12 - Prob. 12.80QPCh. 12 - Prob. 12.81QPCh. 12 - Prob. 12.82QPCh. 12 - Prob. 12.83QPCh. 12 - Prob. 12.84QPCh. 12 - Prob. 12.85QPCh. 12 - Prob. 12.86QPCh. 12 - Prob. 12.87QPCh. 12 - Prob. 12.88QPCh. 12 - Prob. 12.89APCh. 12 - Prob. 12.90APCh. 12 - Prob. 12.91APCh. 12 - Prob. 12.92APCh. 12 - Prob. 12.93APCh. 12 - Prob. 12.94APCh. 12 - Prob. 12.95APCh. 12 - Prob. 12.96APCh. 12 - Prob. 12.97APCh. 12 - Prob. 12.98APCh. 12 - Prob. 12.99APCh. 12 - Prob. 12.100APCh. 12 - Prob. 12.101APCh. 12 - Prob. 12.102APCh. 12 - Prob. 12.103APCh. 12 - Prob. 12.104APCh. 12 - Prob. 12.105APCh. 12 - Prob. 12.106APCh. 12 - Prob. 12.107APCh. 12 - Prob. 12.108APCh. 12 - Prob. 12.109APCh. 12 - Prob. 12.110AP
Knowledge Booster
Background pattern image
Chemistry
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Text book image
Chemistry
Chemistry
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Cengage Learning
Text book image
Chemistry
Chemistry
ISBN:9781259911156
Author:Raymond Chang Dr., Jason Overby Professor
Publisher:McGraw-Hill Education
Text book image
Principles of Instrumental Analysis
Chemistry
ISBN:9781305577213
Author:Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:Cengage Learning
Text book image
Organic Chemistry
Chemistry
ISBN:9780078021558
Author:Janice Gorzynski Smith Dr.
Publisher:McGraw-Hill Education
Text book image
Chemistry: Principles and Reactions
Chemistry
ISBN:9781305079373
Author:William L. Masterton, Cecile N. Hurley
Publisher:Cengage Learning
Text book image
Elementary Principles of Chemical Processes, Bind...
Chemistry
ISBN:9781118431221
Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:WILEY
Unit Cell Chemistry Simple Cubic, Body Centered Cubic, Face Centered Cubic Crystal Lattice Structu; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=HCWwRh5CXYU;License: Standard YouTube License, CC-BY