Chemistry: Atoms First
Chemistry: Atoms First
3rd Edition
ISBN: 9781259638138
Author: Julia Burdge, Jason Overby Professor
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 12, Problem 12.123QP

Iron crystallizes in a body-centered cubic lattice. The cell length as determined by X-ray diffraction is 286.7 pm. Given that the density of iron is 7.874 g/cm3, calculate Avogadro’s number.

Expert Solution & Answer
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Interpretation Introduction

Interpretation:

The Avogadro’s number of Iron atom in its body centered cubic lattice has to be calculated.

Concept Introduction:

In packing of atoms in a crystal structure, the atoms are imagined as spheres. The two major types of close packing of the spheres in the crystal are – hexagonal close packing and cubic close packing.  Cubic close packing forms two types of lattices – body – centered lattice and face – centered lattice.

In body-centered cubic unit cell, each of the six corners is occupied by every single atom. Center of the cube is occupied by one atom.  Each atom in the corner is shared by eight unit cells and a single atom in the center of the cube remains unshared.  Thus the number of atoms per unit cell in BCC unit cell is,

8×18atomsincorners+1atomatthecenter=1+1=2atoms       The edge length of one unit cell is given bya=4R3where  a=edge length of unit cellR=radiusofatom.

Answer to Problem 12.123QP

The Avogadro’s number of Barium atom in its body centered cubic lattice is calculated as 6.01×1023atoms/mol.

Explanation of Solution

One mole of Iron has mass of 55.84 g . Density of Iron is given. Volume of one mole of Iron is obtained by the formula

volume=massdensity .

givendata:density=7.874g/cm3density=massvolumevolume of 1 mole of Iron=massof 1 mole of Irondensity=55.84g7.874 g/cm3=7.09cm3

givendata:edgelength,a=286.7pm=286.7×10-12m=5.02×10-10mvolume,a3=(286.7×10-12m)3=2.36×10-23cm3=2.36×10-23cm3

Edge length of the cubic unit cell is given. The cubic value of edge length gives the volume of the unit cell.  In each cell of unit cell of body centered cubic lattice, 2 Iron atoms are occupied.

The Avogadro’s number of Iron atom in one mole of Iron is,

Number of Fe atoms in1mole of Iron  =volumeof1moleofFevolumeof1Feinunitcell=7.09cm32.36 ×10-23cm32=6.01×1023atoms/mol

Dividing the volume of one mole Iron atoms by volume of one mole of Iron atoms in its unit cell gives the Avogadro’s number of Iron atoms in one mole of Iron.

Conclusion

The Avogadro’s number of Iron atom in its body centered cubic lattice has been calculated.

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Chapter 12 Solutions

Chemistry: Atoms First

Ch. 12.3 - The density of sodium metal is 0.971 g/cm3 and the...Ch. 12.3 - Nickel has a face-centered cubic unit cell with an...Ch. 12.3 - A metal crystallizes in a body-centered cubic unit...Ch. 12.4 - How many of each ion are contained within a unit...Ch. 12.4 - Referring to Figure 12.23, determine how many of...Ch. 12.4 - Referring to Figure 12.23, determine how many of...Ch. 12.4 - Prob. 3PPCCh. 12.4 - The edge length of the NaCl unit cell is 564 pm....Ch. 12.4 - Prob. 4PPACh. 12.4 - NiO also adopts the face-centered cubic...Ch. 12.4 - The metal iridium (Ir) crystallizes with a...Ch. 12.4 - Prob. 5PPACh. 12.4 - Copper crystallizes in a face-centered cubic...Ch. 12.4 - Given that the diameter and average mass of a...Ch. 12.5 - (a) Calculate the amount of heat deposited oil the...Ch. 12.5 - Calculate the amount of energy (in kilojoules)...Ch. 12.5 - Determine the final state and temperature of 100 g...Ch. 12.5 - Prob. 6PPCCh. 12.5 - How much energy (in kilojoules) is required to...Ch. 12.5 - Prob. 12.5.2SRCh. 12.6 - Using the following phase diagram, (a) determine...Ch. 12.6 - Use the following phase diagram to (a) determine...Ch. 12.6 - Prob. 7PPBCh. 12.6 - Prob. 7PPCCh. 12.6 - Prob. 12.6.1SRCh. 12.6 - Prob. 12.6.2SRCh. 12 - Prob. 12.1KSPCh. 12 - Prob. 12.2KSPCh. 12 - Prob. 12.3KSPCh. 12 - Prob. 12.4KSPCh. 12 - Explain why liquids, unlike gases, are virtually...Ch. 12 - What is surface tension? What is the relationship...Ch. 12 - Prob. 12.3QPCh. 12 - Prob. 12.4QPCh. 12 - Prob. 12.5QPCh. 12 - Prob. 12.6QPCh. 12 - Prob. 12.7QPCh. 12 - Why does the viscosity of a liquid decrease with...Ch. 12 - Why is ice less dense than water?Ch. 12 - Prob. 12.10QPCh. 12 - Prob. 12.11QPCh. 12 - Prob. 12.12QPCh. 12 - Prob. 12.13QPCh. 12 - Predict which of the following liquids has greater...Ch. 12 - Prob. 12.15QPCh. 12 - Vapor pressure measurements at several different...Ch. 12 - The vapor pressure of liquid X is lower than that...Ch. 12 - Prob. 12.18QPCh. 12 - Prob. 12.19QPCh. 12 - Define the following terms: crystalline solid,...Ch. 12 - Prob. 12.21QPCh. 12 - Classify the solid states in terms of crystal...Ch. 12 - Prob. 12.23QPCh. 12 - Define X-ray diffraction. What are the typical...Ch. 12 - Prob. 12.25QPCh. 12 - What is the coordination number of each sphere in...Ch. 12 - Calculate the number of spheres that would be...Ch. 12 - Prob. 12.28QPCh. 12 - Barium metal crystallizes in a body-centered cubic...Ch. 12 - Prob. 12.30QPCh. 12 - Europium crystallizes in a body-centered cubic...Ch. 12 - Crystalline silicon has a cubic structure. The...Ch. 12 - Prob. 12.33QPCh. 12 - Prob. 12.34QPCh. 12 - Prob. 12.35QPCh. 12 - Prob. 12.36QPCh. 12 - Shown here is a zinc oxide unit cell. What is the...Ch. 12 - Describe and give examples of the following types...Ch. 12 - Prob. 12.39QPCh. 12 - A solid is hard, brittle, and electrically...Ch. 12 - A solid is soft and has a low melting point (below...Ch. 12 - Prob. 12.42QPCh. 12 - Which of the following are molecular solids and...Ch. 12 - Prob. 12.44QPCh. 12 - Prob. 12.45QPCh. 12 - What is a phase change? Name all possible changes...Ch. 12 - What is the equilibrium vapor pressure of a...Ch. 12 - Use any one of the phase changes to explain what...Ch. 12 - Define the following terms: (a) molar heat of...Ch. 12 - Prob. 12.50QPCh. 12 - What can we learn about the intermolecular forces...Ch. 12 - The greater the molar heat of vaporization of a...Ch. 12 - Prob. 12.53QPCh. 12 - A closed container of liquid pentane (bp = 36.1C)...Ch. 12 - What is critical temperature? What is the...Ch. 12 - Prob. 12.56QPCh. 12 - How do the boiling points and melting points of...Ch. 12 - Prob. 12.58QPCh. 12 - Prob. 12.59QPCh. 12 - Prob. 12.60QPCh. 12 - Which of the following phase transitions gives off...Ch. 12 - Prob. 12.62QPCh. 12 - Prob. 12.63QPCh. 12 - Calculate the amount of heat (in kilo joules)...Ch. 12 - Prob. 12.65QPCh. 12 - The molar heats of fusion and sublimation of lead...Ch. 12 - Prob. 12.67QPCh. 12 - How is the rate of evaporation of a liquid...Ch. 12 - Explain why steam at 100C causes more serious bums...Ch. 12 - The following compounds, listed with then- boiling...Ch. 12 - Prob. 12.71QPCh. 12 - Prob. 12.72QPCh. 12 - Explain how waters phase diagram differs from...Ch. 12 - The blades of ice skates are quite thin, so the...Ch. 12 - A length of wire is placed on top of a block of...Ch. 12 - Prob. 12.76QPCh. 12 - A phase diagram of water is shown. Label the...Ch. 12 - Prob. 12.78QPCh. 12 - Prob. 12.79QPCh. 12 - Prob. 12.80QPCh. 12 - Prob. 12.81QPCh. 12 - Prob. 12.82QPCh. 12 - The average distance between base pairs measured...Ch. 12 - A CO2 fire extinguisher is located on the outside...Ch. 12 - What is the vapor pressure of mercury at its...Ch. 12 - Prob. 12.86QPCh. 12 - The liquid-vapor boundary line in the phase...Ch. 12 - Prob. 12.88QPCh. 12 - Prob. 12.89QPCh. 12 - A student is given four solid samples labeled W,...Ch. 12 - Prob. 12.91QPCh. 12 - The diagram shows a kettle of boiling water....Ch. 12 - The south pole of Mars is covered with solid...Ch. 12 - The properties of gases, liquids, and solids...Ch. 12 - The standard enthalpy of formation of gaseous...Ch. 12 - Prob. 12.96QPCh. 12 - Under the same conditions of temperature and...Ch. 12 - The distance between Li+ and Cl is 257 pm in solid...Ch. 12 - Heat of hydration, that is, the heat change that...Ch. 12 - The fluorides of the second period elements and...Ch. 12 - Calculate the H for the following processes at...Ch. 12 - Prob. 12.102QPCh. 12 - Prob. 12.103QPCh. 12 - Ozone (O3) is a strong oxidizing agent that can...Ch. 12 - A sample of limestone (CaCO3) is heated in a...Ch. 12 - Carbon and silicon belong to Group 4A of the...Ch. 12 - Prob. 12.107QPCh. 12 - A 1.20-g sample of water is injected into an...Ch. 12 - What are the advantages of cooking the vegetable...Ch. 12 - A quantitative measure of how efficiently spheres...Ch. 12 - The phase diagram of helium is shown. Helium is...Ch. 12 - The phase diagram of sulfur is shown. (a) How many...Ch. 12 - Prob. 12.113QPCh. 12 - Argon crystallizes in the face-centered cubic...Ch. 12 - Given the phase diagram of carbon, answer the...Ch. 12 - Prob. 12.116QPCh. 12 - Swimming coaches sometimes suggest that a drop of...Ch. 12 - Prob. 12.118QPCh. 12 - Why do citrus growers spray their trees with water...Ch. 12 - Calcium metal crystallizes in a face-centered...Ch. 12 - A student heated a beaker of cold water (on a...Ch. 12 - The compound diclilorodifluoromethane (CCl2F2) has...Ch. 12 - Iron crystallizes in a body-centered cubic...Ch. 12 - Sketch the cooling curves of water from about 110C...Ch. 12 - Prob. 12.125QPCh. 12 - A sampleof water shows the following behavior as...Ch. 12 - A closed vessel of volume 9.6 L contains 2.0 g of...Ch. 12 - The electrical conductance of copper metal...Ch. 12 - Assuming ideal behavior, calculate the density of...Ch. 12 - Explain why drivers are advised to use motor oil...Ch. 12 - Prob. 12.131QPCh. 12 - Silicon used in computer chips must have an...Ch. 12 - Prob. 12.133QP
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