Chemistry (AP Edition)
Chemistry (AP Edition)
9th Edition
ISBN: 9781133611103
Author: Steven S. Zumdahl, Susan A. Zumdahl
Publisher: Brooks Cole
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 10, Problem 55E

You are given a small bar of an unknown metal X. You find the density of the metal to be 10.5 g/cm3. An X-ray diffraction experiment measures the edge of the face-centered cubic unit cell as 4.09 Å (1 Å = 10−10 m). Identify X.

Expert Solution & Answer
Check Mark
Interpretation Introduction

Interpretation:

            A metal has to be identified given its density and edge length of FCC unit cell.

Concept introduction:

            In crystalline solids, the components are packed in regular pattern and neatly stacked. The components are imagined as spheres and closely packed. This phenomenon is called “close packing” in crystals. The two major types of close packing of the spheres in the crystal are – hexagonal close packing and cubic close packing. Cubic close packing structure has face-centered cubic (FCC) unit cell.

           In face-centered cubic unit cell, each of the six corners is occupied by every single atom. Each face of the cube is occupied by one atom.

           Each atom in the corner is shared by eight unit cells and each atom in the face is shared by two unit cells. Thus the number of atoms per unit cell in FCC unit cell is,

                     8×18atomsincorners+6×12atomsinfaces=1+3=4atoms   The edge length of one unit cell is given bya=2R2where  a=edgelength of unit cellR=atomicradius.

Answer to Problem 55E

Answer

           The metal is identified as “Silver”.

Explanation of Solution

Explanation

Calculate the volume of unit cell of unknown metal.

givendata:edgelength,a=4.09×10-10mvolume,a3=(4.09×10-10m)3=6.84×10-23cm3

             Density of the titanium is given and mass of the titanium is calculated in the previous step. Substituting these two values in the equation density=massvolume and rearranging it, volume of the unit cell is obtained.

Calculate the mass of unit cell of unknown metal.

knowndata: density = 10.5 g/cm3volume=6.84×10-23cm3density=massvolumemass=volume×density=6.84×10-23cm3×10.5g/cm3massofaunitcell=71.82×10-23g

             Density of the unit cell is given. The mass of unit cell is calculated using the equation density=massvolume.The values are substituted and the equation is rearranged to obtain the mass value.

Calculate the atomic mass of unknown metal.

Average mass of one metal atom=massofunitcell4=71.82×10-234=17.95×10-23g  atomicmassofmetal=Average mass of one metal atom×Avogadronumber=17.95×10-23×6.022×1023=108.09u

            In FCC unit cell of a metal, each unit cell has 4 metal atoms. So each metal atom has an average mass of 1/4th of the mass of unit cell. The atomic mass of a metal atom corresponds to the Avogadro number of the average mass of a metal atom.

Identify the metal corresponding to the atomic mass calculated.

            The identified metal is “Silver”.

             Platinum is the metal that possibly matches best with the calculated atomic mass.

Conclusion

Conclusion

           Density and edge length of FCC unit cell of a metal is given and it is identified as “Silver”.

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!
Students have asked these similar questions
reaction scheme for C39H4202 Hydrogenation of Alkyne (Alkyne to Alkene) show reaction (drawing) please
Give detailed mechanism Solution with explanation needed. Don't give Ai generated solution
Show work with explanation needed....don't give Ai generated solution

Chapter 10 Solutions

Chemistry (AP Edition)

Ch. 10 - It is possible to balance a paper clip on the...Ch. 10 - Consider a sealed container half-filled with...Ch. 10 - Explain the following: You add 100 mL water to a...Ch. 10 - Prob. 4ALQCh. 10 - Prob. 5ALQCh. 10 - Why do liquids have a vapor pressure? Do all...Ch. 10 - Prob. 7ALQCh. 10 - What is the vapor pressure of water at 100C? How...Ch. 10 - Prob. 9ALQCh. 10 - Prob. 10ALQCh. 10 - Prob. 11ALQCh. 10 - In the diagram below, which lines represent the...Ch. 10 - Prob. 14QCh. 10 - Atoms are assumed to touch in closest packed...Ch. 10 - Define critical temperature and critical pressure....Ch. 10 - Use the kinetic molecular theory to explain why a...Ch. 10 - Prob. 18QCh. 10 - Prob. 19QCh. 10 - Describe what is meant by a dynamic equilibrium in...Ch. 10 - Prob. 21QCh. 10 - Prob. 22QCh. 10 - Prob. 23QCh. 10 - Prob. 24QCh. 10 - When wet laundry is hung on a clothesline on a...Ch. 10 - You have three covalent compounds with three very...Ch. 10 - Prob. 28QCh. 10 - Compare and contrast the structures of the...Ch. 10 - Silicon carbide (SiC) is an extremely hard...Ch. 10 - How could you tell experimentally if TiO2 is an...Ch. 10 - A common prank on college campuses is to switch...Ch. 10 - A plot of In (Pvap) versus 1/T (K) is linear with...Ch. 10 - Prob. 34QCh. 10 - Identify the most important types of interparticle...Ch. 10 - Prob. 36ECh. 10 - Predict which substance in each of the following...Ch. 10 - Consider the compounds CI2, HCI. F2, NaF, and HF....Ch. 10 - Prob. 39ECh. 10 - Consider the following electrostatic potential...Ch. 10 - In each of the following groups of substances,...Ch. 10 - Prob. 42ECh. 10 - The shape of the meniscus of water in a glass tube...Ch. 10 - Prob. 44ECh. 10 - Hydrogen peroxide (H2O2) is a syrupy liquid with a...Ch. 10 - Carbon diselenide (CSe2) is a liquid at room...Ch. 10 - X rays from a copper X-ray tube ( = 154 pm) were...Ch. 10 - The second-order diffraction (n = 2) for a gold...Ch. 10 - A topaz crystal has an interplanar spacing (d) of...Ch. 10 - X rays of wavelength 2.63 were used to analyze a...Ch. 10 - Calcium has a cubic closest packed structure as a...Ch. 10 - Nickel has a face-centered cubic unit cell. The...Ch. 10 - A certain form of lead has a cubic closest packed...Ch. 10 - Prob. 54ECh. 10 - You are given a small bar of an unknown metal X....Ch. 10 - A metallic solid with atoms in a face-centered...Ch. 10 - Titanium metal has a body-centered cubic unit...Ch. 10 - Barium has a body-centered cubic structure. If the...Ch. 10 - The radius of gold is 144 pm, and the density is...Ch. 10 - The radius of tungsten is 137 pm and the density...Ch. 10 - What fraction of the total volume of a cubic...Ch. 10 - Iron has a density of 7.86 g/cm3 and crystallizes...Ch. 10 - Prob. 63ECh. 10 - Prob. 64ECh. 10 - Selenium is a semiconductor used in photocopying...Ch. 10 - Prob. 66ECh. 10 - Prob. 67ECh. 10 - Prob. 68ECh. 10 - The structures of some common crystalline...Ch. 10 - The unit cell for nickel arsenide is shown below....Ch. 10 - Cobalt fluoride crystallizes in a closest packed...Ch. 10 - The compounds Na2O, CdS, and ZrI4. all can be...Ch. 10 - What is the formula for the compound that...Ch. 10 - Prob. 74ECh. 10 - A certain metal fluoride crystallizes in such a...Ch. 10 - Prob. 76ECh. 10 - The unit cell of MgO is shown below l Does MgO...Ch. 10 - In solid KCl the smallest distance between the...Ch. 10 - The CsCl structure is a simple cubic array of...Ch. 10 - MnO has either the NaCI type structure or the CsCI...Ch. 10 - What type of solid will each of the following...Ch. 10 - What type of solid will each of the following...Ch. 10 - The memory metal, nitinol, is an alloy of nickel...Ch. 10 - Superalloys have been made of nickel and aluminum....Ch. 10 - Perovskite is a mineral containing calcium,...Ch. 10 - A mineral crystallizes in a cubic closest packed...Ch. 10 - Materials containing the elements Y, Ba, Cu, and O...Ch. 10 - The structures of another class of ceramic,...Ch. 10 - Plot the following data and determine Hvap for...Ch. 10 - From the following data for liquid nitric acid,...Ch. 10 - In Breckenridge, Colorado, the typical atmospheric...Ch. 10 - The temperature inside a pressure cooker is 115C....Ch. 10 - Carbon tetrachloride, CCl4, has a vapor pressure...Ch. 10 - Diethyl ether (CH3CH2OCH2CH3) was one of the first...Ch. 10 - A substance, X, has the following properties:...Ch. 10 - Use the heating-cooling curve below to answer the...Ch. 10 - The molar heat of fusion of sodium metal is 2.60...Ch. 10 - Prob. 98ECh. 10 - What quantity of energy does it take to convert...Ch. 10 - Consider a 75.0-g sample of H2O(g) at 125C. What...Ch. 10 - An ice cube tray contains enough water at 22.0C to...Ch. 10 - A 0.250-g chunk of sodium metal is cautiously...Ch. 10 - Prob. 103ECh. 10 - Prob. 104ECh. 10 - Prob. 105ECh. 10 - Prob. 106ECh. 10 - Prob. 107ECh. 10 - Consider the following data for xenon: Triple...Ch. 10 - Some of the physical properties of H2O and D2O are...Ch. 10 - Rationalize the following boiling points:Ch. 10 - Consider the following vapor pressure versus...Ch. 10 - Consider the following enthalpy changes:...Ch. 10 - Prob. 113AECh. 10 - Boron nitride (BN) exists in two forms. The first...Ch. 10 - Prob. 115AECh. 10 - Argon has a cubic closest packed structure as a...Ch. 10 - Prob. 117AECh. 10 - A 20.0-g sample of ice at 10.0C is mixed with...Ch. 10 - In regions with dry climates, evaporative coolers...Ch. 10 - Which of the following compound(s) exhibit only...Ch. 10 - Which of the following statements about...Ch. 10 - Prob. 123CWPCh. 10 - Aluminum has an atomic radius of 143 pm and forms...Ch. 10 - Pyrolusite is a mineral containing manganese ions...Ch. 10 - The structure of the compound K2O is best...Ch. 10 - Prob. 127CWPCh. 10 - Some ice cubes at 0c with a total mass of 403 g...Ch. 10 - The enthalpy of vaporization for acetone is 32.0...Ch. 10 - Prob. 130CWPCh. 10 - When I mole of benzene is vaporized at a constant...Ch. 10 - You and a friend each synthesize a compound with...Ch. 10 - Prob. 133CPCh. 10 - Prob. 134CPCh. 10 - Consider two different organic compounds, each...Ch. 10 - Rationalize the differences in physical properties...Ch. 10 - Prob. 137CPCh. 10 - Some ionic compounds contain a mixture of...Ch. 10 - Some ionic compounds contain a mixture of...Ch. 10 - Spinel is a mineral that contains 37.9% aluminum,...Ch. 10 - Mn crystallizes in the same type of cubic unit...Ch. 10 - You are asked to help set up a historical display...Ch. 10 - Some water is placed in a sealed glass container...Ch. 10 - The molar enthalpy of vaporization of water at 373...Ch. 10 - Prob. 145CPCh. 10 - Rubidium chloride has the sodium chloride...Ch. 10 - Prob. 147IPCh. 10 - A metal burns in air at 600c under high pressure...Ch. 10 - Prob. 149IPCh. 10 - General Zod has sold Lex Luthor what Zod claims to...
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: Principles and Practice
    Chemistry
    ISBN:9780534420123
    Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
    Publisher:Cengage Learning
    Text book image
    Principles of Modern Chemistry
    Chemistry
    ISBN:9781305079113
    Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
    Publisher:Cengage Learning
    Text book image
    Chemistry
    Chemistry
    ISBN:9781305957404
    Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
    Publisher:Cengage Learning
  • Text book image
    Chemistry: The Molecular Science
    Chemistry
    ISBN:9781285199047
    Author:John W. Moore, Conrad L. Stanitski
    Publisher:Cengage Learning
    Text book image
    Chemistry & Chemical Reactivity
    Chemistry
    ISBN:9781337399074
    Author:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
    Publisher:Cengage Learning
    Text book image
    Chemistry by OpenStax (2015-05-04)
    Chemistry
    ISBN:9781938168390
    Author:Klaus Theopold, Richard H Langley, Paul Flowers, William R. Robinson, Mark Blaser
    Publisher:OpenStax
Text book image
Chemistry: Principles and Practice
Chemistry
ISBN:9780534420123
Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Publisher:Cengage Learning
Text book image
Principles of Modern Chemistry
Chemistry
ISBN:9781305079113
Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Publisher:Cengage Learning
Text book image
Chemistry
Chemistry
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Cengage Learning
Text book image
Chemistry: The Molecular Science
Chemistry
ISBN:9781285199047
Author:John W. Moore, Conrad L. Stanitski
Publisher:Cengage Learning
Text book image
Chemistry & Chemical Reactivity
Chemistry
ISBN:9781337399074
Author:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher:Cengage Learning
Text book image
Chemistry by OpenStax (2015-05-04)
Chemistry
ISBN:9781938168390
Author:Klaus Theopold, Richard H Langley, Paul Flowers, William R. Robinson, Mark Blaser
Publisher:OpenStax
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