1. Chemical-Reaction Equilibra ERT 206: Thermodynamics Miss Anis Atikah Ahmad Tel: 04-9763245 Email: anis atikah@unimap.edu.my

2. OUTLINE 1.The Reaction Coordinate 2.Application of Equilibrium Criteria to Chemical Reactions 3.The Standard Gibbs-Energy Change & the Equilibrium Constant 4.Effect of Temperature on the Equilibrium Constant 5.Relation of Equilibrium Constants to Composition 6.Multireaction Equilibria

3. The Reaction Coordinate 1. The Reaction Coordinate The general chemical reaction is written as: is the stoichiometric coefficient * positive (+) for product * negative (-) for reactant stands for chemical formula

4. The Reaction Coordinate 1. The Reaction Coordinate For reaction: the stoichiometric numbers are: If 0.5 mol of CH 4 and 0.5 mol of H 2 O dissappear in reaction; Thus; 0.5 mol of CO and 1.5 mol of H 2 are formed. Reaction coordinate (the extent or degree to which a reaction has taken place)

5. The general relation connecting the differential change dn i with dε: Integrating; Summation over all species; where The Reaction Coordinate 1. The Reaction Coordinate

6. The mole fraction y i of the species: The Reaction Coordinate 1. The Reaction Coordinate

7. Example 1 For a system in which the following reaction occurs: Assume there are present initially 2 mol CH 4, 1 mol H 2 O, 1 mol CO and 4 mol H 2. Determine expressions for the mole fractions y i as a function of ε The Reaction Coordinate 1. The Reaction Coordinate

8. Recall: Example 1-SOLUTION The Reaction Coordinate 1. The Reaction Coordinate

9. Multireaction Stoichiometry: When two or more independent reactions process simultaneously, Where j serves as the reaction index and a separate reaction coordinate ε j applies to each reaction. The Reaction Coordinate 1. The Reaction Coordinate

10. Example 2: Multireaction Consider a system in which the following reaction occur: If there are present initially 2 mol of CH 4, and 3 mol H 2 O, determine expressions for the mole fractions y i as a function of ε 1 and ε 2. The Reaction Coordinate 1. The Reaction Coordinate Recall:

11. Example 2: Multireaction- Solution The Reaction Coordinate 1. The Reaction Coordinate iCH 4 H2OH2OCOCO 2 H2H2 jvjvj 1 1032 2 -20142 j Given: Recall:

12. Criterion of equilibrium at constant T & P: – The total Gibbs energy G t is a minimum – Its differential is zero Application of Equilibrium Criteria to Chemical Reactions 2. Application of Equilibrium Criteria to Chemical Reactions Total Gibbs Energy vs Reaction Coordinate Any reaction that occurs at constant T & P must lead to decrease in the total Gibbs energy of the system

13. From previous chapter, Since, At constant T and P, At equilibrium state, Thus, The Standard Gibbs-Energy Change & The Equilibrium Constant 3. The Standard Gibbs-Energy Change & The Equilibrium Constant

14. Recall fugacity of a species in solution; The fugacity of pure species in its standard state; The difference between these two equations; The Standard Gibbs-Energy Change & The Equilibrium Constant 3. The Standard Gibbs-Energy Change & The Equilibrium Constant (1) (2) (3)

15. Substituting into ; OR In exponential form; where, The Standard Gibbs-Energy Change & The Equilibrium Constant 3. The Standard Gibbs-Energy Change & The Equilibrium Constant Equilibrium constant Standard Gibbs energy change of reaction Depends only on T

16. Effect of Temperature on the Equilibrium Constant 4. Effect of Temperature on the Equilibrium Constant The relation between standard heat of reaction and the standard Gibbs energy change of reaction; Integrating; For exothermic (-ΔH°): As T increases, K decreases. For endothermic (+ΔH°): As T increases, K increases. For exothermic (-ΔH°): As T increases, K decreases. For endothermic (+ΔH°): As T increases, K increases.

17. Equilibrium constant as a function of temperature

18. 5. Relation of Equilibrium Constants to Composition For Gas Phase Reaction: – The standard state for a gas is the ideal gas state of the pure gas at the standard-state pressure P° of 1 bar. – Since the fugacity of an ideal gas is equal to its pressure,, thus becomes:

19. 5. Relation of Equilibrium Constants to Composition Since, becomes; where For pressures sufficiently low or temperature sufficiently high, the equilibrium mixture behaves essentially as an ideal gas. Thus,

20. 5. Relation of Equilibrium Constants to Composition For liquid phase reactions: From previous chapter,. Thus, Can be substituted by Gibbs energy expression

21. 5. Relation of Equilibrium Constants to Composition For liquid phase reactions: Integration of at constant T: Thus, OR or

22. 5. Relation of Equilibrium Constants to Composition Substituting into Since Thus,

23. 5. Relation of Equilibrium Constants to Composition For low to moderate pressure, the exponential term is close to unity and may be omitted. Thus If the mixture is an ideal solution, is unity. Therefore, Law of mass action

24. 5. Relation of Equilibrium Constants to Composition Example 3 The water-gas-shift-reaction, is carried out under the different sets of conditions described below. Calculate the fraction of steam reacted in each case. Assume the mixture behaves as an ideal gas. (a)The reactants consist of 1 mol of H 2 O vapor & 1 mol of CO. The temperature is 1,100 K and the pressure is 1 bar. (b)Same as (a) except the pressure is 10 bar. (c)Same as (a) except that 2 mol of N 2 is included in the reactants. (d)The reactants are 2 mol of H 2 O & 1 mol of CO. Other conditions are the same as in part (a) (e)Same as (a) except that the temperature is 1,650 K.

25. 5. Relation of Equilibrium Constants to Composition Example 3-Solution (a)The reactants consist of 1 mol of H 2 O vapor & 1 mol of CO. The temperature is 1,100 K and the pressure is 1 bar. At T=1100 K, 10 4 /T=9.05. From the ln K vs 1/T graph, At 1/T=9.05, ln K =0 Thus, K= 1

26. 5. Relation of Equilibrium Constants to Composition Example 3-Solution (a)The reactants consist of 1 mol of H 2 O vapor & 1 mol of CO. The temperature is 1,100 K and the pressure is 1 bar. Thus, fraction of steam reacted = 0.5 Substitute into

27. 5. Relation of Equilibrium Constants to Composition Example 3-Solution (b) Same as (a) except the pressure is 10 bar. Because v=0, the increase in pressure has no effect on the ideal-gas reaction and ε e is still 0.5.

28. 5. Relation of Equilibrium Constants to Composition Example 3-Solution (c) Same as (a) except that 2 mol of N 2 is included in the reactants. N 2 does not take part in the reaction, and serves only as diluent. Thus, remain unchanged. Therefore, ε e is still 0.5

29. 5. Relation of Equilibrium Constants to Composition Example 3-Solution (d) The reactants are 2 mol of H 2 O & 1 mol of CO. Other conditions are the same as in part (a) Thus, Thus, fraction of steam reacted 0.667/2= 0.333 Substitute into

30. 5. Relation of Equilibrium Constants to Composition Example 3-Solution (e) Same as (a) except that the temperature is 1,650 K. At T=1650 K, 10 4 /T=6.06. From the ln K vs 1/T graph, At 1/T=6.06, ln K =-1.15 Thus, K= 0.317 Thus, fraction of steam reacted 0.36. Increasing the temperature reduce the conversion.

31. 6. Multireaction Equilibra For liquid-phase reaction; For gas-phase reaction; If equilibrium mixture is an ideal gas;