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Kinetics in Chemical Reactor

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1. The reversible exothermic water-gas shift reaction (seen in attached file), takes place in an isobaric and adiabatic PFR reactor of V=1m3. Ftot = 100 moles/sec contains 40 mol% H20 and 20 mole % of inert I. The total pressure is 3 bar and the inlet temperature is Tin = 500 k. In parallel the methanation reaction (seen in attached file) occurs. What is the CO conversion and temperature at the exit of the reactor.

2. The liquid phase reaction (in attached file) is carried out in a jacketed (cool) CSTR reactor with volume V=1m3. Initially the reactors is at a temperature of 350K and contains only species A at a concentration of 3 moles/liter (fully filled). The rate constants are at 350K are K1 (350K) =10^3 moles^-1s^-1liter and k-1 (350 K) = 10^5 moles^-1s^-1liter with activation barrier of E1=100 kJ/mol and E1=150 kJ/mol. The heat of reaction is -Kj/mol. The heat capacities for A and B are 25 J/mol/k and for C 45J/mol. a cooling medium flows around the reactor with a constant temperature of K, and UA= 100 J/s/K. The flow rate of the cooling medium is high enough that you can assume the temperature of the cooling medium to be constant. At time t=0, a constant flow of A and B at temperature of 350K is added to the reactor and the same volumetric flow rate, V=0.01m3/s of products is removed. In the moment B is added to the reactor, the reaction begins. The concentration in the incoming flow of A and B is 1mol/liter and 2 mol/liter respectively. Plot the temperature and concentration of each species as a function of time, what is the temperature and concentration of A, B, C after 1000s?

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For water-gas shift and methanation reactions, Arrhenius equation applies.

Arrhenius equation is given by,
.... (1)

where k is rate constant, T is temperature (in Kelvin), A is pre-exponential factor, Ea is activation energy, and R is universal gas constant.

So for water-gas shift reaction,
r1 = k1 [CO] [H2O] - k-1 [H2] [CO2] [concentration is denoted by third bracket]

= 100 e -20,000 / (8.314 x 500) - 100 e -60,000 / (8.314 x 500)
[applying equation (1), R = 8.314 J mol-1 K-1]


Similarly for methanation reaction,
r2 = k2 [CO] [H2] - k-2 [CH4] [H2O]

= 100 e -30,000 / (8.314 x 500) - 100 e ...

Solution Summary

This solution provides guidelines to every step on how to solve two numerical problems (on chemical reactors) is provided.

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1. The following data were collected for the rate of disappearance of NO in the reaction 2NO(g)+O2(g)-----> 2NO2(g)

Experiment [NO](M) [O2](M) Initial Rate(M/s)
1 0.0126 0.0125 1.41 x 10^-2
2 0.0252 0.0250 1.13 x 10^-1
3 0.0252 0.0125 5.64 x 10^-2

a) What is the rate law for the reaction?
b) What are the units of the rate constant?
c) What is the average value of the rate constant calculated from the three data sets?
d) What is the rate of disappearance of NO when [NO]= 0.100 M and [O2]= 0.0200 M?
e) What is the rate of disappearance of O2 at the concentrations given in part (d)?

2. From the following data for the first-order gas-phase isomerization of CH3NC at 215 degrees Celsius, calculate the first-order rate constant and half-life for the reaction:

Time(s) Pressure CH3NC(torr)
0 502
2000 335
5000 180
8000 95.5
12000 41.7
15000 22.4

3. a) The activation energy for the isomerization of methyl isonitrile is 160kJ/mol. Calculate the fraction of methyl isonitrile molecules that have an energy of 160.0kJ or greater at 500 K.
b) Calculate this fraction for a temperature of 510 K. What is the ratio of the fraction at 510 K to that at 500 K?

4. The decomposition of hydrogen peroxide is catalyzed by iodide ion. The catalyzed reaction is thought to proceed by a two-step mechanism.
H2O2(aq)+ I-(aq)--->H2O(l)+ IO-(aq) [slow]
IO-(aq) + H2O2(aq)--->H2O(l) + O2(g) + I-(aq) [fast]

a)Write the rate law for each of the elementary reactions of the mechanism.
b) Write the chemical equation for the overall process.
c) Identify the intermediate, if any, in the mechanism.
d) Assuming that the first step of the mechanism is rate determining, predict the rate law for the overall process.

5. Cyclopentadiene(C5H6) reacts with itself to form dicyclopentadiene (C10H12). A 0.0400M solution of C5H6 was monitored as a function of time as the reaction 2 C5H6-----> C10H12 proceeded. The following data was collected:
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0.0 0.0400
50.0 0.0300
100.0 0.0240
150.0 0.0200
200.0 0.0174

Plot [C5H6] versus time, In [C5H6] versus time, and 1/[C5H6] versus time. What is the order of the reaction? What is the value of the rate constant?

6. a) Two reactions have identical values for Ea(activation energy). Does this ensure that they will have the same rate constant if run at the same temperature? Explain.
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7. Consider the following equilibrium, for which Kp=0.0752 at 480 degrees Celsius:
2 Cl2(g) + 2 H2O(g)----> 4 HCl(g) + O2(g)

a) What is the value of Kp for the reaction
4 HCl(g) + O2(g)----> 2 Cl2(g) + 2 H2O(g)?
b) What is the value of Kp for the reaction
Cl2(g) + H2O(g)-----> 2 HCl(g) + 1/2 O2(g)?
c) What is the value of Kc for the reaction in part b?

8. Phosphorous trichloride gas and chlorine gas react to form phosphorous pentachloride gas:
PCl3(g)+ Cl2(g)-----> PCl5(g)
A gas vessel is charged with a mixture of PCl3(g) and Cl2(g), which is allowed to equilibrate at 450 K. At equilibrium the partial pressures of the three gases are PpCl3= 0.124 atm, PCl2= 0.157atm, and PpCl5= 1.30atm.
a) What is the value of Kp at this temperature?
b) Does the equilibrium favor reactants or products?

9. Kp for the equilibrium
N2(g) + 3 H2(g)----->2 NH3(g)
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a) 105atm NH3, 35atm N2, 495atm H2
b) 35atm NH3, 595atm H2, no N2
c) 26atm NH3, 42atm H2, 202atm N2

10. Methanol (CH3OH) can be made by the reaction of CO with H2:
CO(g) + 2 H2(g)----> CH3OH(g)
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b) In order to maximize the equilibrium yield of methanol, would you use a high or low temperature?
c) In order to maximize the equilibrium yield of methanol, would you use a high or low pressure?

11. At 1200 K, the approximate temperature of automobile exhaust gases, Kp for the reaction, 2 CO2(g)----> 2 CO(g) + O2(g)
is about 1 x 10^-13. Assuming that the exhaust gas(total pressure 1atm) contains 0.2% CO, 12% CO2, and 3% O2 by volume, is the system at equilibrium with respect to the above reaction? Based on your conclusion, would the CO concentration in the exhaust be decreased or increased by a catalyst that speeds up the reaction above?

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pH pOH [H+] [OH-] Acidic or Basic?
6.5 x 10^-3M
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d) A mixture formed by adding 50.0 mL of 0.020 M HCl to 150 mL of 0.010 M HI.

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e) Benzoic acid (C6H5COOH) is a stronger acid than phenol (C6H5OH)

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