Chemical Equilibrium

1. Chemical Equilibrium Chapter 15

2. Chemical Equilibrium • Concentrations of all reactants and products remains constant with time • All reactions carried out in a closed vessel will reach equilibrium: • If little product is formed, equilibrium lies far to the left. • If little reactant remains, equilibrium lies far to the right

3. Reactions are reversible • A + B C + D ( forward) • C + D A + B (reverse) • Initially there is only A and B so only the forward reaction is possible • As C and D build up, the reverse reaction speeds up while the forward reaction slows down. • Eventually the rates are equal

4. Forward Reaction Reaction Rate Equilibrium Reverse reaction Time

5. What is equal at Equilibrium? • Rates are equal • Concentrations are not. • Rates are determined by concentrations and activation energy. • The concentrations do not change at equilibrium.

6. The Haber Process • A process used to convert N2 and H2 into NH3: N2 + 3H2 2NH3 • Hydrogen is consumed at 3x the rate of nitrogen. • Ammonia is formed at 2x the rate at which nitrogen is consumed.

7. Equilibrium Achieved H2 Partial Pressure N2 NH3 Time

8. Law of Mass Action • For any reaction • jA + kB lC + mD • K = [C]l[D]m = [PRODUCTS]power [A]j[B]k [REACTANTS]power • K is called the equilibrium constant. • is how we indicate a reversible reaction

9. Playing with K • If we write the reaction in reverse. • lC + mD jA + kB • Then the new equilibrium constant is • K’ = [A]j[B]k = 1/K[C]l[D]m

10. Playing with K • If we multiply the equation by a constant • njA + nkB nlC + nmD • Then the equilibrium constant is • K’ = [A]nj[B]nk= ([A] j[B]k)n= Kn [C]nl[D]nm ([C]l[D]m)n

11. The units for K • Are determined by the various powers and units of concentrations. • They depend on the reaction.

12. Equilibrium Expression Summary • The equilibrium-constant depends only on the stoichiometry of the reaction, not its mechanism. • When the balanced equation for a reaction is multiplied by a factor, n, the equilibrium expression for the new reaction is the original expression raised to the nth power • Knew = (Koriginal)n • For a reaction at a given temp., the value of K is constant regardless of the amounts of starting materials

13. Equilibrium Constant One for each Temperature

14. Calculate K • N2 + 3H2 2NH3 • Initial At Equilibrium • [N2]0 =1.000 M [N2] = 0.921M • [H2]0 =1.000 M [H2] = 0.763M • [NH3]0 =0 M [NH3] = 0.157M

15. Calculate K • N2 + 3H2 2NH3 • Initial At Equilibrium • [N2]0 = 0 M [N2] = 0.399 M • [H2]0 = 0 M [H2] = 1.197 M • [NH3]0 = 1.000 M [NH3] = 0.157M • Think about which way this reaction is proceeding.

16. Equilibrium and Pressure • Some reactions are gaseous • PV = nRT • P = (n/V)RT • P = CRT • C is a concentration in moles/Liter • C = P/RT

17. Equilibrium and Pressure • 2SO2(g) + O2(g) 2SO3(g) • Kp = (PSO3)2 (PSO2)2 (PO2) • K = [SO3]2 [SO2]2 [O2]

18. Equilibrium and Pressure • K =(PSO3/RT)2 (PSO2/RT)2(PO2/RT) • K =(PSO3)2(1/RT)2 (PSO2)2(PO2) (1/RT)3 • K = Kp (1/RT)2= Kp RT (1/RT)3 • Therefore K = KpRT

19. General Equation • jA + kB lC + mD • Kp= (PC)l (PD)m= (CCxRT)l (CDxRT)m (PA)j (PB)k (CAxRT)j(CBxRT)k • Kp=(CC)l (CD)mx(RT)l+m (CA)j(CB)kx(RT)j+k • Kp =K (RT)(l+m)-(j+k) = K (RT)Dn • Dn=(l+m)-(j+k)=Change in moles of gas

20. Homogeneous Equilibria • So far every example dealt with reactants and products where all were in the same phase. • We can use K in terms of either concentration or pressure. • Units depend on reaction.

21. Heterogeneous Equilibria • If the reaction involves pure solids or pure liquids the concentration of the solid or the liquid doesn’t change. • As long as they are not used up we can leave them out of the equilibrium expression. • For example…

22. For Example • H2(g) + I2(s) 2HI(g) • Before we got… K = [HI]2 [H2][I2] • But the concentration of I2 does not change because it is a pure solid, so • K= [HI]2 [H2]

23. Applications of the Equilibrium Constant: • K > 1: • The concentrations of the products are greater than the concentrations of the reactants. • Equilibrium lies far to the right. • Generally, large, negative DE.

24. Applications of the Equilibrium Constant: • K < 1: • The concentrations of the reactants are greater than the concentrations of the products. • Equilibrium position is far to the left

25. The time required to achieve equilibrium: • Related to reaction rate and activation energy • Not related to the magnitude of K In summary: • DE influences K • Ea influences rate

26. The Reaction Quotient • Tells you the direction the reaction will go to reach equilibrium • Calculated the same as the equilibrium constant, but for a system not at equilibrium • Q = [Products]coefficient [Reactants] coefficient • Compare value to equilibrium constant

27. What Q tells us • If Q<K • Not enough products, reactants are consumed • Shift to right • If Q>K • Too many products, products are consumed • Shift to left • If Q=K system is at equilibrium

28. Solving Equilibrium Problems Type 1

29. Example • for the reaction • 2NOCl(g) 2NO(g) + Cl2(g) • K = 1.55 x 10-5 M at 35ºC • In an experiment 0.10 mol NOCl, 0.0010 mol NO(g) and 0.00010 mol Cl2 are mixed in 2.0 L flask. • Which direction will the reaction proceed to reach equilibrium?

30. Solving Equilibrium Problems • Given the starting concentrations and one equilibrium concentration. • Use stoichiometry to figure out other concentrations and K. • Learn to create a table of initial and final conditions. (ICE Charts)

31. Consider the following reaction at 600ºC • 2SO2(g) + O2(g) 2SO3(g) • In a certain experiment 2.00 mol of SO2, 1.50 mol of O2 and 3.00 mol of SO3 were placed in a 1.00 L flask. At equilibrium 3.50 mol of SO3 were found to be present. • Calculate the equilibrium concentrations of O2 and SO2, K and KP • Use stoich (ICE chart) to solve for equilibrium concentrations of Reactants

32. Consider the same reaction at 600ºC • In a different experiment .250 mol O2, .500 mol SO2 and .350 mol SO3 were placed in a 1.000 L container. When the system reaches equilibrium 0.045 mol of O2 are present. • Calculate the final concentrations of SO2 and SO3 and K and Kp

33. What if you’re not given equilibrium concentration? • The size of K will determine what approach to take. • First let’s look at the case of a LARGE value of K ( >100). • Allows us to make simplifying assumptions.

34. Example • H2(g) + I2(g) 2HI(g) • K = 7.1 x 102 at 25ºC • Calculate the equilibrium concentrations if a 5.00 L container initially contains 15.9 g of H2 294 g I2 . • [H2]0 = (15.9g/2.02)/5.00 L = 1.59 M • [I2]0 = (294g/253.8)/5.00L = 0.232 M • [HI]0 = 0

35. Q= 0<K so more product will be formed. • Assumption since K is large reaction will go to completion. • Stoichiometry tells us I2 is limiting so it will be smallest at equilibrium (let it be x) • Set up an I.C.E chart

36. H2(g) I2(g) HI(g) initial 1.59 M 0.232 M 0 M change final X • Choose X so it is small. • For I2 the change in X must be X-.232 M • Final must = initial + change

37. H2(g) I2(g) HI(g) initial 1.59 M 0.232 M 0 M change X-0.232 final X • Using to stoichiometry we can find • Change in H2 = X-0.232 M • Change in HI = -twice change in H2 • Change in HI = 0.464-2X

38. H2(g) I2(g) HI(g) initial 1.59 M 0.232 M 0 M change X-0.232 X-0.232 0.464-2Xfinal X • Now we can determine the final concentrations by adding.

39. H2(g) I2(g) HI(g) initial 1.59 M 0.232 M 0 M change X-0.232 X-0.232 0.464-2X final 1.36+X X 0.464-2X • Now plug these values into the equilibrium expression • K = (0.464-2X)2 = 7.1 x 102 (1.328+X)(X) • Now you can see why we made sure X was small.

40. Why we chose X • K = (0.464-2X)2 = 7.1 x 102 (1.328+X)(X) • Since X is going to be small, we can ignore it in relation to 0.464 and 1.328 • So we can rewrite the equation • 7.1 x 102 = (0.464)2 (1.328)(X) • Makes the algebra easy

41. H2(g) I2(g) HI(g) initial 1.56 M 0.232 M 0 M change X-0.232 X-0.232 0.464-2X final 1.36+X X 0.464-2X • When we solve for X we get 2.2 x 10-4 • So we can find the other concentrations • I2 = 2.2 x 10-4 M • H2 = 1.36 M • HI = 0.464 M

42. Checking the assumption • The rule of thumb is that if the value of X is less than 5% of all the other concentrations, our assumption was valid. • If not we would have had to use the quadratic equation • More on this later. • Our assumption was valid.

43. Practice • For the reaction Cl2 + O2 2ClO(g) K = 156 • In an experiment 0.100 mol ClO, 1.00 mol O2 and 0.0100 mol Cl2 are mixed in a 4.00 L flask. • If the reaction is not at equilibrium, which way will it shift? • Calculate the equilibrium concentrations.

44. Problems with small K K< .01

45. Process is the same • Set up table of initial, change, and final concentrations. • Choose X to be small. • For this case it will be a product. • For a small K the product concentration is small.

46. For example • For the reaction 2NOCl 2NO +Cl2 • K= 1.6 x 10-5 • If 1.20 mol NOCl, 0.45 mol of NO and 0.87 mol Cl2 are mixed in a 1 L container • What are the equilibrium concentrations • Q = [NO]2[Cl2] = (0.45)2(0.87) = 0.15 M [NOCl]2 (1.20)2

47. 2NOCl 2NO Cl2 Initial 1.20 0.45 0.87 Change Final • Choose X to be small • NO will be limiting • Choose NO to be X

48. 2NOCl 2NO Cl2 Initial 1.20 0.45 0.87 Change Final X • Figure out change in NO • Change = final - initial • change = X-0.45

49. 2NOCl 2NO Cl2 Initial 1.20 0.45 0.87 Change X-.45 Final X • Now figure out the other changes • Use stoichiometry • Change in Cl2 is 1/2 change in NO • Change in NOCl is - change in NO

50. 2NOCl 2NO Cl2 Initial 1.20 0.45 0.87 Change 0.45-X X-.45 0.5X - .225 Final X • Now we can determine final concentrations • Add