MS Comprehensive/PhD Qualifying Examination in Physical Chemistry Friday, 5 November, 2010, 9:00 am to 12:00 pm Questions in this examination are distributed in three areas of Physical Chemistry: thermodynamics, chemical kinetics and quantum chemistry. The questions in quantum chemistry are on the basis of a research article. Write clearly and show your work in order for any partial credits. Include all your worksheets with each question. Use your time wisely. Do not spend more than one hour on questions in one area unless you complete questions in another area in less than one hour.

Section  2   Chemical  Kinetics    1. Gaseous  ozone  O3  undergoes  decomposition  according  to  the  stoichiometric  equation  2  O3  (g)  →  3  O2  (g).    Two  alternative  mechanisms  have  been  proposed  to  account  for  this  reaction:  

         

     

(a) Derive  rate  laws  for  the  formation  of  O2  for  each  of  these  mechanisms.    Express  with  [O3],  [O2],  k1,  K1  and  k2.  

(b) Devise  a  kinetic  procedure  for  distinguishing  between  the  two  mechanisms.    State  clearly  the  nature  of  the  experiments  you  would  perform  and  what  results  you  would  use  to  make  the  distinction.  

(c) Thermodynamic  measurements  give  standard  enthalpies  of  formation  for  each  of  the  following  species  at  298  K:    ΔfH°298  (O2)  =  0.0  kJ/mol;  ΔfH°298  (O3)  =  142.3  kJ/mol;    ΔfH°298  (O)  =  249.4  kJ/mol.  

 The  observed  activation  enthalpy  ΔH‡  for  the  overall  reaction  is  125.5  kJ/mol  of  O3.    Sketch  a  diagram  of  enthalpy  (per  mole  of  O3)  vs.  reaction  coordinate  for  each  of  the  two  proposed  mechanisms.    Label  with  numerical  values  for  the  ΔH  between  reactants,  products,  intermediates,  and  transition  states.    Can  you  exclude  either  of  these  mechanisms  on  the  basis  of  the  thermodynamic  and  activation  enthalpy  values  of  part  (b)?    Explain  your  answer.  

(d) If  a  catalyst  is  used  in  Mechanism  (I),  how  does  it  impact  the  kinetics  and  the  thermodynamic  equilibrium  of  the  reaction?    Briefly  explain  your  answer.  

     

2. Consider  the  following  reaction  of  methane  with  molecular  chlorine:  

CH4  (g)  +  Cl2  (g)  →  CH3Cl  (g)  +  HCl  (g)  Experimental  studies  have  shown  that  the  rate  law  for  this  reaction  is  one-­‐half  order  with  respect  to  Cl2.    Is  the  following  mechanism  consistent  with  this  behavior?                        Derive  the  rate  law  for  HCl  formation  to  prove  your  statement.    Hint:  Apply  the  steady-­‐state  approximation  to  the  expression  for  [CH3·]  and  [Cl·].  

Section 3 Quantum Chemistry

You have been given a short part of a review of large electronic spin systems. Most of the questions revolve around section 3.

1) What is special about the single molecule magnets

2) In section 3 you are given a Hamiltonian (Eq 2) and an energy level equation as a function of Ms (Eq. 3). For Fig. 3b what term in Eq. 3 is responsible for the dip in the right well.

3) Given a simplified energy equation similar to Eq 3

E(Ms)= DMs2 + gµBMsH

Sketch the energy level diagram with H = 0 and D positive. Would this be conducive to single molecule magnetism, why or why not?

Choose one of the following:

4a) The energy level diagrams in Fig. 3 indicates a "zero point energy" similar to vibrational energy wells. Is this correct given the Hamiltonian, explain your reasoning.

4b) EPR involves an absorption of energy between adjacent levels. Using the equation in question 3, solve for the energy separation between EPR transitions (Ms = 10 to Ms =9) and (Ms=9 to Ms = 8) in terms of D. (Hint: Do this for H=0)