Chemistry, The Central Science, 11th edition Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten Chapter 15 Chemical Equilibrium Directions: Carefully read all slides. Copy into your notes only the slides written in BLACK font! Also – Please proofread and correct any errors (if needed). Equilibrium Chemical Equilibrium Equilibrium Chemical Equilibrium 1. Equilibrium is a state of balance between two opposing reactions. Some examples of opposing reactions: Evaporation & Condensation Melting & Freezing Dissolving & Re-crystallization 2. The reactions must occur in a closed system so that neither product nor reactant can escape. Equilibrium Chemical Equilibrium (con’t) 3. When equilibrium is achieved, the two opposing reactions are occurring at the same rate or speed. 4. As a result, at equilibrium, the concentrations of the reactants and products are constant. (NOT EQUAL) Equilibrium Chemical Equilibrium (con’t) 5. Equilibrium is a dynamic process. It looks like nothing is happening, but the reactions have not stopped. 6. Double arrows are used to represent a system at equilibrium. Example: Equilibrium N2O4 2 NO2 The Concept of Equilibrium N2O4 gas is nearly colorless. As it is heated, it dissociated into brown NO2 gas. This reaction is reversible. NO2 can also reform N2O4. Equilibrium Eventually, equilibrium is reached. The Concept of Equilibrium Chemical equilibrium occurs when a reaction and its reverse reaction proceed at the same rate. Equilibrium The Concept of Equilibrium • As a system approaches equilibrium, both the forward and reverse reactions are occurring. • At equilibrium, the forward and reverse reactions are proceeding at the same rate. Equilibrium A System at Equilibrium Once equilibrium is achieved, the amount of each reactant and product remains constant. Equilibrium Depicting Equilibrium In a system at equilibrium, both the forward and reverse reactions are being carried out; as a result, we write its equation with a double arrow N2O4 (g) 2 NO2 (g) Equilibrium Check Yourself by Answering the Questions that Appear Throughout the Slideshow Equilibrium When a reaction is at a state of equilibrium, the rate of the forward reaction __________ the rate of the reverse reaction. a. b. c. d. is equal to is slower than is faster than is the reverse of Equilibrium When a reaction is at a state of equilibrium, the rate of the forward reaction __________ the rate of the reverse reaction. a. b. c. d. is equal to is slower than is faster than is the reverse of Equilibrium When a reaction is at a state of equilibrium, the concentration of the reactants and the concentration of the products are _____________. a. b. c. d. equal to each other constant, but not usually equal constantly increasing constantly decreasing Equilibrium When a reaction is at a state of equilibrium, the concentration of the reactants and the concentration of the products are _____________. a. b. c. d. equal to each other constant, but not usually equal constantly increasing constantly decreasing Equilibrium The Equilibrium Constant Kc Equilibrium The Equilibrium Constant • Forward reaction: N2O4 (g) 2 NO2 (g) • Rate law: Rate = kf [N2O4] Equilibrium The Equilibrium Constant • Reverse reaction: 2 NO2 (g) N2O4 (g) • Rate law: Rate = kr [NO2]2 Equilibrium The Equilibrium Constant • Therefore, at equilibrium Ratef = Rater kf [N2O4] = kr [NO2]2 • Rewriting this, it becomes kf kr [NO2]2 = [N2O4] Equilibrium The Equilibrium Constant The ratio of the rate constants is a constant at that temperature, and the expression becomes kf Keq = kr [NO2]2 = [N2O4] Equilibrium The Equilibrium Constant (Kc) (K means constant, c means concentration) • To generalize this expression, consider the reaction aA + bB cC + dD • The equilibrium expression for this reaction would be [C]c[D]d Kc = [A]a[B]b Equilibrium The Equilibrium Constant (Kc) con’t • Note: K expressions are written as “products over reactants”. • Include only gases & aqueous substances in the expression. • Omit all solids and liquids. Equilibrium The Equilibrium Constant (Kc) con’t • Example - For the equilibrium: • N2(g) + 3 H2 (g) 2 NH3 (g) Kc = [NH3]2 [N2] [H2]3 Equilibrium The Equilibrium Constant (Kc) con’t • You try this equilibrium: • 2 Cl2(g) + 2 H2O(g) 4 HCl(g) + O2 (g) • Kc = ? Equilibrium 2 Cl2(g) + 2 H2O(g) 4 HCl(g) + O2 (g) • Answer: Kc = [HCl]4 [O2 ] [Cl2]2 [H2O]2 Equilibrium What Are the Equilibrium Expressions for These Equilibria? SnO2(s) + 2 CO(g) Sn(s) + 2 CO2(g) CaO(s) + CO2(g) CaCO3(s) Zn(s) + Cu2+(aq) Cu(s) + Zn2+(aq) Copy answers to your notes! Equilibrium Answers Kc = [CO2]2 [CO]2 Kc = 1 [CO2] Kc = [Zn2+] [Cu2+] Equilibrium At equilibrium, the equilibrium constant is equal to: a. b. c. d. [reactants]/[products] [products]/[reactants] [reactants] x [products] [reactants] + [products] Equilibrium At equilibrium, the equilibrium constant is equal to: a. b. c. d. [reactants]/[products] [products]/[reactants] [reactants] x [products] [reactants] + [products] Equilibrium The Equilibrium Constant Because pressure is proportional to concentration for gases in a closed system, the equilibrium expression can also be written (PC)c (PD)d Kp = (PA)a (PB)b Equilibrium Relationship between Kc and Kp • From the ideal gas law we know that PV = nRT • Rearranging it, we get n P= RT V Equilibrium Relationship between Kc and Kp Plugging this into the expression for Kp for each substance, the relationship between Kc and Kp becomes Kp = Kc (RT)n Where R = 0.0821 L-atm/mol-K and T = Kelvin temp and n = (moles of gaseous product) − (moles of gaseous reactant) Your teacher will do problems like this with you later. Equilibrium More About Equilibrium Systems Equilibrium Equilibrium Can Be Reached from Either Direction As you can see, the ratio of [NO2]2 to [N2O4] remains constant at this temperature no matter what the initial concentrations of NO2 and N2O4 are. Note: K values are temp dependent. Equilibrium Equilibrium Can Be Reached from Either Direction This is the data from the last two trials from the table on the previous slide. See how concentration becomes constant at equilibrium. Equilibrium Equilibrium Can Be Reached from Either Direction Here is another example. It does not matter whether we start with N2 and H2 or whether we start with NH3. We will have the same proportions of all three substances at Equilibrium equilibrium. What Does the Value of K Mean? • If K >> 1, the reaction is product-favored; product predominates at equilibrium. Equilibrium What Does the Value of K Mean? • If K >> 1, the reaction is product-favored; product predominates at equilibrium. • If K << 1, the reaction is reactant-favored; reactant predominates at equilibrium. Equilibrium What Does the Value of K Mean? • Please note: The values for K change with changes in temperature! Equilibrium A large value of the equilibrium constant indicates that when the reaction reaches equilibrium, mostly ______ will be present. a. b. c. d. reactants products catalysts shrapnel Equilibrium A large value of the equilibrium constant indicates that when the reaction reaches equilibrium, mostly ______ will be present. a. b. c. d. reactants products catalysts shrapnel Equilibrium The equilibrium constant for a reaction is 375. This means the equilibrium mixture is mainly: a. reactant, because 375 is more than 1 b. product, because 375 is more than 1 c. cannot be determined. Equilibrium The equilibrium constant for a reaction is 375. This means the equilibrium mixture is mainly: a. reactant, because 375 is more than 1 b. product, because 375 is more than 1 c. cannot be determined. Equilibrium Rules for Manipulating K Values 1. Reverse the Reaction? Take the Reciprocal of K In other words, 1/K Equilibrium Example: The equilibrium constant of a reverse reaction is the reciprocal of the equilibrium constant of the forward reaction. N2O4 (g) 2 NO2 (g) [NO2]2 2 NO2 (g) Kc = [N O ] = 0.212 at 100C 2 4 [N2O4] 1 K = N2O4 (g) c = [NO2]2 0.212 = 4.72 at 100C Equilibrium You try: • If K = 3.5 x 10-4 for: H2(g) + Br2(g) 2 HBr(g) • What is K for: 2 HBr(g) H2(g) + Br2(g) ? • Answer: Use 1/K = 1/ 3.5 x 10-4 Answer: 2857 or 2.9 x 103 Equilibrium (no units) Rules for Manipulating K Values (con’t) 2. Multiply a Reaction by a factor of ‘n’ ? Use: Kn Equilibrium Example: The equilibrium constant of a reaction that has been multiplied by a number is the equilibrium constant raised to a power that is equal to that number. N2O4 (g) [NO2]2 2 NO2 (g) Kc = [N O ] 2 4 2 N2O4 (g) [NO2]4 4 NO2 (g)Kc = [N O ]2 = (0.212)2 at 100C 2 4 = 0.212 at 100C Equilibrium You try: • If K = 3.5 x 10-4 for: H2(g) + Br2(g) 2 HBr(g) • What is K for: 3 H2(g) + 3 Br2(g) 6 HBr(g) • Answer: Use K3 = (3.5 x 10-4)3 Answer: 4.3 x 10-11 Equilibrium You try: • If K = 3.5 x 10-4 for: H2(g) + Br2(g) 2 HBr(g) • What is K for: ½ H2(g) + ½ Br2(g) HBr(g) • Answer: Use K1/2 = (3.5 x 10-4)1/2 Answer: (Take square root) 1.9 x10-2 Equilibrium Rules for Manipulating K Values 3. Add several reactions together? Multiply the K values together Equilibrium In other words The equilibrium constant for a net reaction made up of two or more steps is the product of the equilibrium constants for the individual steps. Equilibrium You try: • If K1 = 1 x 10-3 for: AB2(g) 2 B(g) + A(g) and • If K2 = 1 x 10-5 for: A(g) + B(g) AB(g) • What is the overall equation when these 2 reactions are added together and what is the K value for the new reaction? • Answers: AB2(g) B(g) + AB(g) (Muliply K values) 1 x 10-8 Equilibrium Equilibrium Calculations Equilibrium Simple Equilibrium Calculations • Given: N2O4 (g) 2 NO2 (g) • Write the Kc expression and calculate its value if the the equilibrium concentrations are: 0.0172 M for NO2 and 0.00140 for N2O4 • Answers on the next slide. Equilibrium Answer Kc = [NO2]2 [N2O4] Kc = [0.0172]2 [0.00140] Kc = 0.211 Equilibrium Simple Equilibrium Calculations • Given: N2(g) + 3 H2 (g) 2 NH3 (g) • What is the partial pressure of the ammonia in the equilibrium mixture if the equilibrium mixture contains 0.982 atm hydrogen gas and 0.432 atm nitrogen gas when Kp = 1.45 x 10-5 at 500 Celsius. • Answers on the next slide. Equilibrium Answer Kp = [NH3]2 [N2] [H2]3 1.45 x 10-5 = [NH3]2 [0.432] [0.982] 3 (1.45 x 10-5 )(0.432) (0.982) 3 = [NH3]2 Answer: [NH3] = 2.48 x 10-3 M Equilibrium Stop Here! Start Homework Textbook Assignment Due Tuesday • Questions #15.13ab, 15.14ab, 15.15, 15.16, 15.19, 15.22ab, 15.27, 15.28, 15.29, 15.30 Equilibrium Warm Up Equilibrium Warm-Up 1. Write the equilibrium expression for the reaction: Ti(s) + 2Cl2(g) TiCl4(l) Answer: Kc = 1 [Cl2]2 Equilibrium Warm-Up (con’t) 2. Write the equilibrium expression for the reaction: CH4(g) + 2 H2S (g) CS2(g) + 4 H2(g) Answer: Kc = [CS2] [H2]4 [CH4] [H2S]2 Equilibrium Warm-Up (con’t) 3. What are the rules for manipulating K values when a Rx is a) reversed? b) doubled? c) tripled? d) halved? e) added to a 2nd Rx? Answers: Equilibrium 2 3 1/2 a) 1/K b) K c) K d) K e) multiply K values Warm-Up (con’t) 4. Given: Kp = 1.5 x 10-10 for N2(g) + O2(g) 2 NO(g) What is the Kp for NO(g) ½ N2(g) + ½ O2(g) Answer: 1/ Kp1/2 = 1/(1.5 x 10-10)1/2 = 8.2 x 104 Equilibrium Warm-Up (con’t) 5. Given: K1 = 67 for CoO(s) + H2(g) Co(s) + H2O(g) And, K2 = 490 for CoO(s) + CO(g) Co(s) + CO2(g) What is K3 for: H2(g) + CO2(g) CO(g) + H2O(g) ? Equilibrium Warm-Up (con’t) 5. Given: K1 = 67 for CoO(s) + H2(g) Co(s) + H2O(g) And, K2 = 490 for CoO(s) + CO(g) Co(s) + CO2(g) What is K3 for: H2(g) + CO2(g) CO(g) + H2O(g) ? Answer: Reverse the Rx for K2 and add it to the Rx for K1 So, take the reciprocal of K2 and multiply it times K1 So, use (1/ K2) x K1 = (1/490) (67) = 0.14 Equilibrium Warm-Up (con’t) 6. Define the term ‘equilibrium’. Answer: A state of balance between 2 opposing reactions that are occurring at the same rate. As a result, the concentrations of the reactants and products are constant. Equilibrium Warm-Up (con’t) 7. A reaction has an equilibrium constant of 8.6 x 10-3. Does the equilibrium mixture favor the production of reactants or products? Answer: Whenever K is << 1, the equilibrium mixture consists primarily of reactants. Equilibrium Kp = Kc n (RT) Equilibrium Kp = Kc (RT)n Where R = 0.0821 L-atm/mol-K and T = Kelvin temp and n = (moles of gaseous product) − (moles of gaseous reactant) If Kc = 0.042 for PCl3(g) + Cl2(g) PCl5(g) at 500 K, what is the value of Kp for this reaction at this temperature? Kp = Kc (RT)n Kp = (0.042)[(0.0821 L-atom/mol-K)(500 K)]1-2 Kp = 1.0 x 10-3 Equilibrium Kp = Kc (RT)n Where R = 0.0821 L-atm/mol-K and T = Kelvin temp and n = (moles of gaseous product) − (moles of gaseous reactant) Calculate Kc at 30.0oC for SO2(g) + Cl2(g) SO2Cl2(g) if Kp = 34.5 for this reaction at this temperature? Kp = Kc (RT)n 34.5 = (Kc)[(0.0821 L-atom/mol-K)(303 K)]1-2 34.5 = (Kc) (0.04019) Equilibrium Kc = 858 The Reaction Quotient (Q) Equilibrium The Reaction Quotient (Q) • To calculate Q, one substitutes the initial concentrations of reactants and products into the equilibrium expression. • Q gives the same ratio the equilibrium expression gives, but for a system that is not at equilibrium. Equilibrium If Q = K, the system is at equilibrium. Equilibrium If Q > K, there is too much product and the reaction shifts to the left to reach equilibrium. Equilibrium If Q < K, there is too much reactant, and the reaction shifts to the right to reach equilibrium. Equilibrium Reaction Quotient Problem N2(g) + 3 H2 (g) 2 NH3 (g) At 723 K, the Kc = 6.0 x 10-2 for ammonia production. If the system contains 61.2 M nitrogen, 122 M hydrogen, and 122 M ammonia. Is the system at equilibrium? If not, which way must it shift to reach equilibrium? Prove your answer. Solution: Q = [NH3]2 = (122) 2 [N2] [H2]3 (61.2)(122) 3 Q = 1.3 x 10-4 Q<K Equilibrium Must shift to right to reach equilibrium ICE Problems Equilibrium ICE Problems I = Initial Concentration C = Change in Concentration E = Equilibrium Concentration Where: E = the difference between I & C Equilibrium ICE Problems We often do not know the equilibrium concentrations of all the chemicals in an equilibrium mixture. If we know the eq conc of at least one chemical, we can use the stoichiometry of the reaction to deduce the eq conc of the other chemicals. Equilibrium ICE Problems Steps to follow: 1)Calculate all the known initial conc’s and equilibrium conc’s Molarity = moles/L moles = mass/gfm 2) Calculate the change in conc for the chemical whose initial conc’s and eq conc’s are known 3) Use the stoichiometry (coefficients) to calculate the changes in conc for the other chemicals 4) Use the change in conc’s & the initial conc’s to determine the equilibrium conc’s Equilibrium 5) Solve the problem ICE Problem A closed system initially containing 1.000 x 10−3 M H2 and 2.000 x 10−3 M I2 At 448C is allowed to reach equilibrium. Analysis of the equilibrium mixture shows that the concentration of HI is 1.87 x 10−3 M. Calculate Kc at 448C for the reaction taking place, which is H2 (g) + I2 (g) 2 HI (g) Equilibrium What Do We Know? [H2], M Initially [I2], M 1.000 x 10-3 2.000 x 10-3 [HI], M 0 Change At equilibrium 1.87 x 10-3 Equilibrium [HI] Increases by 1.87 x 10-3 M [H2], M Initially [I2], M 1.000 x 10-3 2.000 x 10-3 [HI], M 0 Change +1.87 x 10-3 At equilibrium 1.87 x 10-3 Equilibrium Stoichiometry tells us [H2] and [I2] decrease by half as much [H2], M [I2], M [HI], M Initially 1.000 x 10-3 2.000 x 10-3 Change -9.35 x 10-4 -9.35 x 10-4 +1.87 x 10-3 At equilibrium 0 1.87 x 10-3 Equilibrium We can now calculate the equilibrium concentrations of all three compounds… [H2], M [I2], M [HI], M Initially 1.000 x 10-3 2.000 x 10-3 Change -9.35 x 10-4 -9.35 x 10-4 +1.87 x 10-3 At equilibrium 6.5 x 10-5 1.065 x 10-3 0 1.87 x 10-3 Equilibrium …and, therefore, the equilibrium constant [HI]2 Kc = [H2] [I2] = (1.87 x 10-3)2 (6.5 x 10-5)(1.065 x 10-3) = 51 Equilibrium Complex ICE Problems Ask Mrs. Amuso for the worksheet of sample problems using the quadratic equation. For ax2 + bx + c = 0, the value of x is given by: Equilibrium Le Châtelier’s Principle Equilibrium Recall: Equilibrium 1. Equilibrium can only occur in a closed system. 2. Equilibrium is a state of balance between two opposing reactions that are occurring at the same reaction rate or speed. 3. The amounts or concentrations of the reactants and products are constant, but not equal. 4. Equilibrium is a dynamic process. It looks like nothing is changing, but the reactions have not stopped. Equilibrium Le Châtelier’s Principle 1. When a stress is applied to a system at equilibrium, the system shifts to relieve the stress and restore the equilibrium to new conditions. 2. Stresses include changes in: a) Concentration of products or reactants b) Pressure (gases) c) Temperature 3. When a system shifts, either the forward or reverse reaction speeds up and a new equilibrium point is established. Equilibrium When the Forward Reaction Speeds Up The equilibrium point shifts to the Right Reactants Products When equilibrium is reestablished, there will be more product and less reactant. Equilibrium When the Reverse Reaction Speeds Up The equilibrium point shifts to the Left Reactants Products When equilibrium is reestablished, there will be more reactant and less product. Equilibrium Rules for Concentration Changes Stress Inc Product(s) Dec Product(s) Inc Reactant(s) Dec Reactant(s) aA + bB cC + dD Reactants Products Relief Dec Product(s) Inc Product(s) Dec Reactant(s) Inc Reactant(s) Shift Left Right Right Left Equilibrium Concentration Changes N2 (g) + 3H2 (g) Stress Increase N2 2NH3 (g) Relief Shift Decrease N2 Final Result : Less N2 than before To the Right Less H2 More NH3 Equilibrium Concentration Changes If H2 is added to the system, N2 will be consumed and the two reagents will form more NH3. Equilibrium Concentration Changes N2 (g) + 3H2 (g) 2NH3 (g) Equilibrium shifts left to offset stress Add NH3 Equilibrium Pressure Changes 1. Affect only gases. 2. Pressure is increased by decreasing volume. 3. To relieve the stress, the system shifts in the direction which will decrease the number of molecules of gas (fewer moles). 4. Pressure can also be increased by adding an inert gas. This does not cause a shift. Equilibrium Pressure Changes CaCO3(s) Stress The piston is pushed in, decreasing the volume and increasing the pressure. CaO(s) + CO2 (g) Relief Decrease pressure Shift In the direction that consumes CO2(g), lowering the pressure again. Equilibrium Rules for Pressure Changes 2 A (g) + B (g) 3 moles Stress 4 C (g) 4 moles Shift 1. Increase pressure (reduce volume) To fewest moles of gas 2. Decrease pressure (increase volume) To most moles of gas (In this case, to the left) (In this case, to the right) Equilibrium Practice N2 (g) + 3H2 (g) Stress Increase pressure Relief Shift to fewer moles of gas 2NH3 (g) Shift Equilibrium Practice H2 (g) + Cl2 (g) Stress Decrease pressure 2 CO2 (g) Stress 2 HCl (g) Shift No shift CO2 (g) + O2 (g) Shift Increase pressure Equilibrium Rules for Temperature Changes 2 A (g) + heat Stress Increase temperature B (g) Shift In endothermic direction (In this case, to the right) Decrease temperature In exothermic direction (In this case, to the left) Equilibrium Temperature Changes Co(H2O)62+(aq) + 4 Cl(aq) + heat Pink CoCl4 (aq) + 6 H2O (l) Blue When heated When cooled Equilibrium Temperature Changes Ways to represent an exothermic reaction: N2 (g) + 3H2 (g) N2 (g) + 3H2 (g) 2NH3 (g) + 92 kJ 2NH3 (g) H = -92 kJ H value = forward reaction Stress Decrease Temp (+ = endo Relief Increase Temp (Exothermic) - = exo) Shift Equilibrium Temperature & Equilibrium Constants 1. For Endothermic Reactions: Increasing T results in an increase in K 2. For Exothermic Reactions: Increasing T results in a decrease in K Equilibrium Adding a Catalyst 1. Catalysts do not change the equilibrium constant (K value) or shift the equilibrium. 2. Catalysts increase the rate of both the forward and reverse reactions equally. 3. Catalyst lower the Ea for both the forward and reverse reactions. 4. The system reaches equilibrium sooner. . uncatalyzed catalyzed Equilibrium The Haber Process N2 (g) + 3H2 (g) 2NH3 (g) + 92 kJ Under normal conditions the amount of ammonia produced by this reversible reaction is not sufficient for our needs. The Haber Process refers to the economically feasible method of producing ammonia which was developed by German chemist Fritz Haber during WWI. When the Allies blocked off their trade routes, the Germans lost all source of sodium nitrate and potassium nitrate, their source of nitrogen for making explosives. The Germans were forced to use ammonia to make their explosives. Because ammonia can also be used in fertilizer production, Fritz Haber received a Noble Prize for developing this process. This decision was controversial because it is believed that WWI would have ended before 1918 if it weren’t for the Germans being able to use ammonia to make their explosives. Ironically, Haber was expelled from Germany in 1933 because he was Jewish. Under what conditions will the production of ammonia be maximized? Did you guess use a Catalyst at High Pressure and Low Temperature? Actually it’s a catalyst at about 200 atm and 450 Celsius (At a lower temp the reaction is too slow) Equilibrium The Haber Process This apparatus, developed by German Maz Born, helps push the equilibrium to the right by removing the ammonia (NH3) from the system as a liquid. Equilibrium Equilibrium Shift Song http://www.youtube.com/watch?v=qsR5lA_T2B 0&feature=related Equilibrium