ChE/ EEC 503
Spring 2009
Exam 1
(Closed book and notes)
PROBLEM 1
a)
What is a chemical reaction?
b)
What is a mole?
c)
What is reaction stoichiometry?
d)
A typical hydrocarbon fuel can be represented by CxHy. Air contains 79% (molar) N2
and 21% O2. Write a stoichiometric equation for complete combustion of the fuel to final
combustion products and show how many moles of air are needed per mole of fuel if oxygen
and fuel are to be used in stoichiometric ratio. Calculate moles of air needed for complete
combustion of i) C6H12 and ii) C6H6.
*e)
In case of incomplete combustion conducted with stoichiometric amount of air
when for each mole of hydrocarbon, CxHy, F moles of air are used and M moles of combustion
products are formed, while fraction f of the fuel is unburned (i.e. conversion of fuel is 1-f)
calculate the ppm by volume,  , of the unburned fuel in the exhaust gases as a function of F,
M and f.
PROBLEM 2
What is the rate of reaction? Can you deduce the rate form from stoichiometry of reaction
always, sometimes or never??
b)
What is the Arrhenius form of the rate constant?
c)
Which reaction rate constant increases more rapidly with temperature, the one with
lower or higher activation energy? What are typical values of activation energy in kcal/mole or
J/mole?
d)
For a second order gas phase irreversible reaction of activation energy of 20,000
(cal/mol) what will increase the rate more: quadrupling the pressure at constant temperature, or
increasing the temperature at constant pressure by 10˚ C? (R = 1.987 (cal/mol ˚K)). Does
your answer depend on reference temperature at which your reference rate is evaluated? (Try
298 K and 1000 K as reference temperatures!)
*e)
In combustion exhaust gases the following elementary reaction occurs
k
2NO O2 

2NO2
where k = 1.066 x 10-5 T-2e530/Tppm-2 min-1. The temperature range of interest is
300˚C to 800oC.
i)
What is the order of the above elementary reaction?
ii)
If the above rate constant is represented in an equivalent Arrhenius form,
what is the activation energy? Is that the type of value you expected? What does that tell you
about the temperature effect on this reaction? Explain your answer.
PROBLEM 3
a)
What is an elementary reaction?
b)
What are the basic postulates of the transition state theory TST? What is the universal
frequency equal to?
c)
What is a reaction mechanism?
d)
What are the basic postulates of PSSA for derivation of rate forms from a mechanism?
e)
Based on the Lindemann-Christiansen Mechanism for uni-molecular reactions what
reaction order is to be expected at a) high pressures, b) low pressure

A  A A*  A

A*  P

f) What factors, not considered in the gas phase, can affect elementary reactions in
solution?
g) A fast bimolecular liquid phase reaction can be partly or totally controlled by diffusion.
i) What is the rate constant equal to for completely diffusion controlled reaction? (If you do not
remember the exact form tell us what is it proportional to and how could you derive it!)
ii) What is the apparent rate constant equal to for partially diffusion affected liquid bimolecular
reaction in terms of the true kinetic constant and the diffusion controlled constant.? Describe
how to derive it.
*h) Ozone decomposition 203 = 302 is an important reaction both in atmospheric and water
chemistry. In the gas phase, the following mechanism is suggested
k
1


O3  M
O OM

 2
(1)
k 1
k
2
O3  O 

2O2
(2)
where M is a third body i.e. any other molecule.
i)
Based on the above mechanism derive the rate of decomposition of ozone in
the gas phase.
ii)
The data tabulated below was obtained for ozone decomposition in aqueous
acidic solutions at 304K and at HC O4  = 0.0l M. The values of the
pseudo first order rate constant listed below were obtained from the initial rate data (initial
slopes of [03] vs. t) at the conditions indicated.
O2 , M
10
400
1000
1000
1000
O3, M
200
200
200
95
380
 1
ks
1.3 x 10-4
7.0 x 10-5
4.7 x 10-5
2.4 x 10-5
8.0 x 10-5
Is the mechanism of ozone decomposition proposed for the gas phase compatible with
(i.e. can it explain) the data obtained in the liquid phase? Discuss and document your answer.
PROBLEM 4:
a)
What is a CSTR (continuous flow stirred tank reactor)?
b)
What is a PFR (plug flow reactor)?
c)
You are comparing different processes and reactor types for degradation of pollutant A
in a waste stream. Pollutant A concentration in the stream to be treated is [A]0 =10 mM and the
flow rate of the stream is 1000 L/min.
In presence of a dissolved enzyme, E, pollutant A decomposes by Michaelis-Menten kinetics,
with μmax = 50 mM/min and KM = 5 mM when the total enzyme concentration is 10-3 mM.
Note: Michaelis-Menten rate equation is max  A  K M   A where max   E  .
What reactor volume do you need to achieve 99% conversion of A in i) CSTR, ii) PFR?
*d) What reactor volume do you need for CSTR and PFR if you are willing to pay for more
enzyme and raise the enzyme concentration to 10-2 mM? Considering that capital cost is
proportional to reactor size and operating cost to enzyme concentration used, what information
would you need to determine reactor type and enzyme concentration to be used. Explain
clearly.
*e)
For the stream and cleanup duty of part c) which reactor(s) would you choose if the
rate of pollutant degradation (catalyzed by an enzyme ) is given by:
RA- = 750[A]/(5+ [A])2 (mM/min).
Do you note anything peculiar about this rate form? Is there a reaction order? Perhaps
you ought to plot the rate to see its behavior as a function of reactant concentration!
Explain and document your reasoning.
**PROBLEM 5
If a gas reactant only reacts upon dissolving in the liquid droplet with the solute in the liquid
phase, what are the characteristic times (resistances) that should be considered to determine
whether the reaction can be treated as occurring in a well mixed liquid which is in equilibrium
with the surrounding gas? Explain all the phenomena involved and provide the pertinent
criteria for SO2 dissolution and reaction with dissolved ozone. Under what condition can a 10
micron droplet in a haze aerosol at L= 10-10 be considered free of transport limitations and
treated as a well mixed liquid volume for the ozone – SO2 reaction. (Rely on the notes).
We would like to know the rate of sulfate formation through an aqueous S (IV) - O3
reaction in a haze aerosol of L = 10-10. Assume T = 298 K, pH = 5.6 and
pO3 = 5 x 10-8 atm (50 ppb). If the total sulfur concentration concentrations (gas + aqueous) is
'
5 ppb, calculate the rate of sulfate formation in ppb hr-1 and R g in % hr-1.
a) At these conditions is the reaction fee of all transport limitations?
b) What would be the situation if pH was 3?