Review for Exam 1

Review for Exam 1

Review for Chapter 9

Considerations:

Know the formal definition of the rate of the reaction, n, 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 Lineweaver-Burk 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 y*y dt. 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 dt. What is dt 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, dt. 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 y) 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] 1/[A] = kt + 1/[Ao] 1/[A]2 = kt + 1/[Ao]2

[A]=[A]o e-kt t1/2 = 0.693/k t1/2 = 1/([A]o k) t1/2 = [A]o/2k

k = A e-Ea/RT lnk = lnA - Ea/(RT) rate =k [A]m[B]n[C]p E = -RH(1/n12 - 1/n22)

E = hn c = l n l = h/p Hy = Ey Dp Dx /2 [A,B] = AB - BA A = eCl

k = kBT/h exp(DS#/R) exp(-DH#/RT) rate = 2.303(1000)fIoA / l Km = (k-1 + k2)/k1

1/vo=Km/vmax1/[S] + 1/vmax vo= vmax / (1+ Km/[S]) y k = C cos(kx) + Dsin(kx)

y k = Aexp(ikx) + Bexp(-ikx) Ek = k22/2m = p2/2m <A>= ∫ y * A y dt / ∫ y * y dt

yn = (2/L)1/2 sin(npx/L) En = n2h2/(8mL2) ; y n1n2 = 2/(L1 L2) sin(n1px/L1)sin(n2py/L2);

En1 n2 = n12h2/(8mL12) + n22h2/(8mL22); Ephoton = KE + f = h/2p x = x*

px = -i d/dx H(y) = (-2 /2m) v2 + V h = 6.626x10-34Js, k = 1.38 x 10-23 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)

∫ sin2ax dx = x/2 - sin 2ax /(4a)