1. CHE 354 Chemical Reactor Design Rate Laws

2. PFR Steady state This is the integral form. Often the differential form is more useful. Take the derivative with respect to volume of each term.

3. PFR Derivative of a constant is just 0 rArA

4. PFR

5. Rate of Reaction rate = amount/(time x “volume”) amount [=] mol, g time [=] s, min, h “volume” [=] L (dm 3 ), kg cat, m 2 cat r A = mol/s/L r A ’ = mol/s/g r A ” = mol/s/m 2

6. Generic Reaction aA + bB  cC + dD Elementary (irreversible) -r A = k C A a C B b Elementary (reversible) -r A = k f C A a C B b – k r C C c C D d

7. Generic Reaction aA + bB  cC + dD 1st Order -rA = k CA 2nd Order -rA = k CA2 Power Law -rA = CA CB Complex -rA = k1 CA/(1+k2 CA) So how do we know? Experiment!

8. Generic Reaction aA + bB  cC + dD Assume experiment shows reaction is elementary and irreversible: -r A = k C A a C B b Now, rewrite the stoichiometric equation: A + (b/a)B  (c/a)C + (d/a)D What is rate law?

9. So what about the rate constant? Arrhenius Equation k = A exp(-Ea/RT) ln k = ln A – Ea/RT m = -Ea/RT Y = b + mX Y = ln k X = 1/T

10. OK, what is this activation energy?

11. A + B ABP

12. Firefly Flashing Frequency T ( o C) 212530 Flashes/ min 9.012.1616.2

13. Evidently, an activated process!