1. Chemical Equilibrium Glenn V. Lo, Ph.D. Department of Physical Sciences Nicholls State University

2. Learning Objectives Students will be able to Describe equilibrium from an atomic/molecular perspective Calculate and differentiate between reaction quotient (Q) and equilibrium constant (K eq ) Predict direction of reaction by comparing Q and K eq Calculate equilibrium constants from experimental data and literature values Predict how far reactions will go based on Keq and initial conditions Use Le Chatelier’s principle to predict equilibrium shifts Explain Le Chatelier’s Principle in terms of the relationship between Q and Keq

3. Equilibrium Which profile represents reactant? product? When is the reaction fastest? When is the reaction slowest? Equilibrium Forward rate = reverse rate No further changes observed Why is reactant not completely used up?

4. Test Yourself Consider the reaction illustrated here. When did it reach equilibrium? A. between 2 and 4 min B. at 4 min C. between 4 and 6 min D. after 6 min

5. What determines equilibrium? For a given reaction at a given temperature: The reaction quotient (Q) reaches a constant value. The reaction quotient is calculated from activities of species (atoms, ions, or molecules) involved in the reaction. For precise definition of activity, take an advanced course in Chemical Thermodynamics. Activities are unitless quantities; approximate values: Pure Solid or Liquid: a = 1 Solutes in dilute solution: a = molality  Dilute aqueous solution: molality = Molarity Solvent in dilute solution: a = mole fraction (essentially 1) Gas: a = partial pressure (atm)

6. Test Yourself In a 0.010M BaCl 2 solution, the activity of chloride ions is : A. 0.010 B. 0.010 M C. 0.020 D. 0.0050 M E. 0.0050

7. The Reaction Quotient (Q) How to calculate the reaction quotient: Numerator = product of activities of products, each raised to a power equal to its coefficient in the chemical equation Denominator = product of activities of reactants, each raised to a power equal to its coefficient in the chemical equation

8. Test Yourself Write down the expression for the reaction quotient for the following reaction: Mg(s) + 2 H + (aq)  H 2 (g) + Mg 2+ (aq)

9. Test Yourself Consider: H 2 S(aq) + 2 H 2 O(l)  2 H 3 O + (aq) + S 2- (aq) Calculate Q when [H 2 S] = 0.10, [H 3 O + ] = 0.15, [S 2- ] = 0.020

10. The Equilibrium Constant (K or K eq ) K eq = value of Q at equilibrium K eq is constant at a given temperature

11. Determining K eq Carry out the reaction. Determine the activities of reactants and products at equilibrium. Example: X(aq)  3Y(aq), Suppose the initial concentrations of X and Y in a reaction mixture 0.100M and 0.100M, and the concentration of X is found to be 0.050 M at equilibrium. Calculate K eq for the reaction.

12. K eq for gas phase reactions K P, activities are given in in terms of pressure K C, activities are given in terms of concentration Recall: PV=nRT  P = (n A /V)RT = [A]RT K P = K C (RT)  n  Where  n=changes in moles of gas

13. Test Yourself How is K P related to K C for the following reaction: A(g)  2 B(g) A. K c = K p (RT) B. K c = K p (RT) 2 C. K c = K p (RT) -1 D. K c = K p (RT) -2

14. Example Suppose, at 298K: A(g)  2B(g), K P = 10.0 Calculate K c.

15. Test Yourself How is K P related to K C for the following reaction: CaCO 3 (s)  CaO(s) + CO 2 (g) A. K c = K p (RT) B. K c = K p (RT) 2 C. K c = K p (RT) -1 D. K c = K p (RT) -2

16. Determining K eq from other reactions Suppose: A  B, K eq = x, Then: B  A, K eq = ? Suppose: A  B, K eq = x and: C  D, K eq = y then:A + C  B + D, K eq = ?

17. Test Yourself Suppose: A  B, K eq = 2.0, Then: 2B  2A, K eq = ? A. 2.0 B. 0.5 C. 4.0 D. 0.25

18. Net Direction of Reaction Compare Q vs. K eq What happens if Q< K eq ? Net forward reaction occurs until Q= K eq Why does forward reaction makes Q larger? What happens if Q> K eq ?

19. Test Yourself Suppose: A(aq)  2B(aq), K eq = 10.0 Which way will the net reaction occur in a mixture where Q=0.100 A. forward B. reverse C. neither (reaction is at equilibrium)

20. Test Yourself Suppose: A(aq)  2B(aq), K eq = 10.0 Which way will the net reaction occur in a mixture where [A]=0.100, [B]=0. A. forward B. reverse C. neither (reaction is at equilibrium)

21. Test Yourself Suppose: A(aq)  2B(aq), K eq = 10.0 Which way will the net reaction occur in a mixture where [A]=0, [B]=0.100. A. forward B. reverse C. neither (reaction is at equilibrium)

22. Test Yourself Suppose: A(aq)  2B(aq), K eq = 10.0 Which way will the net reaction occur in a mixture where [A]=0.100M and [B]=0.100M. A. forward B. reverse C. neither (reaction is at equilibrium)

23. Determining extent of reaction Information needed: Initial concentrations (activities) K eq Procedure: Set up an “ICE Table” Compare Q vs. K eq to determine net direction of reaction Let x = extent of reaction in the net direction Solve for x knowing that Q=K eq at equilibrium

24. Determining extent of reaction What is the equilibrium pressure in a gas mixture if you start with a mixture where P A =0.10 atm, P B =0.10 atm, P C =0.10 atm, and the reaction is A(g) + B(g)  2 C(g), K P =25.00

25. Determining extent of reaction Simplifying assumption can be made if K eq is very large (>10 3 ) or very small or (<10 -3 ). Assume complete reaction towards the preferred side. Reverse the reaction by a very small amount (x) Make approximations given that x is very small Solve for x knowing that Q=K eq at equilibrium. Be sure to verify if assumption is correct.

26. Example What is the equilibrium pressure in a gas mixture if you start with a mixture where P A =0.10 atm, P B =0.10 atm, P AB =0.10 atm, and the reaction is A(g) + 2 B(g)  3 C(g), K P =2.0x10 10 (assume constant volume)

27. Example Example: What is the equilibrium concentrations of H + and OH - you start with a mixture where [H + ]=0.100, [OH - ]=0.200 and the reaction is H 2 O(l)  H + (aq) + OH - (aq), K eq =1.00x10 -14

28. Le Chatelier’s Principle “If a stress is applied to a system in equilibrium, it will shift in a manner that tends to counteract the stress.” Examples of stress: Addition of more products or reactants Removal of products or reactants Change in temperature Change in total volume (gas) Why? At constant temperature: stress changes Q Change in temperature changes K eq

29. Test Yourself Consider a solution of NaHSO 4 (aq) at equilibrium. HSO 4 - (aq) + H 2 O(l)  SO 4 2- (aq) + H 3 O + (aq) Assuming constant T, what is the effect of adding K 2 SO 4 (s)? A. equilibrium shifts to the left B. equilibrium shifts to the right C. no effect

30. Test Yourself Consider a solution of NaHSO 4 (aq) at equilibrium. HSO 4 - (aq) + H 2 O(l)  SO 4 2- (aq) + H 3 O + (aq) Assuming constant T, what is the effect of adding NaHSO 4 (s) ? A. equilibrium shifts to the left B. equilibrium shifts to the right C. no effect

31. Test Yourself Consider a solution of NaHSO 4 (aq) at equilibrium. HSO 4 - (aq) + H 2 O(l)  SO 4 2- (aq) + H 3 O + (aq) Assuming constant T, what is the effect of adding BaCl 2 (s) ? A. equilibrium shifts to the left B. equilibrium shifts to the right C. no effect

32. Test Yourself Consider a solution of NaHSO 4 (aq) at equilibrium. HSO 4 - (aq) + H 2 O(l)  SO 4 2- (aq) + H 3 O + (aq) Assuming constant T, what is the effect of adding more water? A. equilibrium shifts to the left B. equilibrium shifts to the right C. no effect

33. Test Yourself In a closed bottle of a carbonated drink, a solution of CO 2 (aq) is in equilibrium with 4 atm of CO 2 (g): CO 2 (g)  CO 2 (aq) What happens if the bottle is opened? A. equilibrium shifts to the left B. equilibrium shifts to the right C. no effect NOTE: Henry’s Law: [A]/P A(g) = k H, K eq = k H

34. Test Yourself In a closed container, liquid water is in equilibrium with water vapor: H 2 O(l)  H 2 O(g) What happens if you add NaCl(s) to the water? A. vapor pressure is lowered B. vapor pressure increases C. nothing NOTE: Raoult’s Law: P A(g) = P A * x A, K eq = P A *

35. Test Yourself Consider an equilibrium mixture of NO 2 (g) and N 2 O 4 (g): 2 NO 2 (g)  N 2 O 4 (g) What happens if the mixture is compressed? A. Equilibrium shifts to the left B. Equilibrium shifts to the right

36. Le Chatelier’s Principle Temperature change causes K eq to change Van’t Hoff equation: ln(K eq ) = -(  H/R)(1/T) + c If reaction is endothermic (  H>0), the reverse is exothermic. Higher temperature favors endothermic direction. Higher temperature  larger K eq Conversely, for exothermic reaction, the reverse is endothermic: Higher temperature  smaller K eq

37. Test Yourself Consider the followng fictitious reaction: heat + A(aq)  B(aq) If a mixture of A and B is at equilibrium, what would happen if the temperature is raised? Answer: when equilibrium is re established, [A] would be _______ and [B] would be ________. The new K eq will be _____. A. higher, lower, lower B. higher, lower, higher C. lower, higher, lower D. lower, higher, higher

38. Test Yourself Consider the followng fictitious reaction: A(aq)  B(aq),  H = -95 kJ Suppose A(aq) is yellow and B(aq) is blue, and an equilibrium mixture is of A and B is green. What happens if you increase the temperature? Answer: when equilibrium is re-established, the color of the solution will be ____ and the K eq will be ____. A. more yellowish, higher B. more yellowish, lower C. more bluish, higher D. more bluish, lower

39. Test Yourself Consider the vaporization of water: H 2 O(l)  H 2 O(g) Consider a sample of water in an enclosed container at equilibrium. What would happen if the temperature is raised? The vapor pressure of water will ____ and the new K eq will be ____. A. increase, higher B. increase, lower C. decrease, higher B. decrease, lower

40. Effect of catalyst on equilibrium A catalyst speeds up a reaction, without being consumed, by providing an alternative path that has a lower energy of activation. A catalyst speeds up the establishment of equilibrium, but not the position of equilibrium. The position of equilibrium depends only on temperature and what the overall reaction is.