Given the following reaction and thermodynamic data, what is a reccomended tempe
ID: 1071563 • Letter: G
Question
Given the following reaction and thermodynamic data, what is a reccomended temperature for a 1 L pilot scale reactor and how long (time) does it take for the reaction to take place?
CH3OCH2CH2CH2OCH2NH2 -> CH3OCH2CH2CH2OH + CH2=NH
Species
CH3OCH2CH2CH2OCH2NH2
CH3OCH2CH2CH2OH
CH2NH
Hf (Kcal/mol)
-91.15
-92.23
19.75
S (cal/mol/K)
118.08
97.18
54.18
300
39.13
29.37
8.92
400
48.84
36.69
10.39
500
56.65
42.77
11.99
600
63.34
48.03
13.47
800
74.69
56.74
15.95
1000
82.87
62.98
17.87
1500
0
0
21.02
Hrxn (Kcal/mol)
Srxn (cal/mol/K)
Grxn (Kcal/mol)
Kp
18.67
33.28
8.69E+03
0.985534268
18.494
32.77367955
5.38E+03
0.993248201
18.292
32.31453957
2.13E+03
0.99785361
18.118
32.00460919
-1.08E+03
1.0009103
17.67
31.31834149
-7.38E+03
1.004656425
17.256
30.84797494
-1.36E+04
1.0068639
43.894
67.11038492
-5.68E+04
1.019230233
Kc
A-forward (sec^-1)
Ea(Kcal/mol)
K-forward (sec^-1)
0.001653304
2.10611E+14
53.09
4.40801E-25
0.001249683
2.80815E+14
52.914
3.42895E-15
0.001004382
3.51018E+14
52.712
3.18437E-09
0.000839549
4.21222E+14
52.538
3.06178E-05
0.000632018
5.61629E+14
52.09
3.295681283
0.000506726
7.02037E+14
51.676
3561.584427
0.000341966
1.05305E+15
78.314
4084.744896
Delta S+c (cal/mol/K)
A-backward (sec^-1)
K-backward (sec^-1)
-24.11856204
45429261.35
9.50818E-32
-23.54895154
59940560.67
7.31917E-22
-23.10712731
74049093.99
6.7176E-16
-22.74613063
87957142.2
6.39344E-12
-22.17652012
114260467
6.70489E-07
-21.73469589
139369642.5
0.000707053
-20.93187498
531011737.2
0.002059767
Species
CH3OCH2CH2CH2OCH2NH2
CH3OCH2CH2CH2OH
CH2NH
Hf (Kcal/mol)
-91.15
-92.23
19.75
S (cal/mol/K)
118.08
97.18
54.18
300
39.13
29.37
8.92
400
48.84
36.69
10.39
500
56.65
42.77
11.99
600
63.34
48.03
13.47
800
74.69
56.74
15.95
1000
82.87
62.98
17.87
1500
0
0
21.02
Explanation / Answer
The data shows that at 1500 degree Kelvin, Kp is the highest ( 1.01923) compared to reaction at all other temperatures. Even the delta G of the recation at 15000 K is most negative ( -5.68E+04) compared to reaction at other temperatures showing that reaction becomes most spontaneous at 1500 K [More negative the delta G - free energy of the reaction is, more spontaneous it is] So 1500 K is the temeprature at which reaction is spontaneous to its maximum
Kp = Kc (RT) n
1.019230233 = 0.000341966 [(0.0821 L-atm/mole * K) (1500)]n
Upon solving =
2980.501667 = (0.0821 * 1500)n
2980.501667 = (123.15)n
log 2980.501667 = log (123.15)
3.474289 = n * log (123.15)
= n * (2.0904)
n = 1.662
So 1.662 moles of product is formed once reaction completes
Rate of forward reaction shows Kf = 4084.744896
meaning 4084.744896 moles of product are formed per second
So, formation of 1.662 moles of product takes (1.662 moles * 4084.744896 moles/sec = 4.0685 * 10-4 seconds)
So it takes 4.0685 * 10-4 seconds for the reaction to get completed.
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