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ANSWERS TO THE EXERCISES
ANSWERS TO THE EXERCISES
Chapter
1
1.1)
-302.49 kcal/mole of B ^ ,
1.2)
(i)
1.3)
-8878 kcal/100 kg of ore.
1.4)
-6.5 kcal.
1.5)
318.6 kcal.
1.6)
(a)
1.7)
-69.25 k c a l ,
1.8)
-57.98 kcal/mole.
1.9)
-211.9 k c a l ,
1.10)
ΔΗ° = (0.58 χ I O - 3 T 2 - 3.66T - 4 . 1 7 x l 0 5 T " 1 + 59240) c a l . ' 2 H? - H° = 5.335(T-298) + 1 ι Ζ 1 ϋ Ι ° 1 _ (T 2 - 2982) cal/g-atom,
1.11)
I
8940 kg,
(ii)
-4.343 kcal/g of
15285 kg,
-35.79 kcal/mole,
(b)
(iii)
12745 kg.
21.71 kcal/mole.
-66.0 kcal.
-212.85 k c a l .
C.JO
2
Cp = (5.335 + 3 . 7 4 x l O " 3 T ) 1.12)
62.76 kcal/mole,
1.13)
1511 kcal/kg of zinc.
1.14)
-27.85 kcal.
1.15)
328 kcal/kg of scrap.
1.16)
-223.08 kcal/mole of T i 0 2 .
1.17)
-93.17 kcal/mole of MnO.
1.18)
(a)
2031°C,
B^.
(b)
cal/deg/g-atom.
2.549 kcal/mole.
2956 c a l / c u . f t . of exhaust gas.
244
Answers
to the
Exercises
Chapter
2
2.1)
Zero.
2.2)
(a)
ΔΗ = 125,000 c a l , A S = 129.23 cal/deg.
(b)
ΔΗ = 329,000 c a l , AS = 138.33 cal/deg.
2.3)
7.07 cal/deg/mole.
2.4)
0.121 cal/deg/mole, process spontaneous.
2.5)
-79.94 cal/deg.
2.6)
0.35 cal/deg.
2.7)
0.218 cal/deg.
2.8)
245
-16.5 kcal/mole of Mo, 34.5 kcal/mole of Cr, ' not possible to reduce Cr 2 0 3
by W^
2.9)
1420°C.
2.10)
572.5°C.
2.11)
13.5°C.
2.12)
At or above 1472°C.
2.13)
Titanium.
2.14)
Not possible.
2.15)
Copper.
2.16)
Not spontaneous.
3.1)
6.72 cal/deg/mole.
3.2)
7.10 cal/deg/mole.
3.3)
15.43 cal/deg/mole.
3.4)
Valid.
4.1)
99 kcal/mole
4.2)
32.2 kcal/mole.
4.3)
2577°C.
4.4)
27.35 kcal/mole.
Chapter
3
Chapter
4
246
PROBLEMS IN METALLURGICAL THERMODYNAMICS AND KINETICS
(4.5)
269.65°C.
(4.6)
321.0067°C,
(4.7)
3
6.265 xlO" deg/atm.
(4.8)
818°C.
(4.9)
3.732 x l O " 3 °C,
(4.10)
-6.012°C.
(4.11)
0.5210 mm Hg.
320.9933°C.
-0.7463°C.
Chapter
5
(5.1)
AG° = -32,250 + 14.51 T c a l ,
(5.2)
2.711, 1.595, 1.073, 0.7626, 0.5928,
(5.3)
^
(5.4)
1.608xl0'9atm,
(5.5)
1.57.
(5.6)
13.40 atm each.
(5.7)
8.71 x l O " 3 atm.
(5.8)
13.58 atm.
(5.9)
Will not decompose.
(5.10)
Will reduce.
(5.11)
0.78,
(5.12)
7.53 mm Hg. -3 <1.072x10 volume0^ H 2 0, oxidise.
(5.13)
25,840 - 20.89 T e a l ,
-29,016 c a l . ΔΗ° = -8320 c a l ,
3420 c a l .
8.058 x l O " 6 atm.
no.
Chapter 6 (6.1)
92.30 wt« Al, 7.70 wtX Mg.
(6.2)
Ca 2 + = 0.415,
Mg 2 + = 0.079,
Mn 2 + = 0.011,
SiO^-=0.114, 4
P0 3 "= 0.089, 4
AIO 3 " = o
(6.3)
wt« Al
No.of g-atoms
*Zn in 100 g alloy
19.40 0.6314 25.37 0.5479
1.952 2.083
F e 2 + = 0.06, Fe 3 + = 0.02,
0.038, and free 0 2 " = 0.174.
Density at IVolume of Volume per 25°C, g / c . c . pOO g. of g-atom of i a l l o y , c . c . a l l o y , c.c 5.345 4.953
18.71 20.18
9.585 9.692
Answers to the
247
Exercises
Partial molar volume of zinc = 9.15 c.c./mole, of aluminium = 10.35 c.c./mole. -7100 x 2 cal/mole
(6.4)
T^u
=
(6.5)
H^d
= 665 cal/mole
(6.6)
T^r
=
(6.7)
99.77 w « Cu
(6.8)
0.167 wt« Mn.
(6.9)
0.9570.
(6.10)
Will precipitate.
(6.12)
Silica and magnesia.
(6.13)
-16,410 cal/mole.
(6.14)
-26,840 cal/mole.
(6.15)
-9,650 cal/mole.
(6.16)
-17,330 cal/mole.
and H^n
-1830 cal/mole and
and T^n
and ^ .
80.26
and
(7.2)
14.29 mm Hg.
(7.3)
Yes.
(7.4)
( i ) 25.30 c.c. H2
350 cal/mole. =
-1490 cal/mole.
7
88.9 c.c.
and
( i i i ) 21.91 c.c. N2 and
30.98 c.c. N 2 .
and
(ii)
25.30 c.c. W^
(7.5)
0.0195 wtt N2
(7.6)
-73.84 cal/mole.
(7.7)
aFe
(7.8)
-1724
and
-2212 cal/mole.
(7.9)
-2132
and
-840 cal/mole.
(7.10)
1.73 cal/deg/mole
(7.11)
-1040 cal/mole.
=
-7100 (1 - x ) 2 cal/mole.
0.23wt%Ni.
Chapter (7.1)
=
=
partial molar volume
0.002165 wt« Hg.
0.8594.
and
1.32 cal/deg/mole.
25.30 c.c. N 2 ,
248
PROBLEMS IN METALLURGICAL THERMODYNAMICS AND KINETICS
(7.12)
0.5112
(7.13)
0.5448
(7.14)
0.304
(7.15)
(i)
(7.16)
0.4458.
(7.17)
0.0034 wtX.
(7.18)
-2262 c a l .
(7.19)
0.059 wtX.
(7.20)
0.03134 wt«.
2.236 x l 0 ~ 3 mm Hg,
(ii)
4128 mm Hg.
Chapter -8.017 cal/deg
8
(8.1)
-30,800 c a l ,
(8.2)
-51,830 c a l .
(8.3)
-5 k c a l ,
(8.4)
0.6606,
(8.5)
0.65,
(8.6)
0.4253,
(8.7)
5138 cal/mole, -15,616 cal/deg/mole
(8.8)
12,274 c a l .
-18.12 cal/deg, 0.6066,
1.625
0.5576,
and
and
-29.92 kcal 0.5258
and
and -114 cal/mole.
and -5332 cal/mole.
9
moles/c.c./min.
(9.2)
8.243 x l O "
10
(9.3)
299 min,
1.283xIO" 4 s e c ' 1 .
(9.4)
2.
(9·5)
K
=
1650 K.
0.4999.
-1313 cal/mole, 1.551 cal/deg/mole
5.759x10"
0%Si
and
-662 cal/mole.
Chapter (9.1)
-33,310 c a l .
min"1,
°·018
min
4
(9.8)
3.183xl0~ .
(9.9)
29.5 kcal/mole.
(9.10)
5420 cal/mole.
(9.11)
46.5 kcal/mole.
" >
1.374χ1θ" Ί 1 sec" 1 ,
K
1.4% Si
=
°·024
min
5315 years.
~ ·
Tinswers to the
(9.12)
5.3 kcal/mole.
(9.13)
35.53 kcal/mole.
(9.14)
F i r s t order,
(9.15)
0.188% S.
(9.16)
2 . 2 7 8 x l O 2 0 molecules/cm 2 /sec.
(9.17)
1 . 1 8 8 x l 0 4 molecules/cm 2 /sec.
54.9 kcal/mole.
Exercises
249
Chapter
1
1.1)
-302.49 kcal/mole of B ^ ,
1.2)
(i)
1.3)
-8878 kcal/100 kg of ore.
1.4)
-6.5 kcal.
1.5)
318.6 kcal.
1.6)
(a)
1.7)
-69.25 k c a l ,
1.8)
-57.98 kcal/mole.
1.9)
-211.9 k c a l ,
1.10)
ΔΗ° = (0.58 χ I O - 3 T 2 - 3.66T - 4 . 1 7 x l 0 5 T " 1 + 59240) c a l . ' 2 H? - H° = 5.335(T-298) + 1 ι Ζ 1 ϋ Ι ° 1 _ (T 2 - 2982) cal/g-atom,
1.11)
I
8940 kg,
(ii)
-4.343 kcal/g of
15285 kg,
-35.79 kcal/mole,
(b)
(iii)
12745 kg.
21.71 kcal/mole.
-66.0 kcal.
-212.85 k c a l .
C.JO
2
Cp = (5.335 + 3 . 7 4 x l O " 3 T ) 1.12)
62.76 kcal/mole,
1.13)
1511 kcal/kg of zinc.
1.14)
-27.85 kcal.
1.15)
328 kcal/kg of scrap.
1.16)
-223.08 kcal/mole of T i 0 2 .
1.17)
-93.17 kcal/mole of MnO.
1.18)
(a)
2031°C,
B^.
(b)
cal/deg/g-atom.
2.549 kcal/mole.
2956 c a l / c u . f t . of exhaust gas.
244
Answers
to the
Exercises
Chapter
2
2.1)
Zero.
2.2)
(a)
ΔΗ = 125,000 c a l , A S = 129.23 cal/deg.
(b)
ΔΗ = 329,000 c a l , AS = 138.33 cal/deg.
2.3)
7.07 cal/deg/mole.
2.4)
0.121 cal/deg/mole, process spontaneous.
2.5)
-79.94 cal/deg.
2.6)
0.35 cal/deg.
2.7)
0.218 cal/deg.
2.8)
245
-16.5 kcal/mole of Mo, 34.5 kcal/mole of Cr, ' not possible to reduce Cr 2 0 3
by W^
2.9)
1420°C.
2.10)
572.5°C.
2.11)
13.5°C.
2.12)
At or above 1472°C.
2.13)
Titanium.
2.14)
Not possible.
2.15)
Copper.
2.16)
Not spontaneous.
3.1)
6.72 cal/deg/mole.
3.2)
7.10 cal/deg/mole.
3.3)
15.43 cal/deg/mole.
3.4)
Valid.
4.1)
99 kcal/mole
4.2)
32.2 kcal/mole.
4.3)
2577°C.
4.4)
27.35 kcal/mole.
Chapter
3
Chapter
4
246
PROBLEMS IN METALLURGICAL THERMODYNAMICS AND KINETICS
(4.5)
269.65°C.
(4.6)
321.0067°C,
(4.7)
3
6.265 xlO" deg/atm.
(4.8)
818°C.
(4.9)
3.732 x l O " 3 °C,
(4.10)
-6.012°C.
(4.11)
0.5210 mm Hg.
320.9933°C.
-0.7463°C.
Chapter
5
(5.1)
AG° = -32,250 + 14.51 T c a l ,
(5.2)
2.711, 1.595, 1.073, 0.7626, 0.5928,
(5.3)
^
(5.4)
1.608xl0'9atm,
(5.5)
1.57.
(5.6)
13.40 atm each.
(5.7)
8.71 x l O " 3 atm.
(5.8)
13.58 atm.
(5.9)
Will not decompose.
(5.10)
Will reduce.
(5.11)
0.78,
(5.12)
7.53 mm Hg. -3 <1.072x10 volume0^ H 2 0, oxidise.
(5.13)
25,840 - 20.89 T e a l ,
-29,016 c a l . ΔΗ° = -8320 c a l ,
3420 c a l .
8.058 x l O " 6 atm.
no.
Chapter 6 (6.1)
92.30 wt« Al, 7.70 wtX Mg.
(6.2)
Ca 2 + = 0.415,
Mg 2 + = 0.079,
Mn 2 + = 0.011,
SiO^-=0.114, 4
P0 3 "= 0.089, 4
AIO 3 " = o
(6.3)
wt« Al
No.of g-atoms
*Zn in 100 g alloy
19.40 0.6314 25.37 0.5479
1.952 2.083
F e 2 + = 0.06, Fe 3 + = 0.02,
0.038, and free 0 2 " = 0.174.
Density at IVolume of Volume per 25°C, g / c . c . pOO g. of g-atom of i a l l o y , c . c . a l l o y , c.c 5.345 4.953
18.71 20.18
9.585 9.692
Answers to the
247
Exercises
Partial molar volume of zinc = 9.15 c.c./mole, of aluminium = 10.35 c.c./mole. -7100 x 2 cal/mole
(6.4)
T^u
=
(6.5)
H^d
= 665 cal/mole
(6.6)
T^r
=
(6.7)
99.77 w « Cu
(6.8)
0.167 wt« Mn.
(6.9)
0.9570.
(6.10)
Will precipitate.
(6.12)
Silica and magnesia.
(6.13)
-16,410 cal/mole.
(6.14)
-26,840 cal/mole.
(6.15)
-9,650 cal/mole.
(6.16)
-17,330 cal/mole.
and H^n
-1830 cal/mole and
and T^n
and ^ .
80.26
and
(7.2)
14.29 mm Hg.
(7.3)
Yes.
(7.4)
( i ) 25.30 c.c. H2
350 cal/mole. =
-1490 cal/mole.
7
88.9 c.c.
and
( i i i ) 21.91 c.c. N2 and
30.98 c.c. N 2 .
and
(ii)
25.30 c.c. W^
(7.5)
0.0195 wtt N2
(7.6)
-73.84 cal/mole.
(7.7)
aFe
(7.8)
-1724
and
-2212 cal/mole.
(7.9)
-2132
and
-840 cal/mole.
(7.10)
1.73 cal/deg/mole
(7.11)
-1040 cal/mole.
=
-7100 (1 - x ) 2 cal/mole.
0.23wt%Ni.
Chapter (7.1)
=
=
partial molar volume
0.002165 wt« Hg.
0.8594.
and
1.32 cal/deg/mole.
25.30 c.c. N 2 ,
248
PROBLEMS IN METALLURGICAL THERMODYNAMICS AND KINETICS
(7.12)
0.5112
(7.13)
0.5448
(7.14)
0.304
(7.15)
(i)
(7.16)
0.4458.
(7.17)
0.0034 wtX.
(7.18)
-2262 c a l .
(7.19)
0.059 wtX.
(7.20)
0.03134 wt«.
2.236 x l 0 ~ 3 mm Hg,
(ii)
4128 mm Hg.
Chapter -8.017 cal/deg
8
(8.1)
-30,800 c a l ,
(8.2)
-51,830 c a l .
(8.3)
-5 k c a l ,
(8.4)
0.6606,
(8.5)
0.65,
(8.6)
0.4253,
(8.7)
5138 cal/mole, -15,616 cal/deg/mole
(8.8)
12,274 c a l .
-18.12 cal/deg, 0.6066,
1.625
0.5576,
and
and
-29.92 kcal 0.5258
and
and -114 cal/mole.
and -5332 cal/mole.
9
moles/c.c./min.
(9.2)
8.243 x l O "
10
(9.3)
299 min,
1.283xIO" 4 s e c ' 1 .
(9.4)
2.
(9·5)
K
=
1650 K.
0.4999.
-1313 cal/mole, 1.551 cal/deg/mole
5.759x10"
0%Si
and
-662 cal/mole.
Chapter (9.1)
-33,310 c a l .
min"1,
°·018
min
4
(9.8)
3.183xl0~ .
(9.9)
29.5 kcal/mole.
(9.10)
5420 cal/mole.
(9.11)
46.5 kcal/mole.
" >
1.374χ1θ" Ί 1 sec" 1 ,
K
1.4% Si
=
°·024
min
5315 years.
~ ·
Tinswers to the
(9.12)
5.3 kcal/mole.
(9.13)
35.53 kcal/mole.
(9.14)
F i r s t order,
(9.15)
0.188% S.
(9.16)
2 . 2 7 8 x l O 2 0 molecules/cm 2 /sec.
(9.17)
1 . 1 8 8 x l 0 4 molecules/cm 2 /sec.
54.9 kcal/mole.
Exercises
249