Fundamentals of Chemical Reaction Engineering
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Transcript of Fundamentals of Chemical Reaction Engineering
Fundamentals_of_Chemical_Reaction_Engineering-Kingdwarf/Fundamentals of Chemical Reaction Engineering/davissmch01.docChapter 1
Exercise 1:
At equilibrium:
[1 atm]-1
(1)
Assuming ideal behavior,
(2)
(3)
(4)
Using equations (2), (3), and (4), solve for the three unknown mole fractions and find the fractional conversion of propane at each temperature.
(5)
Or an Alternate Solution:
Write a mole balance for the reaction.
(Where fA = fractional conversion of propane)
Initial MolesChange in MolesFinal Moles
AnAo-nAo fAnAo (1 fA)
B0nAo fAnAo (fA)
C0nAo fAnAo (fA)
TotalnAonAo fAnAo (1 + fA)
Express the mole fraction of each species in terms of fA.
(6)
(7)
(8)
Substitute equations (6), (7), and (8) into equation (2), above, and solve for fractional conversion (fA).
(9)
@ 400o C@ 500o C@ 600o C
Conversion (fA)0.02280.10120.3076
Exercise 2:
Assume 100% conversion of propane at each temperature, because the equilibrium constants are so high. A major impediment is the oxidation of propane to CO2 (not shown).
Exercise 3:
Part a)
Express the equilibrium constants for each step in terms of partial pressures.
(1)
(2)
(3)
Rewrite equation (3) in terms of K1 and K2.
(4)
Therefore, K3 = 0.108.
Part b)
Check the independence of the 3 reactions.
For all 3 equations.
(5)
And
Therefore, all equations are not independent (i.e. only need 2 equations to solve).
Assuming a basis of 1 mole of 1-butene, write a mole balance for the system.
Initial MolesChangeFinal Moles
A1-1-31-1-3
B011
C033
Total101
Rewrite equations (1) and (3) in terms of 1 and 2.
(6)
(7)
Solving for 1 and 3 gives an equilibrium conversion of 1-butene = 0.932.
Mole fractions at equilibrium:
X1-butene = 0.068
Xcis-2-butene = 0.296
Xtrans-2-butene = 0.636
Exercise 4:
First, find K for each reaction from (Go, using equation (1), assuming ideal behavior.
(1)
ReactionG0 (kJ mol-1)1.1.1 K
114.850.078
210.420.167
315.060.075
Write a mole balance on the system of reactions, assuming a basis of 1 mole toluene.
Initial MolesChangeFinal Moles
Toluene (A)1-21-22-231-21-22-23
Ortho-Xylene (B)011
Meta-Xylene (C)022
Para-Xylene (D)033
Benzene (E)01 + 2 + 31 + 2 + 3
TOTAL101
Express the equilibrium constants in terms of 1, 2, and 3.
(2)
(3)
(4)
Solve for 1, 2, and 3 and calculate the equilibrium compositions of each species.
The equilibrium mole fractions are:
Toluene = 0.470
Ortho-Xylene = 0.065
Meta-Xylene = 0.138
Para-Xylene = 0.062
Benzene = 0.265
Since para-xylene has a smaller kinetic diameter than either ortho- or meta-xylene, a shape selective catalyst that allows mostly para-xylene to diffuse out of it will shift the product distribution.
Exercise 5:
Part a)
Assuming a basis of 1 mole of feed, write an overall mole balance.
Initial MolesChangeFinal Moles
Acetylene (A)0.5-10.5 1
HCl (B)0.5-1 20.5 - 1 2
Vinyl Chloride (C)01 21 2
1,2 Dichloroethane (D)022
TOTAL1-1 21 - 1 2
Express the equilibrium constants in terms of 1, 2, and 3.
For the reaction that forms vinyl chloride (C),
[1 atm]
(1)
Assuming ideal behavior,
(2)
Similarly for the reaction that forms 1,2 dichloroethane,
(3)
Solve for 1, 2, and 3 and calculate the equilibrium compositions of each species.
XAcetylene = 0.012
XHCl = 0.002
XVinyl chloride = 0.976
X1,2 Dichloroethane = 0.010
Find the fractional conversion of acetylene.
(4)
Part b)
Write another mole balance similar to part (a) but now add 9 moles of inert gas.
Initial MolesChangeFinal Moles
Acetylene (A)0.5-10.5 1
HCl (B)0.5-1 20.5 - 1 2
Vinyl Chloride (C)01 21 2
1,2 Dichloroethane (D)022
Inert Gas (I)909
TOTAL10-1 210 - 1 2
Express the equilibrium constants in terms of 1, 2, and 3.
(5)
(6)
Solve for 1, 2, and 3 and calculate the equilibrium compositions of each species.
XAcetylene = 0.0014
XHCl = 0.0012
XVinyl Chloride = 0.0510
X1,2 Dichloroethane = 0.0002
XInert = 0.946
Find the fractional conversion of acetylene.
(7)
Exercise 6:
Write the rate expression for the 2-propanol (P) reaction, rearrange, and integrate.
(1)
(2)
(3)
Before plotting the data, convert to .
(4)
(5)
The first order rate constant (k) is the negative of the slope = 8.39 x 10-6 min-1.
Exercise 7:
Assuming constant volume, write the second order rate equation for DMB.
(1)
Now find CB in terms of CA.
And
(2)
Therefore, CB = CA.
Rewrite the rate equation (equation (1)) in terms of fA.
(3)
(4)
Solve this integral
(5)
Finally, plot vs. time at each temperature and find slope, k.
Temperature (K)Rate Constant (L mol-1 hr-1)
3230.100
2980.028
2780.0033
Exercise 8:
This reaction can be assumed to be of the form
Assuming the reaction to be 1st order, write the appropriate first order rate expression and integrate.
(3)
(4)
Now a plot of vs. time should be linear with a slope = -k.
Assuming is equivalent to relative absorbance, a plot of ln(relative adsorbance) vs. time should be linear with slope = -k.The data appear first order with a rate constant, k = 0.0081 min-1. Analogous attempts to fit zero and second order reaction rate experiments failed.
Exercise 9:
Express nA and nB in terms of fractional conversion of A (fA).
(1)
(2)
For constant density (), and constant volume (V), can be expressed as concentration (Ci).
(3)
And = 3 so,
(4)
(5)
Substitute equations (3) and (5) into the given rate expression.
(6)
(7)
Separate variables and integrate.
(8)
Solving for the rate constant (k) gives k = 120 L2 mol-2 min-1.
Exercise 10:
Calculate the total moles of gas initially in the system for N2:H2:He = 3:1:0, assuming ideal gas behavior.
(1)
(2)
Write a gas phase mole balance.
Initial MolesChangeFinal Moles
N29.75 x 10-3-(t)9.75 x 10-3- (t)
H23.25 x 10-3-3(t)3.25 x 10-3- 3(t)
He000
NH3000
Total0.013-4(t)0.013 - 4(t)
Derive the rate expression using the ideal gas law and express the rate in terms of .
(3)
And
(4)
Therefore, is the rate of reaction, and .
(5)
Plot Total Pressure vs. Time to find the rate of change in pressure (i.e. slope)
From the graph = -1.9292 torr min-1.
Repeat the same process for the other gas ratios and solve for .
Ratio
(N2:H2:He)(torr min-1)(mol min-1)
3:1:0-1.92928.17 x 10-6
1:1:2-0.89473.79 x 10-6
1:3:0-0.56682.40 x 10-6
Write the Goldberg-Waage form of the rate equation and take the natural log of both sides.
(6)
(7)
To find plot ln(rate) vs. ln[N2] at a constant [H2], where ln[N2] = ln[moles of N2].
ratemoles N2moles H2
8.17 x 10-631
3.79 x 10-611
2.40 x 10-613
From the graph, = slope. Similarly, find by plotting ln(rate) vs. ln[H2] while holding [N2] constant.
= 0.70
= -0.42
Therefore, the final rate expression is . Finally, find the rates of ammonia synthesis for each ratio.
(8)
Therefore,
N2:H2:He
3:1:08.17 x 10-5
1:1:23.79 x 10-5
1:3:02.40 x 10-5
Exercise 11:
In Example 1.5.6 the following equations for tmax and CB are derived.
(1)
(2)
Assuming = 0 and k2 = k1, CB and . Therefore, use LHopitals rule to find tmax and CB.
(3)
(4)
Substituting for tmax gives:
(5)
Exercise 12:
Part a)
Assign rate constants, ki, to equations 1,2, and 3.
(1)
(2)
(3)
Derive rate equations for each equation.
(4)
(5)
(6)
Express the accumulation rate of each species in terms of the above rates.
(7)
(8)
Substituting equations (4), (5), and (6) gives:
(9)
(10)
Part b)
Solve differential equations using most convenient solver.
With initial conditions
Exercise 13:
Write the rate expression for DEBA, assuming constant volume.
(1)
Find CDEA and CBB in terms of CDEBA.
(2)
(3)
Substitute equations (2) and (3) into equation (1), using the initial conditions given for 1,4-butanediol and acetonitrile, respectively.
(4)
(5)
Rearrange equations (4) and (5), and integrate to find CDEBA as a function of time for each solvent.
1,4-butanediol:
(6)
(7)
acetonitrile:
(8)
(9)
Using equations (7) and (9), find the rate constant (k) for each solvent.
1,4-butanediol:k = 0.000212 L mol-1 min-1
acetonitrile
k = 0.00160 L mol-1 min-1
Exercise 14:
Write the first order rate equation for variable volume, Equation 1.5.3,
(1)
Rearrange and integrate equation (1) to find .
(2)
(3)
Use the ideal gas law to derive an expression for .
(4)
(5)
Define the molar expansion factor and find .
(6)
Where
(7)
(8)
Solving for k in equation (3) gives k = 0.000598 sec-1.
To find the time needed to raise the pressure from 1.8 atm to 2.5 atm, first find .
(9)
Using the value from equation (9), find .
(10)
(11)
Solving for time (t) in equation (3) gives t = 361.7 s.
Exercise 15:
For the constant volume reactor, express equilibrium constant (K) in terms of concentrations.
(1)
Write the mole balance for the reaction.
InitialChangeEquilibrium
A1-1
B2-2
C0
Total3-3
Rewrite equation (1) in terms of and pressure.
(2)
Solving for , gives = 0.719 mol L-1.
Using the ideal gas law, find in terms of .
(3)
(4)
Therefore,
Fractional conversion of A (fA) = 0.719
Final pressure () = 56.2 atm
Write rate equation for species A.
(5)
Express all concentrations in terms of CA.
(6)
(7)
Substitute equations (6) and (7) into equation (5).
(8)
Solve by hand or with a computer solver for each species and plot the composition of the reactor versus time.
Exercise 16:
For the variable volume reactor, express equilibrium constant (K) in terms of mole fractions and total pressure.
(1)
Using the mole balance from Exercise 15, express equation (1) in terms of and Ptot.
(2)
Using the ideal gas law, the equilibrium constant can be rewritten as 0.08124 atm-1.
Again, use the ideal gas law to find Ptot and solve for .
(3)
= 0.7681
(4)
Therefore, the equilibrium conversion of A = 0.7681.
Write the rate equation for species A.
(5)
(6)
Express V in terms of Vo and nA.
(7)
And
(8)
Therefore,
(9)
Express nB and nC in terms of nA.
(10)
(11)
Substitute equations (9), (10), and (11) into equation (6).
(12)
Solve for each species by hand or with a computer solver and plot the composition of the reactor and the volume versus time.
Exercise 17:
Write a new mole balance to account for the inert gas.
InitialChangeEquilibrium
A1-1
B2-2
C0
Inert303
Total6-6
Solve for , using a modified form of equation (2) from Exercise 16.
(1)
Use the ideal gas law to find Ptot and solve for .
(2)
= 0.7417
(3)
Therefore, the equilibrium conversion of A = 0.7417.
Write the rate equation for species A as done in Exercise 16.
(4)
Express V in terms of Vo and nA.
(5)
And
(6)
Therefore,
(7)
Express nB and nC in terms of nA.
(8)
(9)
Substitute equations (7), (8), and (9) into equation (4).
(10)
Solve for each species by hand or with a computer solver and plot the composition of the reactor and the volume versus time.
Population
Lynxes
Rabbits
Time
PAGE 1.1
_1063732998.unknown
_1074328020.unknown
_1081012366.unknown
_1081012850.unknown
_1081013071.xlsChart3
120
0.8021.8020.198
0.5991.5990.401
0.4811.4810.519
0.4091.4090.591
0.3641.3640.636
0.3351.3350.665
0.3161.3160.684
0.3041.3040.696
0.2961.2960.704
0.2911.2910.709
0.2881.2880.712
0.2851.2850.715
0.2841.2840.716
0.2831.2830.717
0.2821.2820.718
0.2821.2820.718
0.2811.2810.719
0.2811.2810.719
0.2811.2810.719
0.2811.2810.719
0.2811.2810.719
0.2811.2810.719
0.2811.2810.719
0.2811.2810.719
0.2811.2810.719
0.2811.2810.719
0.2811.2810.719
0.2811.2810.719
0.2811.2810.719
0.2811.2810.719
A
B
C
Time (hr)
Concentration (mol / L)
Prob 15
Prob 13
1,4-butanediol
Time (min)[DEBA] (mol/L)Rate Constant
000
350.0020.0002294894
1150.0060.0002112304
2220.0120.000221533
4550.0230.0002119474
average0.00021855
acetonitrile
Time (min)[DEBA] (mol/L)Rate Constant
000
310.0040.0013194972
580.0070.001255672
1080.0130.0012981155
1900.0260.0016067902
average0.0013700187
Prob 12
0201
0.116.7775.853
0.26.10216.535
0.31.63719.368
0.40.49418.632
0.50.13717.208
0.60.03715.669
0.70.01114.204
0.83.22E-0312.86
0.91.09E-0311.638
14.05E-0410.531
1.11.66E-049.529
1.27.45E-058.623
1.33.64E-057.802
1.41.92E-057.06
1.51.08E-056.388
1.66.51E-065.78
1.74.15E-065.23
1.82.79E-064.732
1.91.97E-064.282
21.45E-063.874
2.11.11E-063.506
2.28.75E-073.172
2.37.15E-072.87
2.46.01E-072.597
2.55.19E-072.35
2.64.59E-072.126
2.74.14E-071.924
2.83.81E-071.741
2.93.57E-071.575
33.39E-071.425
3.13.28E-071.29
3.23.20E-071.167
3.33.17E-071.056
3.43.17E-070.955
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19.39.79E-013.16E-07
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19.91.78E+003.88E-07
201.97E+004.24E-07
20.12.18E+004.72E-07
20.22.41E+005.37E-07
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20.73.97E+001.55E-06
20.84.39E+002.13E-06
20.94.85E+003.06E-06
215.36E+004.61E-06
21.15.92E+007.32E-06
21.26.54E+001.24E-05
21.37.23E+002.22E-05
21.47.99E+004.30E-05
21.58.83E+009.01E-05
21.69.76E+002.06E-04
21.71.08E+015.20E-04
21.81.19E+011.46E-03
21.91.32E+014.58E-03
221.45E+010.016
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22.73.25E-0116.787
22.88.90E-0215.423
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82.46.09E+007.97E-05
82.56.73E+001.37E-04
82.67.43E+002.51E-04
82.78.22E+004.96E-04
82.89.08E+001.06E-03
82.91.00E+012.49E-03
831.11E+016.46E-03
83.11.22E+011.90E-02
83.21.35E+016.10E-02
83.31.47E+012.22E-01
83.41.55E+019.03E-01
83.51.41E+013.65E+00
83.67.99E+001.02E+01
83.72.45E+001.49E+01
83.80.6821.53E+01
83.90.1941.43E+01
840.0591.31E+01
84.10.021.19E+01
84.27.14E-031.08E+01
84.32.87E-039.73E+00
84.41.26E-038.81E+00
84.56.06E-047.97E+00
84.63.14E-047.21E+00
84.71.75E-046.53E+00
84.81.04E-045.91E+00
84.96.54E-055.34E+00
854.35E-054.84E+00
85.13.03E-054.38E+00
85.22.21E-053.96E+00
85.31.68E-053.58E+00
85.41.32E-053.24E+00
85.51.07E-052.93E+00
85.68.94E-062.65E+00
85.77.68E-062.40E+00
85.86.75E-062.17E+00
85.96.07E-061.97E+00
865.56E-061.78E+00
86.15.19E-061.61E+00
86.24.92E-061.46E+00
86.34.74E-061.32E+00
86.44.62E-061.19E+00
86.54.55E-061.08E+00
86.64.54E-069.76E-01
86.74.57E-068.83E-01
86.84.65E-067.99E-01
86.94.76E-067.23E-01
874.91E-066.54E-01
87.15.10E-065.92E-01
87.25.33E-065.36E-01
87.35.60E-064.85E-01
87.45.90E-064.39E-01
87.56.26E-063.97E-01
87.66.66E-063.59E-01
87.77.11E-063.25E-01
87.87.62E-062.94E-01
87.98.19E-062.66E-01
888.83E-062.41E-01
88.19.53E-062.18E-01
88.21.03E-051.97E-01
88.31.12E-051.78E-01
88.41.22E-051.61E-01
88.51.32E-051.46E-01
88.61.44E-051.32E-01
88.71.58E-051.20E-01
88.81.72E-051.08E-01
88.91.88E-059.80E-02
892.06E-058.90E-02
89.12.26E-058.00E-02
89.22.48E-057.30E-02
89.32.72E-056.60E-02
89.42.99E-055.90E-02
89.53.28E-055.40E-02
89.63.61E-054.90E-02
89.73.97E-054.40E-02
89.84.37E-054.00E-02
89.94.81E-053.60E-02
905.30E-053.30E-02
90.15.84E-052.90E-02
90.26.43E-052.70E-02
90.37.09E-052.40E-02
90.47.82E-052.20E-02
90.58.62E-052.00E-02
90.69.51E-051.80E-02
90.71.05E-041.60E-02
90.81.16E-041.50E-02
90.91.28E-041.30E-02
911.41E-041.20E-02
91.11.56E-041.10E-02
91.21.72E-049.82E-03
91.31.90E-048.88E-03
91.42.10E-048.04E-03
91.52.31E-047.27E-03
91.62.56E-046.58E-03
91.72.82E-045.95E-03
91.83.12E-045.39E-03
91.93.44E-044.88E-03
923.81E-044.41E-03
92.14.20E-043.99E-03
92.24.64E-043.61E-03
92.35.13E-043.27E-03
92.45.67E-042.96E-03
92.56.26E-042.68E-03
92.66.92E-042.42E-03
92.77.64E-042.19E-03
92.88.45E-041.98E-03
92.99.33E-041.80E-03
931.03E-031.62E-03
93.11.14E-031.47E-03
93.21.26E-031.33E-03
93.31.39E-031.20E-03
93.41.54E-031.09E-03
93.51.70E-039.86E-04
93.61.88E-038.92E-04
93.72.08E-038.07E-04
93.82.29E-037.31E-04
93.92.53E-036.61E-04
942.80E-035.99E-04
94.13.10E-035.42E-04
94.23.42E-034.90E-04
94.33.78E-034.44E-04
94.44.18E-034.02E-04
94.54.62E-033.64E-04
94.65.10E-033.29E-04
94.75.64E-032.98E-04
94.86.23E-032.70E-04
94.96.89E-032.44E-04
957.61E-032.21E-04
95.18.41E-032.00E-04
95.29.29E-031.81E-04
95.30.011.64E-04
95.40.0111.49E-04
95.50.0131.35E-04
95.60.0141.22E-04
95.70.0151.11E-04
95.80.0171.00E-04
95.90.0199.10E-05
960.0218.25E-05
96.10.0237.48E-05
96.20.0256.78E-05
96.30.0286.15E-05
96.40.0315.58E-05
96.50.0345.07E-05
96.60.0384.60E-05
96.70.0424.18E-05
96.80.0463.80E-05
96.90.0513.46E-05
970.0563.14E-05
97.10.0622.86E-05
97.20.0692.61E-05
97.30.0762.38E-05
97.40.0842.17E-05
97.50.0931.98E-05
97.60.1021.81E-05
97.70.1131.65E-05
97.80.1251.51E-05
97.90.1381.39E-05
980.1531.27E-05
98.10.1691.17E-05
98.20.1871.08E-05
98.30.2069.95E-06
98.40.2289.20E-06
98.50.2528.53E-06
98.60.2787.93E-06
98.70.3087.38E-06
98.80.346.90E-06
98.90.3766.47E-06
990.4156.09E-06
99.10.4595.76E-06
99.20.5075.47E-06
99.30.5615.22E-06
99.40.625.01E-06
99.50.6854.84E-06
99.60.7574.70E-06
99.70.8364.61E-06
99.80.9244.55E-06
99.91.0224.54E-06
1001.1294.58E-06
Prob 12
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Rabbits
Lynxes
Time
Population
Prob 12
Prob 15
timeABCTotalPressureXaXbXctimeABC
0120373.850.33333333330.666666666700120
6.67E-030.9251.9250.0752.92572.003750.31623931620.65811965810.02564102560.020.8021.8020.198
0.0130.861.860.142.8670.40366666670.30069930070.65034965030.0489510490.0530.5991.5990.401
0.020.8021.8020.1982.80268.97590.28622412560.64311206280.07066381160.0870.4811.4810.519
0.0270.7521.7520.2482.75267.74506666670.2732558140.6366279070.09011627910.120.4091.4090.591
0.0330.7071.7070.2932.70766.63731666670.26117473220.63058736610.10823790170.1530.3641.3640.636
0.040.6671.6670.3332.66765.652650.25009373830.62504686910.12485939260.1870.3351.3350.665
0.0470.6311.6310.3692.63164.766450.23983276320.61991638160.14025085520.220.3161.3160.684
0.0530.5991.5990.4012.59963.97871666670.23047325890.61523662950.15429011160.2530.3041.3040.696
0.060.571.570.432.5763.26483333330.22178988330.61089494160.16731517510.2870.2961.2960.704
0.0670.5441.5440.4562.54462.62480.2138364780.6069182390.1792452830.320.2911.2910.709
0.0730.5211.5210.4792.52162.05861666670.20666402220.60333201110.19000396670.3530.2881.2880.712
0.080.51.50.52.561.54166666670.20.60.20.3870.2851.2850.715
0.0870.4811.4810.5192.48161.073950.19387343810.59693671910.20918984280.420.2841.2840.716
0.0930.4641.4640.5362.46460.65546666670.18831168830.59415584420.21753246750.4530.2831.2830.717
0.10.4481.4480.5522.44860.26160.18300653590.5915032680.22549019610.4870.2821.2820.718
0.1070.4341.4340.5662.43459.91696666670.17830731310.58915365650.23253903040.520.2821.2820.718
0.1130.4211.4210.5792.42159.596950.17389508470.58694754230.2391573730.5530.2811.2810.719
0.120.4091.4090.5912.40959.301550.16977999170.58488999580.24533001250.5870.2811.2810.719
0.1270.3981.3980.6022.39859.03076666670.1659716430.58298582150.25104253540.620.2811.2810.719
0.1330.3891.3890.6112.38958.80921666670.16282963580.58141481790.25575554630.6530.2811.2810.719
0.140.381.380.622.3858.58766666670.15966386550.57983193280.26050420170.6870.2811.2810.719
0.1470.3711.3710.6292.37158.36611666670.15647406160.57823703080.26528890760.720.2811.2810.719
0.1530.3641.3640.6362.36458.19380.15397631130.57698815570.2690355330.7530.2811.2810.719
0.160.3571.3570.6432.35758.02148333330.15146372510.57573186250.27280441240.7870.2811.2810.719
0.1670.3511.3510.6492.35157.87378333330.1492981710.57464908550.27605274350.820.2811.2810.719
0.1730.3451.3450.6552.34557.72608333330.14712153520.57356076760.27931769720.8530.2811.2810.719
0.180.341.340.662.3457.6030.14529914530.57264957260.28205128210.8870.2811.2810.719
0.1870.3351.3350.6652.33557.47991666670.14346895070.57173447540.28479657390.920.2811.2810.719
0.1930.3311.3310.6692.33157.381450.1419991420.5709995710.2870012870.9530.2811.2810.719
0.20.3271.3270.6732.32757.28298333330.14052428020.57026214010.28921357970.9870.2811.2810.719
0.2070.3231.3230.6772.32357.18451666670.13904433920.56952216960.2914334912
0.2130.321.320.682.3257.11066666670.13793103450.56896551720.2931034483
0.220.3161.3160.6842.31657.01220.13644214160.56822107080.2953367876
0.2270.3141.3140.6862.31456.96296666670.13569576490.56784788250.2964563526
0.2330.3111.3110.6892.31156.88911666670.13457377760.56728688880.2981393336
0.240.3091.3090.6912.30956.83988333330.13382416630.56691208320.2992637505
0.2470.3061.3060.6942.30656.76603333330.13269731140.56634865570.300954033
0.2530.3041.3040.6962.30456.71680.13194444440.56597222220.3020833333
0.260.3021.3020.6982.30256.66756666670.13119026930.56559513470.303214596
0.2670.3011.3010.6992.30156.642950.13081269010.56540634510.3037809648
0.2730.2991.2990.7012.29956.59371666670.13005654630.56502827320.3049151805
0.280.2981.2980.7022.29856.56910.12967798090.56483899040.3054830287
0.2870.2961.2960.7042.29656.51986666670.12891986060.56445993030.3066202091
0.2930.2951.2950.7052.29556.495250.1285403050.56427015250.3071895425
0.30.2941.2940.7062.29456.47063333330.12816041850.56408020920.3077593723
0.3070.2931.2930.7072.29356.44601666670.12778020060.56389010030.3083296991
0.3130.2921.2920.7082.29256.42140.1273996510.56369982550.3089005236
0.320.2911.2910.7092.29156.39678333330.12701876910.56350938450.3094718464
0.3270.291.290.712.2956.37216666670.12663755460.56331877730.3100436681
0.3330.2891.2890.7112.28956.347550.1262560070.56312800350.3106159895
0.340.2891.2890.7112.28956.347550.1262560070.56312800350.3106159895
0.3470.2881.2880.7122.28856.32293333330.12587412590.56293706290.3111888112
0.3530.2881.2880.7122.28856.32293333330.12587412590.56293706290.3111888112
0.360.2871.2870.7132.28756.29831666670.12549191080.56274595540.3117621338
0.3670.2871.2870.7132.28756.29831666670.12549191080.56274595540.3117621338
0.3730.2861.2860.7142.28656.27370.12510936130.56255468070.312335958
0.380.2861.2860.7142.28656.27370.12510936130.56255468070.312335958
0.3870.2851.2850.7152.28556.24908333330.1247264770.56236323850.3129102845
0.3930.2851.2850.7152.28556.24908333330.1247264770.56236323850.3129102845
0.40.2851.2850.7152.28556.24908333330.1247264770.56236323850.3129102845
0.4070.2841.2840.7162.28456.22446666670.12434325740.56217162870.3134851138
0.4130.2841.2840.7162.28456.22446666670.12434325740.56217162870.3134851138
0.420.2841.2840.7162.28456.22446666670.12434325740.56217162870.3134851138
0.4270.2841.2840.7162.28456.22446666670.12434325740.56217162870.3134851138
0.4330.2831.2830.7172.28356.199850.12395970210.56197985110.3140604468
0.440.2831.2830.7172.28356.199850.12395970210.56197985110.3140604468
0.4470.2831.2830.7172.28356.199850.12395970210.56197985110.3140604468
0.4530.2831.2830.7172.28356.199850.12395970210.56197985110.3140604468
0.460.2831.2830.7172.28356.199850.12395970210.56197985110.3140604468
0.4670.2821.2820.7182.28256.17523333330.12357581070.56178790530.314636284
0.4730.2821.2820.7182.28256.17523333330.12357581070.56178790530.314636284
0.480.2821.2820.7182.28256.17523333330.12357581070.56178790530.314636284
0.4870.2821.2820.7182.28256.17523333330.12357581070.56178790530.314636284
0.4930.2821.2820.7182.28256.17523333330.12357581070.56178790530.314636284
0.50.2821.2820.7182.28256.17523333330.12357581070.56178790530.314636284
0.5070.2821.2820.7182.28256.17523333330.12357581070.56178790530.314636284
0.5130.2821.2820.7182.28256.17523333330.12357581070.56178790530.314636284
0.520.2821.2820.7182.28256.17523333330.12357581070.56178790530.314636284
0.5270.2821.2820.7182.28256.17523333330.12357581070.56178790530.314636284
0.5330.2821.2820.7182.28256.17523333330.12357581070.56178790530.314636284
0.540.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.5470.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.5530.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.560.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.5670.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.5730.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.580.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.5870.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.5930.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.60.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.6070.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.6130.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.620.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.6270.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.6330.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.640.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.6470.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.6530.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.660.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.6670.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.6730.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.680.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.6870.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.6930.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.70.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.7070.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.7130.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.720.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.7270.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.7330.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.740.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.7470.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.7530.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.760.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.7670.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.7730.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.780.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.7870.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.7930.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.80.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.8070.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.8130.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.820.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.8270.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.8330.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.840.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.8470.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.8530.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.860.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.8670.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.8730.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.880.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.8870.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.8930.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.90.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.9070.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.9130.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.920.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.9270.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.9330.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.940.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.9470.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.9530.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.960.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.9670.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.9730.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.980.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.9870.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
0.9930.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
10.2811.2810.7192.28156.15061666670.12319158260.56159579130.315212626
Prob 15
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
A
B
C
time (hr)
Concentration (mol / L)
Prob 15
Prob 17
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Pressure
Prob 16
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
Xa
Xb
Xc
time (hr)
mole fraction
Prob 15
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
A
B
C
time (hr)
Concentration (mol / L)
Prob 15
timeABCTotalCaCbCcVolumetimeABC
0120612010120
6.67E-030.9251.9250.0755.9250.94871794871.97435897440.07692307690.975
0.0130.8581.8580.1425.8580.90062981111.95031490550.14905528340.9526666667
0.020.7991.7990.2015.7990.85637727761.92818863880.21543408360.933
0.0270.7471.7470.2535.7470.81579905351.90789952680.27630141970.9156666667
0.0330.71.70.35.70.77777777781.88888888890.33333333330.90.0330.71.70.3
0.040.6591.6590.3415.6590.74351259871.87175629940.38473110190.8863333333
0.0470.6211.6210.3795.6210.71079740561.85539870280.43380389160.8736666667
0.0530.5881.5880.4125.5880.68160741891.84080370940.47758887170.8626666667
0.060.5571.5570.4435.5570.65350019551.82675009780.51974970670.8523333333
0.0670.531.530.475.530.6284584981.8142292490.5573122530.84333333330.0670.531.530.47
0.0730.5061.5060.4945.5060.60574620911.80287310450.59138068640.8353333333
0.080.4831.4830.5175.4830.58356826421.79178413210.62464760370.8276666667
0.0870.4631.4630.5375.4630.56394640681.78197320340.65408038980.821
0.0930.4451.4450.5555.4450.54601226991.7730061350.68098159510.815
0.10.4291.4290.5715.4290.52984767391.7649238370.70522848910.80966666670.10.4291.4290.571
0.1070.4141.4140.5865.4140.51449875721.75724937860.72825186410.8046666667
0.1130.41.40.65.40.51.750.750.8
0.120.3881.3880.6125.3880.48743718591.7437185930.76884422110.796
0.1270.3771.3770.6235.3770.47580984431.73790492220.78628523350.7923333333
0.1330.3671.3670.6335.3670.46514575411.73257287710.80228136880.7890.1330.3671.3670.633
0.140.3571.3570.6435.3570.45439117521.72719558760.81841323720.7856666667
0.1470.3491.3490.6515.3490.44572158371.72286079180.83141762450.783
0.1530.3411.3410.6595.3410.43699273811.71849636910.84451089280.7803333333
0.160.3341.3340.6665.3340.42930591261.71465295630.85604113110.778
0.1670.3281.3280.6725.3280.42268041241.71134020620.86597938140.7760.1670.3281.3280.672
0.1730.3221.3220.6785.3220.41602067181.70801033590.87596899220.774
0.180.3161.3160.6845.3160.40932642491.70466321240.88601036270.772
0.1870.3111.3110.6895.3110.40372133281.70186066640.89441800090.7703333333
0.1930.3071.3070.6935.3070.39921976591.6996098830.90117035110.769
0.20.3031.3030.6975.3030.39470256191.69735128090.90794615720.76766666670.20.3031.3030.697
0.2070.2991.2990.7015.2990.3901696391.69508481950.91474554150.7663333333
0.2130.2961.2960.7045.2960.38675958191.69337979090.91986062720.7653333333
0.220.2931.2930.7075.2930.38334060181.69167030090.92498909730.7643333333
0.2270.291.290.715.290.37991266381.68995633190.93013100440.7633333333
0.2330.2871.2870.7135.2870.37647573241.68823786620.93528640140.76233333330.2330.2871.2870.713
0.240.2851.2850.7155.2850.37417943111.68708971550.93873085340.7616666667
0.2470.2821.2820.7185.2820.37072743211.6853637160.94390885190.7606666667
0.2530.281.280.725.280.36842105261.68421052630.94736842110.76
0.260.2791.2790.7215.2790.36726634491.68363317240.94910048270.7596666667
0.2670.2771.2770.7235.2770.36495388671.68247694330.952569170.7590.2670.2771.2770.723
0.2730.2751.2750.7255.2750.36263736261.68131868130.9560439560.7583333333
0.280.2741.2740.7265.2740.36147757261.68073878630.95778364120.758
0.2870.2731.2730.7275.2730.3603167621.6801583810.9595248570.7576666667
0.2930.2711.2710.7295.2710.3579920741.6789960370.9630118890.757
0.30.271.270.735.270.35682819381.67841409690.96475770930.75666666670.30.271.270.73
0.3070.2691.2690.7315.2690.35566328781.67783164390.96650506830.7563333333
0.3130.2681.2680.7325.2680.35449735451.67724867720.96825396830.756
0.320.2681.2680.7325.2680.35449735451.67724867720.96825396830.756
0.3270.2671.2670.7335.2670.35333039261.67666519630.97000441110.7556666667
0.3330.2661.2660.7345.2660.35216240071.67608120040.97175639890.75533333330.3330.2661.2660.734
0.340.2651.2650.7355.2650.35099337751.67549668870.97350993380.755
0.3470.2651.2650.7355.2650.35099337751.67549668870.97350993380.755
0.3530.2641.2640.7365.2640.34982332161.67491166080.97526501770.7546666667
0.360.2641.2640.7365.2640.34982332161.67491166080.97526501770.7546666667
0.3670.2631.2630.7375.2630.34865223161.67432611580.97702165270.75433333330.3670.2631.2630.737
0.3730.2631.2630.7375.2630.34865223161.67432611580.97702165270.7543333333
0.380.2631.2630.7375.2630.34865223161.67432611580.97702165270.7543333333
0.3870.2621.2620.7385.2620.34748010611.67374005310.97877984080.754
0.3930.2621.2620.7385.2620.34748010611.67374005310.97877984080.754
0.40.2621.2620.7385.2620.34748010611.67374005310.97877984080.7540.40.2621.2620.738
0.4070.2611.2610.7395.2610.34630694381.67315347190.98053958430.7536666667
0.4130.2611.2610.7395.2610.34630694381.67315347190.98053958430.7536666667
0.420.2611.2610.7395.2610.34630694381.67315347190.98053958430.7536666667
0.4270.2611.2610.7395.2610.34630694381.67315347190.98053958430.7536666667
0.4330.261.260.745.260.34513274341.67256637170.9823008850.75333333330.4330.261.260.74
0.440.261.260.745.260.34513274341.67256637170.9823008850.7533333333
0.4470.261.260.745.260.34513274341.67256637170.9823008850.7533333333
0.4530.261.260.745.260.34513274341.67256637170.9823008850.7533333333
0.460.261.260.745.260.34513274341.67256637170.9823008850.7533333333
0.4670.261.260.745.260.34513274341.67256637170.9823008850.75333333330.4670.261.260.74
0.4730.261.260.745.260.34513274341.67256637170.9823008850.7533333333
0.480.2591.2590.7415.2590.34395750331.67197875170.9840637450.753
0.4870.2591.2590.7415.2590.34395750331.67197875170.9840637450.753
0.4930.2591.2590.7415.2590.34395750331.67197875170.9840637450.753
0.50.2591.2590.7415.2590.34395750331.67197875170.9840637450.7530.50.2591.2590.741
0.5070.2591.2590.7415.2590.34395750331.67197875170.9840637450.753
0.5130.2591.2590.7415.2590.34395750331.67197875170.9840637450.753
0.520.2591.2590.7415.2590.34395750331.67197875170.9840637450.753
0.5270.2591.2590.7415.2590.34395750331.67197875170.9840637450.753
0.5330.2591.2590.7415.2590.34395750331.67197875170.9840637450.7530.5330.2591.2590.741
0.540.2591.2590.7415.2590.34395750331.67197875170.9840637450.753
0.5470.2591.2590.7415.2590.34395750331.67197875170.9840637450.753
0.5530.2591.2590.7415.2590.34395750331.67197875170.9840637450.753
0.560.2591.2590.7415.2590.34395750331.67197875170.9840637450.753
0.5670.2591.2590.7415.2590.34395750331.67197875170.9840637450.7530.5670.2591.2590.741
0.5730.2591.2590.7415.2590.34395750331.67197875170.9840637450.753
0.580.2591.2590.7415.2590.34395750331.67197875170.9840637450.753
0.5870.2591.2590.7415.2590.34395750331.67197875170.9840637450.753
0.5930.2591.2590.7415.2590.34395750331.67197875170.9840637450.753
0.60.2591.2590.7415.2590.34395750331.67197875170.9840637450.7530.60.2591.2590.741
0.6070.2591.2590.7415.2590.34395750331.67197875170.9840637450.753
0.6130.2591.2590.7415.2590.34395750331.67197875170.9840637450.753
0.620.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.6270.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.6330.2581.2580.7425.2580.34278122231.67139061120.98582816650.75266666670.6330.2581.2580.742
0.640.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.6470.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.6530.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.660.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.6670.2581.2580.7425.2580.34278122231.67139061120.98582816650.75266666670.6670.2581.2580.742
0.6730.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.680.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.6870.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.6930.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.70.2581.2580.7425.2580.34278122231.67139061120.98582816650.75266666670.70.2581.2580.742
0.7070.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.7130.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.720.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.7270.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.7330.2581.2580.7425.2580.34278122231.67139061120.98582816650.75266666670.7330.2581.2580.742
0.740.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.7470.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.7530.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.760.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.7670.2581.2580.7425.2580.34278122231.67139061120.98582816650.75266666670.7670.2581.2580.742
0.7730.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.780.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.7870.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.7930.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.80.2581.2580.7425.2580.34278122231.67139061120.98582816650.75266666670.80.2581.2580.742
0.8070.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.8130.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.820.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.8270.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.8330.2581.2580.7425.2580.34278122231.67139061120.98582816650.75266666670.8330.2581.2580.742
0.840.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.8470.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.8530.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.860.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.8670.2581.2580.7425.2580.34278122231.67139061120.98582816650.75266666670.8670.2581.2580.742
0.8730.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.880.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.8870.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.8930.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.90.2581.2580.7425.2580.34278122231.67139061120.98582816650.75266666670.90.2581.2580.742
0.9070.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.9130.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.920.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.9270.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.9330.2581.2580.7425.2580.34278122231.67139061120.98582816650.75266666670.9330.2581.2580.742
0.940.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.9470.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.9530.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.960.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.9670.2581.2580.7425.2580.34278122231.67139061120.98582816650.75266666670.9670.2581.2580.742
0.9730.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.980.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.9870.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
0.9930.2581.2580.7425.2580.34278122231.67139061120.98582816650.7526666667
10.2581.2580.7425.2580.34278122231.67139061120.98582816650.752666666710.2581.2580.742
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
A
B
C
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
A
B
C
time (hr)
Concentration (mol / L)
Problem 17
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Volume
time (hr)
Volume (L)
Problem 17
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
A
B
C
time (hr)
Concentration (mol / L)
Problem 17
timeABCTotalCaCbCcVolumetimeABC
0120312010120
6.67E-030.9241.9240.0762.9240.94801641591.97400820790.07797537620.9746666667
0.0130.8571.8570.1432.8570.89989499471.94994749740.15015750790.9523333333
0.020.7961.7960.2042.7960.85407725321.92703862660.21888412020.932
0.0270.7421.7420.2582.7420.81181619261.90590809630.28227571120.914
0.0330.6931.6930.3072.6930.77200148531.88600074270.3419977720.89766666670.0330.6931.6930.307
0.040.6491.6490.3512.6490.73499433751.86749716870.39750849380.883
0.0470.611.610.392.610.70114942531.85057471260.44827586210.87
0.0530.5751.5750.4252.5750.66990291261.83495145630.49514563110.8583333333
0.060.5431.5430.4572.5430.64058198981.82029099490.53912701530.8476666667
0.0670.5141.5140.4862.5140.61336515511.80668257760.57995226730.8380.0670.5141.5140.486
0.0730.4881.4880.5122.4880.58842443731.79421221860.61736334410.8293333333
0.080.4641.4640.5362.4640.56493506491.78246753250.65259740260.8213333333
0.0870.4431.4430.5572.4430.54400327471.77200163730.6839950880.8143333333
0.0930.4241.4240.5762.4240.52475247521.76237623760.71287128710.808
0.10.4061.4060.5942.4060.5062344141.7531172070.74064837910.8020.10.4061.4060.594
0.1070.391.390.612.390.4895397491.74476987450.76569037660.7966666667
0.1130.3761.3760.6242.3760.47474747471.73737373740.78787878790.792
0.120.3631.3630.6372.3630.46085484551.73042742280.80871773170.7876666667
0.1270.3511.3510.6492.3510.4478945131.72394725650.82815823050.7836666667
0.1330.341.340.662.340.43589743591.71794871790.84615384620.780.1330.341.340.66
0.140.3311.3310.6692.3310.4259974261.7129987130.8610038610.777
0.1470.3221.3220.6782.3220.41602067181.70801033590.87596899220.774
0.1533.14E-011.3140.6862.3140.40708729471.70354364740.88936905790.7713333333
0.160.3071.3070.6932.3070.39921976591.6996098830.90117035110.769
0.1670.31.30.72.30.39130434781.69565217390.91304347830.76666666670.1670.31.30.7
0.1730.2941.2940.7062.2940.38448125541.69224062770.92327811680.7646666667
0.180.2881.2880.7122.2880.37762237761.68881118880.93356643360.7626666667
0.1870.2831.2830.7172.2830.37187910641.68593955320.94218134030.761
0.1930.2791.2790.7212.2790.36726634491.68363317240.94910048270.7596666667
0.20.2751.2750.7252.2750.36263736261.68131868130.9560439560.75833333330.20.2751.2750.725
0.2070.2711.2710.7292.2710.3579920741.6789960370.9630118890.757
0.2130.2671.2670.7332.2670.35333039261.67666519630.97000441110.7556666667
0.220.2641.2640.7362.2640.34982332161.67491166080.97526501770.7546666667
0.2270.2611.2610.7392.2610.34630694381.67315347190.98053958430.7536666667
0.2330.2591.2590.7412.2590.34395750331.67197875170.9840637450.7530.2330.2591.2590.741
0.240.2561.2560.7442.2560.34042553191.6702127660.98936170210.752
0.2470.2541.2540.7462.2540.3380656611.66903283050.99290150840.7513333333
0.2530.2521.2520.7482.2520.33570159861.66785079930.99644760210.7506666667
0.260.2511.2510.7492.2510.3345179921.6672589960.9982230120.7503333333
0.2670.2491.2490.7512.2490.33214762121.66607381061.00177856830.74966666670.2670.2491.2490.751
0.2730.2471.2470.7532.2470.32977303071.66488651541.00534045390.749
0.280.2461.2460.7542.2460.32858414961.66429207481.00712377560.7486666667
0.2870.2451.2450.7552.2450.32739420941.66369710471.0089086860.7483333333
0.2930.2441.2440.7562.2440.32620320861.66310160431.01069518720.748
0.30.2431.2430.7572.2430.32501114581.66250557291.01248328130.74766666670.30.2431.2430.757
0.3070.2421.2420.7582.2420.32381801961.66190900981.01427297060.7473333333
0.3130.2411.2410.7592.2410.32262382861.66131191431.0160642570.747
0.320.241.240.762.240.32142857141.66071428571.01785714290.7466666667
0.3270.2391.2390.7612.2390.32023224651.66011612331.01965163020.7463333333
0.3330.2391.2390.7612.2390.32023224651.66011612331.01965163020.74633333330.3330.2391.2390.761
0.340.2381.2380.7622.2380.31903485251.65951742631.02144772120.746
0.3470.2381.2380.7622.2380.31903485251.65951742631.02144772120.746
0.3530.2371.2370.7632.2370.3178363881.6589181941.0232454180.7456666667
0.360.2371.2370.7632.2370.3178363881.6589181941.0232454180.7456666667
0.3670.2361.2360.7642.2360.31663685151.65831842581.02504472270.74533333330.3670.2361.2360.764
0.3730.2361.2360.7642.2360.31663685151.65831842581.02504472270.7453333333
0.380.2351.2350.7652.2350.31543624161.65771812081.02684563760.745
0.3870.2351.2350.7652.2350.31543624161.65771812081.02684563760.745
0.3930.2351.2350.7652.2350.31543624161.65771812081.02684563760.745
0.40.2351.2350.7652.2350.31543624161.65771812081.02684563760.7450.40.2351.2350.765
0.4070.2341.2340.7662.2340.31423455681.65711727841.02864816470.7446666667
0.4130.2341.2340.7662.2340.31423455681.65711727841.02864816470.7446666667
0.420.2341.2340.7662.2340.31423455681.65711727841.02864816470.7446666667
0.4270.2341.2340.7662.2340.31423455681.65711727841.02864816470.7446666667
0.4330.2341.2340.7662.2340.31423455681.65711727841.02864816470.74466666670.4330.2341.2340.766
0.440.2331.2330.7672.2330.31303179581.65651589791.03045230630.7443333333
0.4470.2331.2330.7672.
