Student name (print)__________________________________________
EECE 503
1.
Spring 2010
COURSE OUTCOME ASSESSMENT No.1
(closed book, closed notes)
Why are chemical reactions important to energy, environmental and process
engineering? Name as many reasons as you can think of.
Chemical reactions play a key role in a. generation of pollutant (e.g.
combustion of fossil fuels); b. pollution abatement (e.g. automobile exhaust
catalytic conversion)
2.
What is a chemical reaction?
A process that leads to the transformation of one set of chemical substances
to another.
3.
What do we mean by reaction stoichiometry? What does stoichiometry
represent?
Reaction stoichiometry is the calculation of quantitative relationships of the
reactants and products in a balanced chemical reaction. It represents the
quantitative relationship between all substances in a balanced chemical
reaction. It is represented by the stoichiometry coeffients based on the
principle of conservation of atomic species.
4.
What is a mole? What is the relationship between a kmol and mol? What is the
relationship between a lbmol and a mol?
A mole is the count of substances of a system that contains as many
elementary entities as there are carbon atoms in 0.012kg of carbon-12.
nj(lbmol)=mj(lb)/Mj.
5.
Progress of single reaction can be represented by a single molar extent of
reaction, X. What is the relationship between the initial moles of reactants and
products, nj0, the moles for each of the above after some reaction time, nj, the
stoichiometric coefficients, νj, and reaction extent, X? Express this relation by a
single equation.
nj=nj0+νjX; nj : moles after time t; nj0:initial moles; νj: stoichiometry
coeffients; X: reaction extent
1
6.
Relate molar extent of reaction to the fractional conversion of the limiting
reactant. What is the limiting reactant?
X=x•nj0/abs(νj); The limiting reactant is the one present in amounts less than
required by stoichiometry and limits the reaction extent to Xmax= nj0/νj.
7.
What is the relationship between mole fraction of various products and reactants
and reaction extent?
yi 
8.
n j0  v j X
ntot  X  v j
Extend the relationship developed in answering question 5 to multiple reactions
consisting of R independent reactions between S species? Denote the molar extent
of reaction I by Xi.
S
R
j 1
i 1
 vij Aj  0; n j  n j 0   vij X i ; j  1,2,3...S; i  1,2,...R.
9.
What is the stoichiometric coefficient of an inert?
0
10.
In a set of R’ stoichiometric reactions between S species how would you
determine the set R of independent reactions?
Rank(matrix of stoichiometry coeffients matrix)
11.
What is the rate of reaction? Define it.
The number of moles of j produced by reaction per unit time per unit volume
of the system
12.
What does the rate of reaction depend on? List the variables that affect it.
Temperature, pressure, composition, catalytic activity, etc
13.
What is activation energy for the reaction? Can it be defined always?
Activation energy is defined as the energy that must be overcome in order for
a reaction to occur. It cannot be always defined. Sometimes reaction rates
cannot be fitted by the power law form, thus reaction order and activation
energy cannot be defined.
14.
Which reaction rate increases more rapidly with temperature, the one with lower
or higher activation energy?
2
ln k  ln k0 
15.
E
, higher activation energy results in a steeper slope.
RT
What is the Arrhenius form of the rate constant?
k  k0 exp( E / RT )
16.
How can an n-th order reaction rate be represented?
rA  kC An  k0 exp(  E / RT )C An
17.
Can the temperature and composition dependence term be separated in reaction
rates that follow the Langmuir-Hinshelwood (Hougen-Watson) form? Can an
activation energy be defined for the rate form of that type?
r
k0 exp(  E / RT )C A
, hence the temperature and composition
k0 exp(  E / RT )  C A
dependence term cannot be separated; the activation energy cannot be
defined.
18.
What is molar internal energy? What is it a function of?
Molar internal energy of a thermodynamic system is the total of the kinetic
energy due to the motion of molecules (translational, rotational, vibrational)
and the potential energy associated with the vibrational and electric energy
of atoms within molecules. It is a function of temperature and pressure.
19.
How is molar enthalpy defined? What about partial molar enthalpy? What
information is needed to calculate it at a given temperature and composition?
H=E+PV per mole; E is the molar internal energy
20.
What is the standard heat of reaction?
H ro,i   vij H of , j , at standard condition (298K, 1 atm)
j
21.
What is molar Gibbs free energy in terms of molar enthalpy and entropy?
G  H  T S
22.
What is the thermodynamic condition for equilibrium in a reactive system?
S
Minimum in gibbs free energy of the system,
v G
j 1
23.
j
j
0
How is the thermodynamic equilibrium constant defined?
3
S
K   a j j  exp( G / RT )
v
j 1
24.
How is the standard Gibbs free energy for reaction calculated and how does it
relate to the equilibrium constant?
S
Gro   v j G f , j ; Gro   RT ln K298
j 1
25.
What is Van’t Hoff’s equation for variation of equilibrium constant with
temperature?
d ln K H r

dT
RT 2
26.
How can one calculate the heat of reaction as a function of temperature?
or
27.
Does the equilibrium constant have units?
No.
28.
How does one relate activity to mole fraction? Activity to concentration?
ai   i  X i   i 
29.
Ci
P
; ai   i yi
C0
P0
Would the equilibrium conversion of SO2 reacting with air at 25˚C and at 600˚C
and P= 1 atm be larger for a feed that contains
1) stoichiometric ratio of reactants, or
2) large excess of air?
What would happen to the equilibrium conversion if your raised the pressure of
operation to 100 atm. Would it be affected more for case 1 or case 2?
Assume constant heat or reaction. Clearly outline your reasoning.
1) 0.777; 2)X=1; 3) conversion increase; case 2
4
30.
What is the kinetic definition of equilibrium? What constraint does that impose on
the reaction forms for the reverse and forward reactions?
At equilibrium, the net rate of reaction is 0, that is rf=rb.
31.
If Arrhenius form is used to represent the rate constant kc ((mol/L)1-n s-1) and the
rate constant for the same gas phase reaction expressed as kp (mol/L) atm-n s-1),
what is the relationship between kco and kpo and EP and Ec? Show how would you
go about finding this relationship.
r  kc C An  k p PAn
PA  C A RT
kc  k p ( RT ) n
kc 0  k p 0 ( RT ) n e n
Ec  E p  nRT
32.
What are the basic postulates of the transition state theory (TST)?
1) r=νCz (ν: frequency of occurrence of exchange), equilibrium between
transition states and reactants is always established
2) ν=kBT/hp, is not dependent on the nature of the molecular system
3)The reaction system is “symmetric” with respect to the transition state
33.
What is the universal frequency of TST equal to?
ν=kBT/hp, kB=1.38062×10-23 J/K, hp=6.6262×10-34 J∙s
34.
How does the expression for the rate constant derived by TST account for system
non-ideality?
kBT  RTG
r
e
a A aB
hp  z
*
35.
Using TST and Debye-Huckel theory what relation results for the dependence of
the rate constant on ionic strength of the solution.
ln  j   Az 2j I , k1c  k1
36.
 A B
, ln k1c  ln k1  2 Az A zB I
 Z*
What is an elementary reaction? What can one say about stoichiometric
coefficients for an elementary reaction? How are they related to reaction order?
Elementary reactions are those that proceed in one step. The stoichiometry of
elementary reactions is not arbitrary and the stoichiometric coefficients must
be integers reflecting the molecularity of the process
5
37.
What is the law of mass action? When does it apply?
Stoichiometric coefficients are equal to molecularity of the species involved.
Only for elementary reactions, the law of mass action applies.
38.
In gas phase reactions bimolecular reactions can occur between what type of
species? The rate of bimolecular reactions is of what order?
The reaction can occur between two molecules, a free radical and a molecule, an ion
and molecule, two free radicals. It is 2nd order.
39.
What gas phase trimolecular reactions do you know? What is the overall reaction
order?
2NO+X2=2NOX, X=Cl, O, Br, etc
Overall reaction order is always 3.
40.
Are gas phase unimolecular reactions always first order?
No. At very low pressure, 2nd order is observed
41.
What is the Lindemann – Christansen mechanism for unimolecular reactions?
A PR

k1
A  A 
 A*  A
k 1
A *  P  R
k2
k1k2 [ A]2
Rp 
k1[ A]  k 2
42.
How do we obtain the rate forms for free radical recombination reactions?
By using the fact that the net rate of R2* formation is 0.
(For reactions
k1
R*  R* 
 R2*
k 1
k2
R  M 
 R2  M
*
2
)
43.
What are the key differences between gas phase reactions and reactions in
solution?
1) The medium (solvent) is considerably denser and more viscous
2) The solvent may affect the reaction rate
3) Many molecules ionize in solution, leading to reactions among ions and ions
44.
What relationship between reaction rate constant and solvent properties does TST
predict?
6
 Ad  Bd
k  k0 d for A+B→Z
Z
k0 is the rate constant in an ideal solution and activity coefficient now relate to
infinite dilution
45.
What is diffusion?
Diffusion is the process of molecular mixing based on random motion due to
molecular kinetic energy and velocity distribution
46.
If elementary reactions in solution involve ions or other charged species how does
TST account for the effect of the electric field?
Total Gibbs free energy change consists of the electrostatic and non-electrostatic
contribution as
*o
G *o  Ges*o  Gnes
47.
What dependence of the rate constant on solvent and ion properties is obtained by
TST via the dual sphere and single sphere model?
*o
z A zB e 2
k T
o
dual : ln k  ln k 
, k o  B e Gnes / RT
4 0 d AB k BT 
hP
single : ln k  ln k o 
48.
e2
8 0 k B
(
( z A  zB ) 2 z A2 z B2

 )
rA rB
r*
What is Ficks First Law of diffusion?
C
X
J   DC
J  D
49.
What is Ficks Second Law of diffusion?
C
 D 2 C
t
50.
What is the RMS displacement equal to according to the diffusion equation?
2
X  2 Dt
7
51.
What is the meaning of a diffusion limited reaction in the liquid state? What is
the value of the rate constant?
Very rapid reactions with the overall rates of reaction controlled totally or partly by
the diffusion process. The rate constant kD=4π(rA+rB)(DA+DB)=4πDABdAB.
52.
What is the expression for the apparent rate constant for a bimolecular liquid
phase reaction that is controlled both by kinetics (i.e transition state complex
transformation) and diffusion.
Partial Diffusion Effects:
kchem
k
kchem
1
4 DAB d AB
53.
What is a reaction mechanism?
It is a sequence of elementary events that represents the detailed pathway of
transformation of the reactants through highly reactive intermediates (active
centers) to final products
What is the difference between an “open” and “closed” reaction mechanism
sequence?
Open: active center is not reproduced in other step s of the sequence, non-catalytic
Closed: an active center is reproduced so that a cyclic pattern repeats itself,
catalytic; (a large number of molecules of products can be made from only one
active center)
54.
55.
What is the relationship between the stoichiometry of individual mechanistic steps
and the overall stoichiometry for mechanisms containing a closed sequence?
The weighted sum of the steps of closed system must result in the overall
stoichiometry.
56.
What are the steps for deriving an overall rate expression in terms of the
concentrations of stable species when applying PSSA to a postulated mechanism?
1) hypothesized mechanism; 2) set up the net rate of formation for every active
intermediate 3) set all the net rates above to be zero and calculate the concentration
of all active intermediate; 4) set up the expression in terms of the concentration of a
stable species which appears in fewest steps by eliminating all the concentration of
active intermediate 5) simplify if possible
57.
What are the key features in deriving a rate form based on RLSA application to a
postulated mechanism?
1) rate limiting step determines the overall rate
2) all other steps may be presumed in equlibrium
58.
What is characteristic reaction time? Reaction half life?
8
Characteristic time: defined as τR=1/kCj0n-1, time for Cj to decay to e-1 of Cj0 in a
Cj0
closed system. Half life:
R 

Cj0
dC j
R j , time needed for the reactant concentration
2
to be reduced to half of its original value in a closed system
59.
How is quantum yield defined?
It is defined as the ratio of the number of radicals A* reacting by that process to the
number of photons absorbed.
60.
What is the maximum ozone concentration proportional to if one considers only
NO, NO2, and O3?
[O3 ] max  [ NO2 ]
61.
What are the NOx and CO roles in ozone formation?
62.
Where does sulfur conversion occur in the atmosphere, in the gas phase or liquid
phase?
Homogeneous gas phase reaction; heterogeneous reactions in droplets or on the
surface of droplets
63.
What are the key reactions in oxidation of S(IV) to S(VI)?
Gas phase: 2SO2+O2→2SO3;O3+SO2→O2+SO3
Liquid phase: SO32-+1/2O2→ SO42-; SO32-+O3→ SO42-+O2; HSO32-+H2O2↔HSO4+H2O
64.
What are the key five characteristic times for reaction of a gas phase reactant in a
liquid droplet?
τdg, τp, τi, τdl, τrl or τrg
65.
Which of the characteristic times are most likely to be rate controlling for a:
a) highly soluble gas, b) slightly soluble gas.
a) τrl b) τp
9
66.
Write the basic conservation law for a chemical species j in a single phase well
mixed system that is: a) closed, b) open. Identify all the terms.
d (VC j )
 VR j ; t  0, C j  C j 0
dt
d (C j )
 VR j  Q(C jin  C j ); t  0, C j  C j 0
b) V
dt
Cj (mol/L): molar concentration; V(L): volume of the system; Rj(mol j/L/s):
reaction rate of production species j; Cj0 (mol/L): initial concentration; Q:
volumetric flow rate; Cjin (mol/L): concentration of j in the incoming flow;
a)
67.
Write the basic conservation law for a chemical species j in a two phase well
mixed system that is : a) closed , b) open. Identify all the terms. Do not assume
that the system is equilibrated.
a)
b)
68.
Modify the equations developed in answering question 67 to the form appropriate
when all species are equilibrated between the two phases.
a)
b)
10
69.
Explain the meaning of the modified Henry’s constant for a soluble gas that upon
dissolution dissociates. Use ammonia as a n example.
Modified Henry’s constant is an apparent Henry constant for a soluble gas, which is
a function of pH of the solution.
NH 3  H 2 O 
 NH 3  H 2 O; H NH3
NH 3  H 2 O 
 NH 4  OH  ; K N 1
[OH  ]  [ NH 4 ] 
 [ N ( III )]  H NH3
K N 1  H NH3  PNH3
[OH  ]
K N1
 PNH3 (1 
)  H *NH  PNH 3

3
[OH ]
 H *NH  H NH3 (1  K N 1 *10 pH 14 )
3
70.
Illustrate the use of equations developed to treat sulfur dioxide oxidation in ar that
contains L volume fraction of water in droplets form. Assuming that the only
species originally present in the gas phase are nitrogen, oxygen, carbon dioxide,
sulfur dioxide, ozone show which equations would need to be solved to monitor
the evolution of pH, S(VI) concentration in the liquid phase. Do not forget to
specify the electroneutrality equation. Assume a closed system.
11
CO2  H 2 O
CO2  H 2O; H CO2
H 2 CO3
H   HCO3 ; K C1
HCO3
H   CO32  ; K C 2
SO2  H 2 O
SO2  H 2O; H SO2
H 2 SO3
H   HSO3 ; K S1
HSO3
H   SO32  ; K S 2
1
SO32   O2  SO4 2  ; K S 3
2
2
SO3  O3  SO4 2   O2 ; K S 4
2 SO2  O2
2SO3 ; K S 5
SO3  H 2 O
SO3  H 2 O; H SO 3

H 2 SO4
H  HSO4  ; K S 6
HSO4 
H   SO4 2  ; K S 7
[ H  ]  [OH  ]  [ HCO3 ]  2[CO32  ]  [ HSO3 ]  2[ SO3 2  ]  2[ SO4 2  ]  [ HSO4  ];
12