Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010

1. This course is approximately at this level CHEMISTRYE182019 CH8 Reaction equilibriaRate of chemical reactions Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010

2. CHEMICAL REACTIONS CH8 • Typical reactions • Addition C+O2→ CO2 • Decomposition CaCO3→CaO+CO2(calcium carbonate) • Neutralization H2SO4+2NaOH→Na2SO4+2H2O (sodium sulfate) • Reversible C2H4+H2O↔C2H5OH (ethylalcohol)

3. REACTION PROGRESS CH8 During chemical reaction the number of moles of participating reactants and products are changing according to stoichiometry of reaction. These changes and also corresponding molar concentrations are expressed by only one scalar value REACTION PROGRESS  nA-nA0 corresponds only to one reaction. In the case of more reactions with the component A it is necessary to sum up of all reactions. [A] means molar concentration of A therefore it is the same as cA Changes of concentrations depend only upon the changes of reaction progress and are independent of initial concetrations

4. REACTION RATE CH8 Reaction progress is a positive parameter (concentration of reactants decreases during reaction) and its value increases from zero up to a limiting value at equilibrium. This increase is a monotonous function and therefore the reaction rate is also positive and monotonically decreasing towards zero for i= A,B,C,D

5. RATE EQUATION CH8 Reaction rate of forward reaction depends upon concentration of reactants, temperature (reaction rate always increases with temperature) and to a lesser extent also upon pressure. It is independent of concentrations of products! Reaction order with respect A (it need not be an integer or even positive number for complicated reactions) Rate coefficient (dependent upon temperature) Overall reaction order m = mA + mB

6. ARRHENIUS LAW CH8 Reaction constant depends upon temperature according to Arrhenius law Activation energy of chem.reaction J/mol Preexpontial factor (the same unit as k) Relative amount of molecules having kinetic energy greater than Ea is given by Maxwell distribution of energies The greater is temperature the more molecules have energy greater than E Collision theory: only the molecules having energy greater than Ea react at mutual collision

7. ARRHENIUS LAW CH8 Reaction rate can be increased either by the temperature increase or by decreasing activation energy Activation energy of chem.reaction can be decreased by catalyst (changing reaction mechanism with intermediate transition complex) Preexponential factor A is not a constant and slightly depends upon temperature.

8. Ea and CATALYSIS CH8 Activation energy Ea is a barrier which must be overcome so that the colliding molecules can react. The activation energy Ea depends on the bonding energy of the so called activated complex, a temporary molecule having only partially formed bonds. The smaller the energy of the activated complex the higher the probability that a collision will result in a chemical change. There are usually many ways to decompose a summary chemical reaction into intermediate elementary reactions (e.g., decomposition of reactants to free elements - radicals and subsequent formation of products). Every elementary reaction has its own activation energy and the actual reaction mechanism (sequences of elementary reactions) leads through the valley of the lowest activation energies. Sometimes species not explicitly enumerated in lists either of reactants or products take part in the intermediate reactions. These species, which are not consumed in the overall chemical reaction, are called catalysts. Catalysts open other possible reaction paths, characterised by lower activation energies, and thus their presence increases the overall reaction rate.

9. B A A A A A C Monomolecular reaction CH8 AB+C Reaction of the first order, exponentially decreasing concentration of reactant. I do not know why the decomposition of A could not be initiated by collisions with products B and C.

10. B B B B A C C B A B A B A A A C A B A B B A B B A A A A B C A A A A A A A Bimolecular reaction CH8 A + B  C Nothing happens at A-A or B-B collision Nothing happens at low energy collision Only if A-B energy of impact is > Ea the components react Reaction is of the second order. Precious information of bimolecular reaction data are available at NIST

11. B A B B B B B A C C B A C B A B A A A C A B C A A A A A A A A A Reversible reactions CH8 A + B  C + D  Forward reaction Backward reaction At equilibrium the rate of forward reaction is the same as the rate of backward reaction K-equilibrium constant (will be discussed later)

12. Calculation of concentrations CH8 Problem: Given initial concentrations cA0, cB0, cC0, cD0 calculate evolution of concentrations at time for specified temperature and pressure. During reaction T,p is assumed constant and only number of moles of participating reactants and products are changing according to stoichiometry of reaction. Solution: Concentrations in rate equation must be expressed in terms of reaction progress Ordinary differential equation for unknown c with initial condition c=0 must be solved numerically for real reaction orders

13. Calculation of concentrations CH8 Analytical solution exists for the case of bimolecular reactions when mA=mB=1. Let us assume unit stoichiometric coefficients for simplicity Final result (time course of concentrations)

14. Calculation of concentrations CH8 What to do if reactants A,B are in stoichiometric ratio? cAo=cB0 Reaction progress Use Taylor’s expansion (only linear term) Stoichiometric ratio cA cB

15. Calculation of concentrations CH8 What are equilibrium concentrations at t ? If cB0>cA0 cA=0 cB=cB0-cAo cC=cC0+cAo cD=cD0+cAo else cA=cAo-cBo cB=0 cC=cC0+cB0 cD=cD0+cBo Equilibrium constant is infinitely large, because it is not reversible reaction

16. Tutorial NO2 reduction (1/2) CH8 Rate equation for bimolecular equations holds only at high temperatures above 225 oC and at lower temperatures different rate equation should be applied

17. Tutorial NO2 reduction (2/2) CH8 Overall reaction can be decomposed to two reactions Slow reaction Fast reaction. Resulting reaction rate determines the slowest reaction in the reaction chain

18. Tutorial NO-removal (1/4) CH8 This overall reaction assumes simultaneous collision of 4 molecules. This is improbable and therefore overall reaction is substituted by several simpler reaction steps

19. Tutorial NO-removal (2/4) CH8 Production of intermediate compounds N2O2 and N2O are determined from previous rate equations. Assuming that the production rate of these intermediates is fast and close to equilibrium, these concentrations can be calculated without necessity to solve differential equations

20. Tutorial NO-removal (3/4) CH8 N2 is produced only from the last reaction The rate equation for the overall reaction

21. Tutorial NO-removal (4/4) CH8 Assuming that the first two reversible reactions are at equilibrium And therefore rate equation for the overall reaction Conclusion: Reaction is of the second order with respect NO but only of the first order with respect H2.

22. Tutorial HCl (1/4) CH8 Production of hydrochlorid acid Gaseous HCl Water spray Combustor (reactor) Hydrochlorid acid Cl2 H2

23. Tutorial HCl (2/4) CH8 This overall reaction assumes simultaneous collision of 2 molecules and looks like a standard bimolecular reaction. However, actual reaction mechanisms is more complicated

24. Tutorial HCl (3/4) CH8 Intermediate radicals Cl and H react so fast that their equilibrium values can be assumed subtract this term

25. Tutorial HCl (4/4) CH8 HCl is produced in the third and fourth reactions The rate equation for the overall reaction First order reaction with respect hydrogen, but only 0.5 order reaction with respect chlorine.

26. REACTION Equilibrium CH8 It was demonstrated that for reversible reactions there exists an equilibrium constant, determining concentrations of all participating components This relationship follows from equality of reaction rates of forward and backward reactions expressed in terms of activation energies E and preexponential factors. Equilibrium constant K can be derived in a different way, without resorting to reaction rates, just from a general requirement of equilibria at constant pressure: Gibbs reaction change at given pressure p and temperature T

27. REACTION Equilibrium CH8 Molar Gibbs energy of component i at pressure p and temperature T Molar Gibbs energy of component i at standard pressure p and temperature T Gibbs energies of formation at standard pressure g=h-Ts How to calculate entropy changes, corresponding to partial pressure of i-th component?

28. REACTION Equilibrium CH8 Derived previously for ideal gas Partial pressure of component at equilibrium

29. REACTION Equilibrium CH8 Kp- equilibrium constant expressed in terms of partial pressures of participating components Special case Gibbs energy change for FORWARD reaction at standard pressure 100kPa

30. REACTION Equilibrium CH8 • Consequencies: • Negative value of G increases equilibrium constant and shifts equlibrium composition towards the forward reaction products. • Equilibrium composition is independent of applied catalyser (catalyser decreases activation energies Ea, but has no effect upon Gibbs energy). Catalyser only shortens the time necessary for equilibrium achievement.

31. REACTION Equilibrium CH8 • Le Chatelier's principle: • The chemical equilibrium shifts in a way that tends to undo the external stress. Mother Nature does not like sudden changes, and promotes that reaction (forward or reversal) which helps to restore the previous state. Examples: A temperature increase shifts the equilibrium towards the endothermic reaction, which consumes the superfluous heat. If the volume of the products is less than the volume of the reactants (i<0), the total pressure decreases. Therefore the increase of pressure increases the equilibrium constant.

32. Tutorial Equilibriumsteam reforming CH8 Calculate equilibrium constants if the molar fraction of carbon dioxide (CO2) in the equilibrium mixture is 27%. Initial composition Final composition

33. Tutorial Equilibriumsteam reforming CH8 Theoretical calculation of equilibrium constant

34. Tutorial Equilibriumsteam reforming CH8 JANAF tables (NIST) NSRD-NBS-37 Example Kp=1.378

35. Tutorial Equilibriumsteam reforming CH8 this only very rough approximation. It is better to use entropy and enthalpy