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( H 0)CH4
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(Cp)CH4 dT 6995 kJ / mol
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7485 HCHO(g, 150 C):
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(Cp)HCHO dT 11115 kJ / mol
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In the last two integrals Cp is substituted from Eq (417) (see below) (see Table 46 for values of coef cients of a, b, and c)
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FIGURE 43 Flow chart of methane oxidation process
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TABLE 46 Molar Heat Capacities of Some Gases
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Cp(J / mol
cT 2
dT 3; T in C a 2910 2884 2900 2895 3611 3346 3428 3431 b 102 1158 000765 02199 04110 4233 06880 4268 5469 c 105 06076 03288 05723 03548 2887 07604 00 0366 d 109 1311 08698 2871 2220 7464 3593 8864 110
Compound Oxygen Hydrogen Nitrogen Carbon monoxide Carbon dioxide Water Methane Formaldehyde
Formula O2 H2 N2 CO CO2 H2O(g) CH4 CH2O
Note: Data shown in this table can also be found in Refs 2 through 5
CO2(150 C):
H ( H 0)CO2(g)
[125Cp(150 C)]
Taking H 0 from Table 92 of Ref 1 and Cp from Table 47, (HCO2)out
3886 kJ / mol
H2O(g, 150 C):
H ( H 0)H2O(g)
125Cp(150 C)
Taking H 0 from Table 91 of Ref 1 and Cp from Table 47,
TABLE 47 Mean Heat Capacities of Combustion Gases
Cp(J / mol T( C) 0 25 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500
C); reference state: Pref Air 2894 2905 2921 2945 2971 2997 3025 3053 3081 3110 3138 3165 3192 3218 3242 3265 3285 O2 2924 2939 2980 3032 3080 3124 3165 3202 3239 3271 3302 3330 3355 3379 3402 3423 3442
1 atm, Tref N2 2903 2906 2916 2932 2952 2974 2998 3024 3051 3079 3107 3134 3162 3188 3213 3237 3258
25 C H2 2884 2884 2886 2890 2895 2903 2912 2923 2935 2948 2963 2978 2994 3012 3029 3047 3066 CO 2900 2906 2923 2947 2972 2999 3027 3056 3085 3114 3142 3170 3197 3223 3247 3269 3289 CO2 3663 3715 3863 4045 4210 4359 4493 4614 4723 4820 4907 4985 5054 5118 5175 5228 5277 H2O 3355 3363 3392 3434 3480 3529 3581 3636 3692 3749 3808 3866 3924 3981 4037 4091 4142
Source: From Felder and Rousseau,7 which in turn was taken from data presented in Himmelblau8
APPLIED CHEMISTRY
23756 kJ / mol
Evaluate H From Eq (411) H
ni Hi
ni Hi
15,300 kJ
For the energy balance, neglecting kinetic energy changes Q H 15,300 kJ
Choice 2 Reference conditions: reactant and product species at T0 in the state r of aggregation for which H 0 is known, and nonreactive species at any convenient temperature (such as the reactor inlet temperature, or the reference temperature of a mean heat capacity table) If these reference conditions are chosen, the enthalpy change for the process may be determined by setting up and lling in a table of inlet and outlet stream component ow rates ni and speci c enthalpies Hi, and calculating H where A nAR
vA 0 nAR H r vA
outlet
niHi
inlet
niHi
(412)
any reactant or product moles of A produced or consumed in the process (not necessarily moles fed or moles present in the product) stoichiometric coef cient of A
Both nAR and vA are positive numbers r If multiple reactions occur, a term of the form nA H 0 / A must be included in Eq (412) for each reaction (Method 1 is generally easier to use in such a case)
Example 43 Simultaneous material and energy balances The ethanol dehydrogenation reaction is carried out with the feed entering at 300 C The feed contains 90 mol % ethanol and the balance acetaldehyde To keep the temperature from dropping too rapidly and hence quenching the reaction at a low conversion, heat is added to the reactor Observe that when the heat addition rate is 5300 kJ per 100 mol of the feed gas, the outlet temperature is 265 C Calculate the fractional conversion of ethanol achieved in the reactor using the heat capacity data given in Tables 46 and 47 A ow chart of the process is shown in Fig 44 Solution Basis: 100 mol feed gas; also, C2H5OH(g) CH3CHO(g)
r H2(g): H 0
6895 kJ / mol
There are three unknowns, and no three material balance equations will enable one to
FIGURE 44 Flow chart of ethanol dehydrogenation process
CHAPTER FOUR
solve for ni, n2, and n3 The problem must be solved by writing and simultaneously solving two material balance equations and an energy balance equation Balance on C: (90)(2) (10)(2) n1 Balance on H: (90)(6) 6n1 Energy balance (at 25 C): Substance C2H5OH(g) CH3CHO(g) H2(g) nin 90 10
Hin
2n1 100
2n2 (1)
(10)(4) 4n2 2n3
6n1 580
2n3 (2)
nout n1 n2 n3
Hout
303 220
264 192 70
n in mol H in kJ / mol
H Cp(T 25): heat capacities from Table 47 The table* provides the following information:
(C2H5OH)inlet:
(0110 kJ / mol
C)(300 C
25 C)
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