Advanced Inorganic Chemistry

Test 3

Name:  ________________________                                                                        April 19, 2017

81 possible

3.1.   (4 pts)  Draw a three-dimensional sketch of the rock salt (NaCl) lattice.  Distinguish Na+ from Cl in your sketch.

 

figure 3-04

 

2.   (2 pts)  Name the type of centering that the unit cell on the right has.

body-centered

 

 

3.   (5 pts) Sketch a projection diagram for the structure of polonium, shown below.

      An oblique view of the simple cubic unit cell        Projection diagram of the unit cell

4.   (2 pts)  Which type of lattice does the figure on the right represent?  In this figure, all the spheres represent the same element.  The colors show the relation between layers.  ____________________

Hexagonal closest packed (hcp)

 

5.   (3 pts)  In closest packed structures, if the number of spheres is n, then the number of octahedral holes is _______, n

      and the number of tetrahedral holes is _______.  2n

6.   (2 pts)  Carbon steel is quite hard.  Is carbon steel more likely to be a substitutional or an interstitial alloy?

interstitial

This page:  18 pts

7.   (8 pts)  Models of wurtzite (the white and yellow balls) and fluorite (the red and white balls) are in the classroom. 

For wurtzite, which type of closest packed lattice is formed by the yellow balls? 

hcp

For wurtzite, which type of hole is occupied by the white balls?

tetrahedral

For fluorite, which type of lattice is formed by the red balls? 

          primitive

For fluorite, which type of hole is occupied by the white balls?

cubic

8.   (2 pts)  Which is apt to be more soluble in water, NH4F or NH4I?  The radii of the ions are:  NH4+, 151 pm; F-, 131 pm; I-, 206 pm.

NH4I.  The difference in sizes between anion and cation is larger for this compound.

9.   (7 pts)  On the right is the unit cell of perovskite.  ” is a calcium ion, “” is a titanium ion, and “” is an oxygen ion.  How many of each atom are in this unit cell?  What is the formula of perovskite?

 

CaTiO3 2 pts for the 1, 1, & 3; 1 pt for formula

 

 

 

 

This page:  17 pts


 

10. (6 pts)  Sketch the band structure for a p-type extrinsic semiconductor.

figure 3-60

(4 pts)  Explain how conductivity occurs in this material.

As the temperature increases, electrons move from the filled band into the acceptor band, producing holes in the previously filled band, which, being partially filled, can now conduct. 

(3 pts)  Explain what causes the change in conductivity as the temperature is raised.

As the temperature is raised, more electrons move to the acceptor band, leaving more holes, which results in greater conductivity.

11. (14 pts)      Use the following data to construct a Born-Haber cycle.  Show a graph of the cycle, and calculate the enthalpy change for the reaction Mg(s) + Br2(l) ® MgBr2(s).

 

Mg(s) à Mg(g)

Datomization

147.12 kJ/mol

1st ionization energy of Mg

 

737.7 kJ/mol

2nd ionization energy of Mg

 

1450.7 kJ/mol

½ Br2(l) ® Br(g)

Datomization

111.86 kJ/mol

e + Br(g) ® Br(g)

Delectron gain

-324.54 kJ/mol

MgBr2(s) ® Mg2+(g) + 2Br(g)

Dlattice

2202 kJ/mol

Here are my calculations, from a spreadsheet.

Mg(s) ® Mg(g)

Df(298 K)

147.1

147.1

Mg(g) ® Mg2+(g) + 2e(g)

Dionization

2200.8

I1, I2, … I7

737.7

1450.7

Br2(l) ® 2Br(g)

Df(298 K)

223.7

111.86

2e(g) + 2Br(g) ® 2Br(g)

Delectron gain

-661.5

EA1, 2, 3, & 4

324.536

 

Mg2+(g) + 2Br(g) ® MgBr2(s)

-Dlattice

-2201.9

 

 

 

Mg(s) + Br2(l) ® MgBr2(s)

DHformation

-291.7

kJ/mol

And here’s the graph of the data (a little fancier than necessary).    3 pts for graph

This page:  27 pts


 

12. (14 pts)      Determine the lattice enthalpy of LiF from the data below.  (Use the radius ratio to select the best Madelung constant.) 

; ; d* = 34.5 pm

Note:  the sizes of ions for all different possible coordination numbers are not available.  If the coordination number you need is not provided, use the closest value available.

 

 

 

Ionic Radii / pm

 

 

Charge

C.N.

Spin

r / pm

Li

-1

6

 

244

 

+1

4

 

59

 

 

6

 

76

 

 

8

 

92

 

F

-1

2

 

129

 

 

3

 

130

 

 

4

 

131

 

 

6

 

133

 

Madelung Constant, A

 

 

 

radius ratio

 

A

C. N.

min

max

Sphalerite (ZnS)

1.638

(4, 4)

0.225

0.414

Rock Salt (NaCl)

1.748

(6, 6)

0.414

0.73

Cesium Chloride (CsCl)

1.763

(8, 8)

0.73

--

 

Here are the formulas, from the first page:

; ; d* = 34.5 pm

z+ = +1; z= -1.  d is the sum of radii.  Let’s start with a coordination number of 6 (got to start somewhere).  The radius ratio is 76/133 = 0.57, which is consistent with the rock salt structure.  That gives d = 209 pm.  Putting all these values into the equation gives V = -970 kJ/mol

1.13. (5 pts)  Arrange in order of increasing lattice energy:  MgO, NaCl, and LiF.  Give your reasoning.  (No calculations needed.)

                                          NaCl < LiF < MgO

Lithium and fluoride ions are both smaller than sodium and chloride ions, so the LiF lattice would be expected to be “harder” than the NaCl lattice. 

MgO has a 2+ cation and anion.  The lattice enthalpy would be four times “greater” (more negative, which makes it confusing) than for a hypothetical crystal of Mg+O-, if the ions were the same size.  Although Mg2+ and O2-‑ ions are larger than Li+ and Cl- ions, which would make the crystal “softer”, the size difference is unlikely to overcome the 4-fold increase in lattice strength due to having +2 and –2 charges on the ions.

This page:  19 pts