1. L11-1 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. Review: Nonelementary Reaction Kinetics Nonelementary reaction kinetics No direct correspondence between reaction order and stoichiometry Result of multiple elementary reaction steps and reactive intermediates (an intermediate so reactive it is consumed as fast as it is formed) How do we determine the reaction mechanism? 1.Postulate a reaction mechanism that is a series of elementary reactions 2.Derive a rate equation for the postulated mechanism 3.Determine whether the rate eq for the postulated mechanism consistent with the experimental results. If it is, you’re done. If they are not consistent, go back to step 1.

2. L11-2 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. Review: Postulating a Reaction Mechanism Based on an Experimentally Observed Rate Law 1.If C B appears in the denominator of the experimentally observed rate law, then one elementary reaction step is probably: where A * is a reactive intermediate 2.If the denominator contains a constant (by itself, not multiplied by a concentration), then one reaction step is probably: 3.If the numerator contains a species concentration, then one rxn step is probably: Derive a rate equation for the postulated mechanism and check if it describes the experimentally observed rate equation This will definitely be on quiz 3!

3. L11-3 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. Review: Deriving a Rate Equation for a Postulated Mechanism 1)Write rate equation for postulated mechanism 2) For concentrations of reactive intermediates C I* that appear in the rate equation –r A a) Write out the rate equation for reactive intermediates r I* b) Apply Pseudo-Steady State Hypothesis, which states that the net formation of reactive intermediates is zero (r I* =0) c) Solve for C I* in terms of measurable species d) Substitute the new expression for C I* in terms of measurable species back into -r A 3) Rearrange –r A to check if it matches the experimentally observed rate equation

4. L11-4 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. Review: Free Radical Polymerizations M M M M M M M-M-M n monomer polymer 1. Initiation: 2. Propagation: 3. Chain transfer: 4a. Termination by addition: Initiator (I) decomposes to 2 free radicals Radical (1) Chain elongation, new monomers add to chain “Live” polymer chain transfers radical to monomer. Polymer chain is no longer reactive (dead). Can also transfer to solvent or other species 4b. Termination by disproportionation:

5. L11-5 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. Review: PSSH Applied to Thermal Cracking of Ethane The thermal decomposition of ethane to ethylene, methane, butane and hydrogen is believed to proceed in the following sequence: Initiation: Propagation: Termination: (a) Use the PSSH to derive a rate law for the rate of formation of ethylene (b) Compare the PSSH solution in Part (a) to that obtained by solving the complete set of ODE mole balance

6. L11-6 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. L11: Thermochemistry for Nonisothermal Reactor Design The major difference between the design of isothermal and non- isothermal reactors is the evaluation of the design equation –What do we do when the temperature varies along the length of a PFR or when heat is removed from a CSTR? Today we will start nonisothermal reactor design by reviewing energy balances Monday we will use the energy balance to design nonisothermal steady-state reactors Nonisothermal Energy balance

7. L11-7 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. Why do we need to balance energy? FAFA X A = 0.7 Mole balance: Rate law: Stoichiometry: Arrhenius Equation Need relationships: X T V Consider an exothermic, liquid-phase reaction operated adiabatically in a PFR (adiabatic operation- temperature increases down length of PFR): F A0 We can get them from the energy balance

8. L11-8 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. Clicker Question The concentration of a reactant in the feed stream (inlet) will be greatly influenced by temperature when the reactant is a)a gas b)a liquid c)a solid d)either a gas or a liquid e)extremely viscous Gas phase: Liquid & solid phase: Hints:

9. L11-9 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. Thermodynamics in a Closed System First law of Thermodynamics –Closed system: no mass crosses the system’s boundaries dÊ: change in total energy of the system  Q: heat flow to system  W: work done by system on the surroundings QQ WW

10. L11-10 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. Ẇ F in H in F out H out Thermodynamics in an Open System Open system: continuous flow system, mass crosses the system’s boundaries Mass flow can add or remove energy Energy balance on system: Rate of accum of energy in system work done by system energy added to sys. by mass flow in energy leaving sys. by mass flow out Heat in =-+- Let’s look at these terms individually

11. L11-11 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. The Work Term, Ẇ Work term is separated into “flow work” and “other work”. Flow work: work required to get the mass into and out of system Other work includes shaft work (e.g., stirrer or turbine) other work (shaft work) P : pressure Ẇ : Rate of work done by the system on the surroundings Flow work Plug in: Accum of energy in system Other work Energy & work added by flow in Energy & work removed by flow out Heat in =-+ -

12. L11-12 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. The Energy Term, E i Accum of energy in system Other work Energy & work added by flow in Energy & work removed by flow out Heat in =-+ - Internal energy Kinetic energyPotential energy Electric, magnetic, light, etc. Usually: Plug in U i for E i : Internal energy is major contributor to energy term

13. L11-13 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. Recall eq for enthalpy, a function of T unit : (cal / mole) Steady state: Accumulation = 0 = in - out + flow in – flow out Total Energy Balance

14. L11-14 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. In Terms of Conversion: If X A0 =0, then: Steady state: Total energy balance (TEB) Relates temperature to X A Multiply out: Must use this equation if a phase change occurs

15. L11-15 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. What is (H i0 – H i )? When NO phase change occurs & heat capacity is constant: Enthalpy of formation of i at reference temp (T R ) of 25 °C What is the heat of reaction for species i (H i )? Change in enthalpy due to heating from T R to rxn temp T

16. L11-16 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. What is ΔH RX (T)? How do we calculate ΔH RX (T), which is the heat of reaction at temperature T? For the generic reaction:

17. L11-17 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. Example: Calculation of ΔH RX (T) For the reaction N 2 (g) + 3H 2 (g) → 2NH 3 (g), calculate the heat of reaction at 150 °C in kcal/mol of N 2 reacted. Extra info:

18. L11-18 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. Example: Calculation of ΔH RX (T) For the reaction N 2 (g) + 3H 2 (g) → 2NH 3 (g), calculate the heat of reaction at 150 °C in kcal/mol of N 2 reacted. Extra info: Convert T and T R to Kelvins

19. L11-19 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. Example: Calculation of ΔH RX (T) For the reaction N 2 (g) + 3H 2 (g) → 2NH 3 (g), calculate the heat of reaction at 150 °C in kJ/mol of H 2 reacted. Extra info: Convert kcal to kJ Put in terms of moles H 2 reacted

20. L11-20 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. Q and H i in Terms of T Ignore enthalpy of mixing (usually an acceptable assumption) Look up enthalpy of formation, H i ◦ (T R ) in a thermo table, where the reference temperature T R is usually 25 ◦ C Compute H i (T) using heat capacity and heats of vaporization/melting Phase change at T m (solid to liquid): Solid at T R For T m < T < T b ←boiling If constant of average heat capacities are used, then: For T m < T < T b melting

21. L11-21 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. Insert ΔH RX (T) & (H i0 – H i ) into EB Example calculations of ∆H° RX (T R ) & ΔC p are shown on the previous slides If the feed does not contain the products C or D, then: (T i0 – T) = - (T – T i0 )

22. L11-22 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. Clicker Question If the reactor is at a steady state, which term in this equation would be zero? a)dE sys /dt b) c) Ẇ d)F A0 e)∆C P Accum of energy in system Other work Energy & work added by flow in Energy & work removed by flow out Heat in =-+ - At the steady state:

23. L11-23 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. How do we Handle Q in a CSTR? CSTR with a heat exchanger, perfectly mixed inside and outside of reactor T, X F A0 T, X TaTa TaTa The heat flow to the reactor is in terms of: Overall heat-transfer coefficient, U Heat-exchange area, A Difference between the ambient temperature in the heat jacket, T a, and rxn temperature, T

24. L11-24 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. Integrate the heat flux equation along the length of the reactor to obtain the total heat added to the reactor : Heat transfer to a perfectly mixed PFR in a jacket a: heat-exchange area per unit volume of reactor For a tubular reactor of diameter D, a = 4 / D For a jacketed PBR (perfectly mixed in jacket): Heat transfer to a PBR Tubular Reactors (PFR/PBR):