ChE 521
Solution to Midterm
Spring 2000
1.
The Arrhenius form of the rate expression for a 1st order reaction is as follows:
Rate = Aexp(-Ea/RT)C
Typical values for A and Ea are as follows:
A ~ 1013 s-1
Ea ~ 20 – 50 kcal/mol
2.
The basic assumptions of T.S.T. are as follows:
i.
There is a short-live intermediate called the transition state (or
activated complex). The transition state is defined as the highest
energy point on the potential energy vs. reaction coordinate. Once
formed any perturbation of the transition state will result in the
formation of products.
ii.
The reactants and the activated complex are in quasi-equilibrium. This
allows classical thermodynamics to be used to determine the
concentration of the activated complex.
3.
The pre-exponential factor depends on the entropy of activation and has a 1/T
temperature dependency.
4.
The shape of the TPD peak is asymmetric and is consistent with that expected for a
1st order process. The activation energy can be estimated from the equation:
Ea(in kcal/mol) ~ Tp/16
Based on this equation Ea ~ 750/16 = 47 kcal/mol
5.
A Langmuir isotherm describes the equilibrium surface coverage as a function of
concentration in the gas phase for a single adsorbate interacting with a fixed number
of adsorption sites.
1

0
P
6.
The basics assumptions for the BET isotherm are the following:
i.
Molecules adsorb in stacks.
ii.
Sticking coefficients are independent of stack height except that for
adsorption on to bare site.
iii.
Adsorption/desorption rate constants are independent of stack height
except those for adsorption/desorption onto bare site.
iv.
Equilibrium between adsorption/desorption on i and i+1 high stacks of
molecules
v.
Gas-liquid equilibrium can be used to describe adsorption on infinitely
high stack.
Vol.
adsorbed
P
7.
Reactions of metal surfaces are generally described to be either structure sensitive
or structure insensitive. A reaction is structure sensitive when the turn-over
frequency (TOF) is found to vary with the metal crystallite size of with the exposed
crystallographic planes. Structure sensitive reactions are thought to take place an
ensemble of surface metal atoms. Ammonia synthesis and hydrogenolysis are
classic examples of structure sensitive reactions. Reactions for which the TOF is
independent of the structure of the metal crystallites are called structure insensitive.
These reactions are thought to proceed on one or possibly two exposed metal atoms.
Selective and complete oxidation, and hydrogenation/dehydrogenation reactions are
generally found to be structure insensitive.
8.
Answers will vary.
9.
The goal of a reforming process is to transform low octane molecules into high
octane molecules. This is done using through a complex set of reactions the most
important of which are hydrogenation, dehydrogenation, and isomerization.
10. A typical reforming catalyst is composed of small crystallites of Pt or Pt mixed with
another metal (i.e. Sn, Re, Ge) supported on a high surface area acidic alumina. The
catalyst is called bifunctional because both the metal and the alumina are involved
in catalyzing reactions. The metal catalyzes primarily hydrogenation and
dehydrogenation reactions and some isomerization reactions, while the alumina is
active for acid-catalyzed isomerizations. Alkenes play an import role in interacting
between the metal and oxide functions. Alkenes are required for isomerization to
occur on the alumina. Alkenes formed on the metal can migrate to the oxide,
undergo isomerization and then be re-hydrogenated on the metal.
11. These was no problem 11.
12. The octane rating of a fuel is an empirically derived index which describes how
“fast” a fuel combusts. Low octane molecules undergo explosive combustion;
while high octane molecules undergo a slower more controlled combustion.
Internal combustion engines require high octane fuels for efficient operation. Isooctane has been assigned an octane number of 100, while n-heptane has been
assigned an octane number of 0.
13. The title of your paper.
14. Dispersion = no. of surface metal atoms / total no. of metal atoms
15.
K1K 2 k3 PA PB
r

L2 1  K P  K P
1 A
2 B


2
L = total no. of adsorption sites