PROPRIETARY MATERIAL
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τ2.256=TτT0
:= T 1202.8 K=
Ans.
T 1705.4degF=
4.3 Assume air at the
g
iven conditions an ideal
g
as. Basis of calculation is 1 second
.
P 1 atm:= T0122 degF:= V 250 ft3
:= T 932 degF:=
Convert given values to SI units V 7.079 m3
=
T T 32degF( ) 273.15K+:= T0T032degF
()
273.15K+:=
T 773.15 K=T0323.15 K=
nPV
RT
0
:= n 266.985 mol=
For air: A 3.355:= B 0.575 10 3
:= C 0.0:= D 0.016105
:=
H R ICPH T0T,A,B,C,D,
()
:=
τ3:= (guess) Given
QnRAT
0
⋅τ1
()
B
2T02
⋅τ
21
()
+
C
3T03
⋅τ
31
()
+
=
τFind τ
()
:= τ 2.652=TτT0
:= T 1413.8 K=Ans.
τFind τ
()
:=
77
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Given T2T1
P2
P1
R
CP
=CPFind CP
()
:= CP56.95 J
mol K
=Ans.
Hncalc RT
n
1.092 ln Pc
bar
1.013
0.930 Trn
:= Hncalc 30.108 kJ
mol
=Ans.
H 13.707 kJ
mol
=QnH:=
Q 3.469 103
×BTU=Ans.
H R ICPH T0T,A,B,C,D,
()
:=
H 9.441 104
×J
mol
=QnH:= Q 9.4315 106
×kJ=Ans.
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To compare with the value listed in Table B.2, calculate the % error.
%error
Hncalc Hn
Hn
:= %error 3.464 %=
PROPRIETARY MATERIAL
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The ln P vs. 1/T relation over a short range is very nearly linear. Our
procedure is therefore to take 5 points, including the point at the
temperature of interest and two points on either side, and to do a linear
least-squares fit, from which the required derivative in Eq. (4.11) can be
found. Temperatures are in rankines, pressures in psia, volumes in cu
ft/lbm, and enthalpies in Btu/lbm. The molar mass M of tetrafluoroethane is
102.04. The factor 5.4039 converts energy units from (psia)(cu ft) to Btu.
4.10
The values calculated with Eq. (4.13) are within 2% of the handbook values.
%error
0.072
0.052
0.814
1.781
%=
H2
26.429
31.549
33.847
32.242
kJ
mol
=
Ans.
H2calc
26.448
31.533
33.571
32.816
kJ
mol
=
%error
H2calc H2
H2
⎯⎯⎯⎯
:=
Eq. (4.13)
H2calc H1
1T
r2
1T
r1
0.38
⎯⎯⎯⎯⎯⎯⎯
:=
H2
26.429
31.549
33.847
32.242
kJ
mol
=Tr1
0.658
0.673
0.628
0.631
=
H1Hn
:=H2H25 M
()
⎯⎯
:=Tr2
25 273.15+()K
Tc
:=Tr1
Tn
Tc
:=
M
72.150
86.177
78.114
82.145
gm
mol
:=H25
366.3
366.1
433.3
392.5
J
gm
:=Tn
36.0
68.7
80.0
80.7
273.15+
K:=
Hn
25.79
28.85
30.72
29.97
kJ
mol
:=Pc
33.70
30.25
48.98
43.50
bar:=
Tc
469.7
507.6
562.2
560.4
K:=
b)
80
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H 85.817=85.834()
(c) H 81.034=81.136()
(d) H 76.007=75.902()
(e) H 69.863=69.969()
4.11
M
119.377
32.042
153.822
gm
mol
:= Tc
536.4
512.6
556.4
K:= Pc
54.72
80.97
45.60
bar:= Tn
334.3
337.9
349.8
K:=
Hexp is the given
value at the normal
boiling point.
H is the value at
0 degC. Tr1
273.15K
Tc
:= Tr2
Tn
Tc
:=
(a) T 459.67 5+:= ∆V 1.934 0.012:= i15..:=
Data: P
18.787
21.162
23.767
26.617
29.726
:= t
5
0
5
10
15
:= xi
1
ti459.67+
:= yiln Pi
()
:=
slope slope x y,():= slope 4952=
dPdT
P()
3
T2slope:= dPdT 0.545=
HTVdPdT
5.4039
:= ∆H 90.078=Ans.
The remaining parts of the problem are worked in exactly the same
way. All answers are as follows, with the Table 9.1 value in ( ):
(a) H 90.078=90.111()
(b)
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Pr0.022=Pr
P
Pc
:=Tr0.648=Tr
Tn
Tc
:=
Hn29.1 kJ
mol
:=P 1atm:=Tn329.4K:=Vc209 cm3
mol
:=
Zc0.233:=Pc47.01bar:=Tc508.2K:=ω 0.307:=
Acetone4.12
PCE
0.34
8.72
0.96
%=
Hn
247.7
1195.3
192.3
J
gm
=
PCE
0.77
4.03
0.52
%=
Hn
245
1055.2
193.2
J
gm
=
This is the % error
PCE
HnHexp
Hexp
100%
⎯⎯⎯⎯⎯⎯⎯
:=
HnH1T
r2
1T
r1
0.38
⎯⎯⎯⎯⎯⎯
:=
(a) By Eq. (4.13)
Tr2
0.623
0.659
0.629
=
Tr1
0.509
0.533
0.491
=
Hexp
246.9
1099.5
194.2
J
gm
:=H
270.9
1189.5
217.8
J
gm
:=
82
PROPRIETARY MATERIAL
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C 228.060:=B 2756.22:=A 14.3145:=
V 2.602 104
×cm3
mol
=VVV
sat
:=
HTVB
TC+()
2
e
AB
TC+()
=
gives
Psat e
AB
TC+
=
with Antoine’s Equation
HTV
T
Psat
d
d
=
Combining the Clapyeron equation (4.11)
Vsat 70.917 cm3
mol
=
Eq. (3.72)
Vsat VcZc
1T
r
()
2
7
:=
Liquid Volume
V 2.609 104
×cm3
mol
=VZRTn
P
:=
(Pg. 102)
Z 0.965=Z1B
0
Pr
Tr
B1
Pr
Tr
+:=
Eq. (3.66)
B10.924=B10.139 0.172
Tr4.2
:=
Eq. (3.65)
B00.762=
B00.083 0.422
Tr1.6
:=
Vapor Volume
Generalized Correlations to estimate volumes
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Hcalc TnVB
Tn273.15K
KC+
2e
AB
Tn273.15K
KC+
kPa
K
:=
Hcalc 29.662 kJ
mol
=Ans. %error
Hcalc Hn
Hn
:= %error 1.9 %=
Acetic Acid 37.6 58.7%
Acetonitrile 31.3 3.5%
Benzene 30.8 0.2%
iso-Butane 21.2 -0.7%
n-Butane 22.4 0.0%
1-Butanol 43.5 0.6%
n-Pentane 25.9 0.2%
Phenol 45.9 -0.6%
1-Pro
p
anol 41.9 1.1%
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p
2-Propanol 40.5 1.7%
Toluene 33.3 0.5%
Water 41.5 2.0%
o-Xylene 36.7 1.2%
m-Xylene 36.2 1.4%
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Q 1.372 103
×kW=Ans.
(b) Benzene: Hv28.273 kJ
mol
=H 55.296 kJ
mol
=Q 1.536 103kW=
(c) Toluene Hv30.625 kJ
mol
=H 65.586 kJ
mol
=Q 1.822 103kW=
4.15 Benzene Tc562.2K:= Pc48.98bar:= Tn353.2K:=
T1sat 451.7K:= T2sat 358.7K:= Cp162 J
mol K
:=
CPV T() A
V
BV
KT+ CV
K2T2
+
R:=
P 3bar:= Tsat 368.0K:= T1300K:= T2500K:=
H
T1
Tsat
TCPL T()
dHv
+
Tsat
T2
TCPV T()
d+:= ∆H 49.38 kJ
mol
=
n 100 kmol
hr
:= QnH:=
86
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HvHn
1T
r
1T
rn
0.38
:= Hv6.638 kJ
mol
=
Hf227480 J
mol
:= ∆H298 HfHv
:= ∆H298 220.8 kJ
mol
=Ans.
Estimate Hv using Riedel equation (4.12) and Watson correction (4.13)
Trn
Tn
Tc
:= Trn 0.628=Tr2sat
T2sat
Tc
:= Tr2sat 0.638=
Hn
1.092 ln Pc
bar
1.013
0.930 Trn
RTn
:= ∆Hn30.588 kJ
mol
=
HvHn
1T
r2sat
1T
rn
0.38
:= Hv30.28 kJ
mol
=
Assume the throttling process is adiabatic and isenthalpic.
Guess vapor fraction (x): x 0.5:=
Given CpT1sat T2sat
()
xHv
=x Find x():= x 0.498=Ans.
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or dQ CPdTRdTRdT
1δ
+=
which reduces to dQ CPdTδ
1δRdT+=
or dQ CP
R
δ
1δ
+
RdT=(C)
Since CP is linear in T, the mean heat capacity is the value of
CP at the arithmetic mean temperature. Thus Tam 675:=
(b) For 1,3-butadiene: H298 88.5 kJ
mol
=
(c) For ethylbenzene: H298 12.3kJ
mol
=
(d) For n-hexane: H298 198.6kJ
mol
=
(e) For styrene: H298 103.9 kJ
mol
=
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Parts (a) – (d) can be worked exactly as Example 4.7. However, with
Mathcad capable of doing the iteration, it is simpler to proceed differently.
H298 2 241818()2 393509()+ 52510[]
J
mol
:=
C2H4 + 3O2 = 2CO2 + 2H2O(g)4.19
Comparison is on the basis of equal numbers of C atoms.
Ans.
H298 3=770,012 J,H298 3770012=
H298 6 393509()6 241818()+ 41950():=
For the combustion of 1-hexene:
C6H12(g) + 9O2(g) = 6CO2(g) + 6H2O(g)
Ans.
H298 4=058,910 J,
For 6 MeOH:
H298 676485=
Ans.
P211.45 bar=P2P1
T2
T1
δ
δ1
:=P11 bar:=
Ans.
Q 6477.5 J
mol
=QCPm
R
δ
1δ
+
RT2T1
()
:=
δ1.55:=T1400 K:=T2950 K:=
Integrate (C):
CPm R 3.85 0.57 10 3
Tam
+
()
:=
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τFind τ
()
:= τ 8.497=TT
0τ:= T 2533.5 K=Ans.
(b) nO20.75=nn214.107=T 2198.6 K=Ans.
(c) nO21.5=nn216.929=T 1950.9 K=Ans.
(d) nO23.0=nn222.571=T 1609.2 K=Ans.
Index the product species with the numbers:
1 = oxygen
2 = carbon dioxide
3 = water (g)
4 = nitrogen
(a) For the product species, no excess air:
n
0
2
2
11.286
:= A
3.639
5.457
3.470
3.280
:= B
0.506
1.045
1.450
0.593
10 3
K
:= D
0.227
1.157
0.121
0.040
105
K2
:=
i14..:= A
i
niAi
()
:= B
i
niBi
()
:= D
i
niDi
()
:=
A 54.872=B 0.012 1
K
=D 1.621105
×K2
=
For the products, HPR
T0
T
T
CP
R
d=T0298.15K:=
The integral is given by Eq. (4.7). Moreover, by an energy balance,
H298 HP
+0=
τ2:= (guess)
Given H298
RAT
0
⋅τ1
()
B
2T02
⋅τ
21
()
+ D
T0
τ1
τ
+
=
90
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Ans.
T 2282.5 K K=TT
0K⋅τ:=τ 7.656=τ Find τ
()
:=
H298
−∆Hair
RAT
0
⋅τ1
()
B
2T02
⋅τ
21
()
+
D
T0
τ1
τ
+
=
Given
(guess)
τ2:=
D 1.735105
×K2
=B 0.016 1
K
=A 78.84=
D
i
niDi
()
:=
B
i
niBi
()
:=
A
i
niAi
()
:=
D
0.227
1.157
0.121
0.040
105
K2
:=
B
0.506
1.045
1.450
0.593
10 3
K
:=A
3.639
5.457
3.470
3.280
:=
n
1.5
2
2
16.929
:=
H298 Hair
+∆HP
+0=
The energy balance here gives:
Hair 309399J
mol
=
Hair 21.429 8.3143.65606298.15 773.15()J
mol
:=
MCPH 773.15 298.15,3.355,0.575 10 3
, 0.0,0.016105
,
()
3.65606=
For one mole of air:
Hair MCPH 298.15 773.15()=
Hair H298
+∆HP
+0=
(e) 50% xs air preheated to 500 degC. For this process,
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4.20 n-C5H12 + 8O2 = 5CO2 + 6H2O(l)
By Eq. (4.15) with data from Table C.4:
H298 5 393509()6 285830()+ 146760():=
H298 3=535,765 J, Ans.
(b) -905,468 J
(c) -71,660 J
(d) -61,980 J
(e) -367,582 J
(f) -2,732,016 J
(g) -105,140 J
(h) -38,292 J
(i) 164,647 J
(j) -48,969 J
(k) -149,728 J
(l) -1,036,036 J
(m) 207,436 J
(o) 178,321 J
(p) -132,439 J
(q) -44,370 J
(r) -68,910 J
(s) -492,640 J
(t) 109,780 J
(u) 235,030 J
(v) -132,038 J
(w) -1,807,968 J
(x) 42,720 J
(y) 117,440 J
(z) 175,305 J
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4.22 The solution to each of these problems is exactly like that shown in
Example 4.6. In each case the value of Ho
298 is calculated in Problem
4.21. Results are given in the following table. In the first column the
letter in ( ) indicates the part of problem 4.21 appropriate to the Ho
298
value.
T/K A 103 B 106 C 10-5 D IDCPH/J HoT/J
(a) 873.15 –5.871 4.181 0.000 -0.661 -17,575 -109,795
(b) 773.15 1.861 -3.394 0.000 2.661 4,729 -900,739
(f) 923.15 6.048 9.779 0.000 7.972 15,635 2,716,381
(i) 973.15 9.811 9.248 2.106 1.067 25,229 189,876
(j) 583.15 -9.523 11.355 -3.450 1.029 -10,949 -59,918
(l) 683.15 -0.441 0.004 0.000 -0.643 -2,416 -1,038,452
(m) 850.00 4.575 -2.323 0.000 -0.776 13,467 220,903
(t) 733.15 4.016 4.422 0.991 0.083 7,424 117,204
(u) 750.00 7.297 -9.285 2.520 0.166 12,172 247,202
(v) 900.00 2.418 3.647 0.991 0.235 3,534 -128,504
(w) 673.15 2.586 -4.189 0.000 1.586 4,184 1,803,784
(x) 648.15 0.060 0.173 0.000 -0.191 125 42,845
(y) 1083.15 4.175 -4.766 1.814 0.083 12,188 129,628
(g) –3.629 8.816 -4.904 0.114
(h) –9.987 20.061 -9.296 1.178
(k) 1.704 -3.997 1.573 0.234
(z) -3.858 -1.042 0.180 0.919
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HcCH4 890649J
mol
=
Ans.
n HigherHeatingValue5dollar
GJ
7.985 105
×dollar
day
=
n 1.793 108
×mol
day
=nq
P
RT
:=
Assuming methane is an ideal gas at standard conditions:
4.24 q 150 106
ft3
day
:= T6032()
5
9K273.15K+:= T 288.71 K=P 1atm:=
The higher heating value is the negative of the heat of combustion with water
as liquid product.
Calculate methane standard heat of combustion with water as liquid product:
CH4 + 2O2 –> CO2 +2H2O
Standard Heats of Formation:
HfCH4 74520J
mol
:= ∆HfO2 0J
mol
:=
HfCO2 393509J
mol
:= ∆HfH2Oliq 285830J
mol
:=
HcHfCO2 2HfH2Oliq
+∆HfCH4
2HfO2
:=
HigherHeatingValue Hc
:= ∆Hc8.906105
×J
mol
=
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0.85 HcCH4
0.07 HcC2H6
+ 0.03 HcC3H8
+ 932.875kJ
mol
=
c)
Gas b) has the highest standard heat of combustion. Ans.
.
N2(g)+2H2(g)+C(s)+1/2O2(g)=(NH2)2CO(s)
H298 Hf1 Hf2
+∆H+:= ∆H298 333509J=Ans.
Calculate ethane standard heat of combustion with water as liquid product:
Standard Heats of Formation:C2H6 + 7/2O2 –> 2CO2 +3H2O
HfC2H6 83820J
mol
:=
HcC2H6 2HfCO2 3HfH2Oliq
+∆HfC2H6
7
2HfO2
:=
HcC2H6 1560688J
mol
=
0.95 HcCH4
0.02 HcC2H6
+ 0.02 HcC3H8
+ 921.714kJ
mol
=
a)
0.90 HcCH4
0.05 HcC2H6
+ 0.03 HcC3H8
+ 946.194kJ
mol
=
b)
95
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