Review for Exam 1
Review for Chapter 9
Considerations:
Know the formal definition of the rate of the reaction, , in terms of the derivative of the
concentration of reactants or products with respect to time. How is the rate written in
terms of one reactant or product related to the rate written in terms of another product or
reactant?
Be able to identify the various parts of the rate law of a reaction. You should know what
the overall order of a rate law is, and the order with respect to a given component. What
is pseudo 1st order? Be familiar with both the differential and integrated forms of the
rate expression, and know how to derive them. How can one get the half-life expression
from this information? Be able to use the integrated forms to determine the concentration
of a product or reactant at a given time. How do you determine the order of a reaction by
plotting information about the reactants?
You should remember that the rate expression may not be written down from the overall
balanced reaction. The elementary steps that make up a reaction are called the
mechanism. What is the molecularity? The rate law for the elementary step may be
written down directly from the reaction step. One should be able to take a mechanism
and derive the overall rate expression for the reaction IN TERMS OF STABLE SPECIES
(usually the product and reactant concentrations) by making some assumptions:
1) steady state for concentrations of intermediates
2) pre-equilibrium
3) slow step
The rate laws for the elementary steps can be written directly from the step as the product
of the rate constant times the reactant concentrations raised to a power which is the
stoichiometric coefficient of that reactant. This will be a positive term if the step makes
more of the species which whose concentration we are interested in as a function of time.
If it is disappearing there should be a negative in front of the rate constant. THIS ONLY
WORKS FOR THE ELEMENTARY STEP.
Be able to explain and develop the differential form of the rate law formulas for the
following types of reactions. 2nd order renaturation of DNA, parallel reactions, series
reactions, equilibrium kinetics. What information is needed to determine the Arrhenius
parameters like the activation energy and the preexponential factor. What about the
features of transistion state theory. What is a transition state? What are the transition
state Gibbs Free Energy, Enthalpy, and Entropy. How are they related to the Arrhenius
parameters? What is the advantage of transition state theory over the Arrhenius
parameters.
For very fast reactions, how is the rate of the reaction measured (temp. jump, pressure
jump, flash/laser pulse)? Be able to explain the isotope effect.
What is a diffusion controlled reaction? How is the diffusion coefficient related to the
pre-exponential factor (A) in the Arrhenius expression.
Chapter 10
In the next chapter we discussed catalysis. What are a substrate, an enzyme, a catalyst, a
cofactor, a ribozyme, turnover number, protein, Michaelis-Menten kinetics. General
qualities of enzyme catalyzed reactions include: the rate of substrate conversion
increases linearly with enzyme concentration, the rate is linear in substrate concentration
at low values of [S} for fixed enzyme concentration, and the rates of enzyme reaction
approach a maximum velocity at high substrate concentrations. You should be able to
recognize the Michaelis Menten mechanism and the expression for the rate in terms of
Vmaz, the substrate concentration, and the Michaelis constant, km. How can the Michaelis
expression for the rate be linearized. You should know the Lineweaver-Burk plot, the
Dixon equation and the Eadie-Hofstee eqn. Given the linearized eqn., you should be able
to tell what information the slope and the intercept yield. Remember that Km is equal to
the substrate concentration when the velocity equals ½Vmax.
What are competition and inhibition? What are the meanings of competitive inhibition,
noncompetitive inhibition, and uncompetitive inhibition? How does the LineweaverBurk plot change for each of these types of inhibition. How does the V vs [S] plot differ?
What is the MWC Theory? Is this concerted or not concerted. What is the sequential
model. What are allosteric effectors and allosteric inhibitors.? Are the catalytic
constants for different molecules all the same. What is a Hill Plot?
Chapter 11
You should be familiar with some of the history of the development of Quantum
Mechanics. Specifically, blackbody radiator, photoelectric effect, and the electron-slit
experiment are important in the development of quantum mechanics. What are these, and
how did they help define the theory of small particles/waves? What is the work function?
How is the wavelength of light or its frequency related to the energy of the light? Find
for small particles that it matters if we measure the momentum or position first. How
does this correlate with the idea of commutation of operators. What does DeBroglie’s
relationship tell us about particles and wavelength? What is the relative size and
wavelength for an atomic sized particle? What does it mean if two operators are said to
commute? What is an operator? Be able to determine the value of the commutator.
Why use operators to represent the physical observables? What are the Hamiltonian and
the Laplacian? What are an eigenvalue eqn., an eigenvalue, an eigenstate and a linear
combination. You should be able to tell if a particular function is an eigenfunction of an
operator. What is the relationship between the Heisenberg uncertainty principle and
operators? What are the Correspondence Principle and the Complimentary Principle?
Quantum Theory can be written down in terms of the postulates. You should be familiar
with the postulates and understand all that they define. Postulate one tells about the
wavefunction and the idea that all the information about the system is in the
wavefunction. The Born interpretation, tells us about d What are the restrictions
on the wavefunctions that are solutions to an eigenvalue eqn. of a physical observable?
Postulate 2 defines the operators in the position representation where x = x, and p = ihd/dx in x dimension, and associates the Hermitian Operators with physical observables.
Postulate 3 links observables to operators in terms of the average or expectation value of
an observable D, specified as <D>. Remember that this is an integral expression. What
are the limits on the integral. What is dWhat is d for spherical polar coordinates?
Remember that the limits and the volume element depend on the system that we are
describing. For instance for a 1 dimensional particle in a box, d is simply dx and the
limits on the integral are over the dimensions of the box, (i.e. 0 to L). Is the denominator
in this expression always necessary? Postulate 4 describes what observation is expected
if the system is in an eigenstate of the operator. Postulate 5 describes what happens if the
system is in some arbitrary state which can be written as a linear combination (a
superposition) of the eigenstates and gives the probability that the result is a particular
eigenvalue based upon the coefficients in the linear combination. We’ll talk more about
this later! Postulate 6 tells us about the time dependence of a wavefunction; gives time
dependent Schrodinger eqn. ANOTHER subpostulate based on the commutator relations
says that if two observables are to have simultaneous precisely defined values, then their
corresponding operators must commute. Be able to find the commutator of two
operators. Remember to do this it is best to let the commutator operate on a function.
Two observables that cannot be determined simultaneously are said to be complementary
(Heisenberg Uncertainty Principle again).
Know the definitions of normalization, orthogonality and orthonormal as they pertains to
wavefunctions and eigenfunctions. Be able to perform a normalization and to determine
orthogonality as it pertains to wavefunctions. Also you should know how to find the
expectation or average value of some quantity using the eigenfunctions that are a solution
to the system you are interested in. Also remember that in a spectrum the peaks
correspond to the energy of the photons that were absorbed or emitted during a transition
from one energy state to another.
Much of what we did was to get the correct form of the Hamiltonian (sometimes we had
to switch coordinate systems and manipulate the form a bit) for the particular system that
we were interested, and then solved Schrodinger’s eqn. to determine the energy
eigenfunctions and the energy eigenstates. Remember that the eigenfunction (we often
have used the symbol ) gives us information about the system (Born Hypothesis) and
the energy eigenstates give us the allowed energies of the system. The systems that we
are studying are simple solvable models for translation, rotation, vibration, and electronic
energies. Also there were restrictions on the allowed quantum numbers for the system.
For the cases we studied, we found that when the particle was bound, the energies for that
system were quantized.
Can quantization occur for a free 1d particle, a 1d particle with a potential barrier only on
one side, a 1d particle surrounded by barriers? Looking at the form of the wavefunction
for translational motion, should be able to indicate the momentum direction. Complex
wavefunctions correspond to definite states of linear momentum. You should be familiar
with how the energy eigenvalues were determined for the particle in the box and how
they are spaced. What is zero point energy? You should be able to determine the
probability that a particle is in some region of the box, or the positions where it has the
highest probability of existing? Can you calculate the average energy, momentum,
and/or position? What are the allowed values for the quantum number. How about a two
dimensional box? How do we get degeneracy (define) for a two or higher dimensional
box? This models translational motion; translation of electrons in dye molecules for
instance or in nanoparticles.
What is tunneling? To what is the transmission probability related. How are the
transmission probability and the reflection probability related to each other? How is the
transmission probability related to the mass of the particle, the width of the barrier, and
the barrier height? If the energy of the particle is greater than the potential barrier,
quantum mechanically speaking, will the particle have a transmission probability of
100%.
The exam will be the same format as last semester with multiple choice and a problem
section. Problems will be based on concepts learned through homework and quizzes.
Equations, Constants
ln[A] = -kt + ln[Ao] [A] = -kt + [Ao]
[A]=[A]o e- k t
t1/2 = 0.693/k
1/[A] = kt + 1/[Ao]
t1/2 = 1/([A]o k)
k = A e-Ea/RT lnk = lnA - Ea/(RT)
1/[A]2 = kt + 1/[Ao]2
t1/2 = [A]o/2k
rate =k [A]m[B]n[C]p
E = -RH(1/n12 - 1/n22)
E = hc =    = h/p
H = Ep x > h/2
/
[A,B] = AB - BA A = Cl

k = kBT/h exp(S# /R) exp(-H# /RT) rate = 2.303(1000)IoA / l Km = (k-1 + k2)/k1
1/vo=Km/vmax1/[S] + 1/vmax vo= vmax / (1+ Km/[S])  k = C cos(kx) + Dsin(kx)

 k = Aexp(ikx) + Bexp(-ikx) Ek = k2h/ 2/2m = p2 /2m  <A>= ∫ * A  d∫ *  d

n = (2/L)1/2 sin(nx/L) En = n2h2/(8mL2) ; n1n2 = 2/(L1 L2) sin(n1x/L1)sin(n2y/L2);
En1 n2 = n12h2/(8mL12) + n22h2/(8mL22);
px = -i h/ d/dx
H(y) = (-h/ 2 /2m) v2 + V
Ephoton = KE + 
h = 6.626x10-34Js,
h/ = h/2
x = x*
k = 1.38 x 10- 2 3 J/K
c = 3.00 x 108 m/s me = 9.109 x 10-31 kg, 1 amu = 1.66 x 10-27 kg R = 8.314 J/(mol K)
∫ sin2 ax dx = x/2 - sin 2ax /(4a)