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ANSWER KEY SECOND MIDTERM EXAM Chemistry 465 Professor Buhro

12 April 2011

ANSWER KEY

ANSWER KEY

__________________________________ Signature

__________________________________ Print Name Clearly

ID Number:_______________________ Information. This is a closed-book exam; no books, notes, other students, other student exams, or any other resource materials may be consulted or examined during the exam period. Calculators are permitted. Partial credit will be given for partially correct reasoning in support of incorrect or correct final answers. Additional space for answers is provided at the end of this exam; please clearly label any answers you place there. Please find “Potentially Useful Information” attached as the last pages of this exam.

1.

____________________________ (15 pts)

2.

____________________________ (20 pts)

3.

____________________________ (25 pts)

4.

____________________________ (20 pts)

5.

____________________________ (10 pts)

6.

____________________________ (10 pts)

______________________________________________________

Total ____________________________ (100 pts)

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1. 15 total pts. The compound having the nominal composition CeO2 has the fluorite crystal structure and exhibits good oxide-ion (O2–) conductivity. This compound easily becomes oxygen deficient, and its formula is best described as CeO2-x where x may have the values 0 < x < 0.5. Ionic conductivity data for CeO2-x specimens having different compositions are plotted below. Please answer the questions below. For your reference the ionic radii are r(Ce3+) = 1.28 Å, r(Ce4+) = 1.11 Å, and r(O2–) = 1.24 Å. The Pauling electronegativities are (Ce) = 1.12 and (O) = 3.44.

CeO1.75

ln 

CeO1.92

1/T (a) 05 pts. The ln  vs. T data for both compounds give linear plots. What conclusion may be drawn from the linearity in these plots? Please explain briefly. –1

Both plots are single, straight lines, indicating that a single conductivity mechanism applies in each case. (b) 05 pts. Please identify the conductivity mechanism or mechanisms active in CeO2-x and provide a brief justification for your answer. The compound is has high ionic character with cations and anions of nearly equal size, and easily becomes oxygen deficient. Thus, anion or oxide-ion vacancy conduction operates. (c) 05 pts. The plots above differ greatly (quantitatively) from one another. Please explain the physical or chemical origin of this difference. CeO1.75 has a higher oxide-vacancy concentration, and consequently shows higher ionic conductivity than does CeO1.92.

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2. 20 total pts. The following description of the alumina-silica (Al2O3-SiO2) phase diagram dates back to the 1960s (it has since been revised). Al2O3 and SiO2 melt at 2060 and 1720 C, respectively. Only one compound forms from alumina and silica, having the composition 3Al2O32SiO2 or Al6Si2O13. This compound is known as “mullite” and it melts congruently at 1850 C. Eutectic points occur at 5 mol % Al2O3 and 1595 C, and at 67 mol % Al2O3 and 1840 C. Please sketch this 1960s-era phase diagram in the space below, and label all regions. (The corrected alumina-silica phase diagram is found in F. J. Klug et al. J. Am. Ceram. Soc. 1987, 70, 750-759.)

L

Al + L

M+L

T (C) L + Si

M+L Al + M M + Si

mol % SiO2

Al2O3

SiO2

“Al” = Al2O3 “M” = mullite, Al6Si2O13 “Si” = SiO2 1 pt. for each correct region label (for a total of 7 such pts.) 13 pts. for correctly drawn diagram; –2 pts. each minor mistake; –5 pts. each major mistake.

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3.

25 total pts. Please consider the Ti–Ni phase diagram shown below and provide the requested information:

(a)

01 pt. Please identify each line compound on the diagram by writing its formula below. TiNi3 (1 pt.); no credit if additional compounds are listed.

(b)

04 pts. Please identify each congruent melting point on the diagram by writing its temperature and the corresponding component composition below. 1310 C – 50% Ni 1380 C – 75% Ni (2 pts. each. –1 pt for each additional incorrect answer. The mps for pure Ti and Ni may also be listed.)

(c)

05 pts. Please identify each phase that forms solid solutions by writing its (nominal) formula below. -Ti, -Ti, Ti2Ni, TiNi, Ni (1 pt. each)

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(d)

03 pts. Please identify each eutectic point on the diagram by writing its temperature and the corresponding component composition below. 942 C – 24% Ni 1118 C – 61% Ni 1304 C – 83% Ni (1 pt. each correct answer; –1 pt. each incorrect answer.)

(e)

03 pts. Please identify the peritectic point on the diagram by writing its temperature and the corresponding component composition below. Please indicate if this peritectic point is also an incongruent melting point. 984C – 33% Ni (2 pts.; –1 pt. for extra answers) Yes, this is an incongruent melting point (1 pt.)

(f)

04 pts. Assume that a liquid having a component composition of Ti:Ni = 30:70 is cooled infinitely slowly from 1600 oC to 1000 oC. Please give the component composition, the phase composition, and the composition(s) of the phase(s) present in the specimen at 1000 o C. component composition: phase composition: TiNi composition: TiNi3 composition:

(g)

30% Ti, 70% Ni ~20% TiNi, ~80% TiNi3 ~45% Ti, ~55% Ni 25% Ti, 75% Ni

(1 pt.) (1 pt.) (1 pt.) (1 pt.)

05 pts. Now assume that the same liquid (as in part f) having a component composition of Ti:Ni = 30:70 is cooled at a normal cooling rate from 1600 oC to 1000 oC. Please sketch the microstructure of the specimen at 1000 oC. Please be sure to clearly label all phases and microconstituents that are present. primary TiNi3 microconstituent

(–2 pts. for incorrect labels)

TiNi3

TiNi

eutectic microconstituent

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4. 20 total pts. The Madelung constant A for the NaCl structure is 1.75. Here you will calculate the Madelung constants for three small fragments of (clusters from) the NaCl structure in (a)(c) below. Assume that the nearest cation-anion separations in these clusters are the same as in a NaCl crystal. Please show your work, and then answer the following questions. (a) 05 pts. Determine A for a cluster consisting of one anion and one cation: 1 or 1.00 (5 pts.) A = ___________

–

+

Vcoul = (1)(–1)e2/(d) (0 pts.) A = –[(1)(–1)] = 1 (0 pts.) (b) 05 pts. Determine A for a cluster consisting of two anions and two cations positioned at the vertices of a square: –

+ 1.29 (0 pts.) A = ___________ –

+

A = 2 – 1/21/2 = 1.29

(5 pts.)

(c) 05 pts. Determine A for a cluster consisting of four anions and four cations positioned at the vertices of a cube:

–

+

+

– +

– 1.46 (0 pts.) A = ___________ +

–

A = 3 – 3/21/2 + 1/31/2 = 1.46

(5 pts.)

(d) 05 pts. Why is NaCl normally found as an extended, nonmolecular crystal lattice rather than as small molecular clusters like those shown above? Please explain briefly. The Madelung constants for molecular clusters of NaCl are less than 1.75 (2 pts.). Consequently, NaCl maximizes its lattice energy by forming a nonmolecular crystal lattice (3 pts.)

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5. 10 total pts. The compound formed when graphite is fully intercalated with elemental K has the formula KC8. The XRD pattern in the region of the 004 reflection (2 = 16.56º) of KC8 is shown below. KC8 can be de-intercalated by heating, which expels and vaporizes the K. The XRD pattern undergoes changes as this process occurs, as described below. The experiment considered here was discontinued before all of the K was removed. 3

2

1

1 pt. each for first four correct labels.

Intensity (a.u.)

5 4

4

5

6

7

8

9

10

11

12

13

14 15

16

17

18

Degrees 2-Theta

(a) 03 pts. As the de-intercalation proceeded, the XRD peak at 16.46º 2 gradually disappeared as another peak grew in to a maximum intensity at one of the positions indicated by the vertical lines. This second peak then gradually disappeared as another peak grew in to a maximum intensity at one of the other positions indicated. Eventually peaks had appeared at all the positions marked by the verticals. What process was responsible for this behavior? Please give your answer in a single sentence. This behavior indicates a staged (3 pts.) de-intercalation. (b) 03 pts. Which new peak was the first to appear and which the last to appear as deintercalation proceeded? Please identify these peaks by their 2 values. First new peak = 10.2; last new peak = 4.7; 2 pts. for first correct answer and 1 pt. for the second correct answer

(c) 04 pts. Please provide an appropriate stage label for each vertical in the space above it.

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6. 10 total pts. A and B are metallic elements having fcc crystal structures and the lattice parameters a = 3.52 and 4.95 Å, respectively. A partial A-B phase diagram, for the temperature range below the solidus, is given below. Please determine the lattice parameter(s) of the phase or phases present at state point p. Be sure to show your work.

T (C)

p

0

A

10

20

30

40

50

60

70

mol % B

80

90

100

B

Two solid solutions form at point p. (2 pts. for indicating in any way that two solid solutions exist at point p) A-rich ss = A0.65B0.35 (2 pts.) ass = (0.65)(3.52 Å) + (0.35)(4.95 Å) = 4.02 Å (2 pts.) B-rich ss = A0.36B0.64 (2 pts.) ass = (0.36)(3.52 Å) + (0.64)(4.95 Å) = 4.44 Å (2 pts.)

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