Equilibrium means that the rxn rates are equal. evaporation H20(l) condensation

Reversible reactions Most chemical reactions are reversible they can occur backwards as well as forwards reactants products Consider an open container of water (non-equilibrium) A closed water bottle is an example of a dynamic equilibrium Closed system Number of liquid phase and gas phase particles do not change this does NOT mean that [H2O(l)] = [H2O(g)] Equilibrium means that the rxn rates are equal evaporation H20(l) condensation H2O(g) Macroscopic (everyday) level Microscopic level (atoms and molecules) We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 1 of 22

A thought exercise: Consider the following chemical system A + B C + D We start with only the reactants A and B gas in a container and watch as they react [A] and [B] decrease as they are consumed, and forward rate slows Soon the forward and reverse processes occur at the same rate and there is no further change in concentration of any component At equilibrium there is no further change in concentration of any component Concept Check A reaction is at equilibrium. This means that a. the product concentrations are equal to the reactant concentrations b. the rate of the forward reaction is zero c. the reaction has proceeded 100 % to completion d. None of the above are correct Consider the following chemical system 2 NO2(g) N2O4(g) From experimental data we know that the forward and reverse rate laws are We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 2 of 22

At equilibrium; ratefor = raterev K = is the equilibrium constant Write the form of equilibrium constant, KC, for the following reactions The decomposition of dinitrogen pentaoxide: 2 N2O5(g) 4 NO2(g) + O2(g) The combustion of propane: C3H8(g) + 5 O2(g) 3 CO2(g) + 4 H2O(g) Concept Check Below is a concentration vs. time plot for the reaction A B. What is the value of the equilibrium constant for this reaction? a. Kc < 1. b. Kc = 0 c. Kc = 1 d. Kc > 1 We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 3 of 22

The equilibrium constant (K) and the extent of reaction A small K (<10-3 ) indicates the reaction yields little product before reaching equilibrium reaction vessel will contain mostly reactants @ equilibrium We say The reaction favors the reactants A large K (<10 +3 )indicates the reaction reaches equilibrium with very little reactant remaining reaction vessel will contain mostly products @ equilibrium we say the products are favored Concept Check Which one of the following equilibrium proceeds hardly at all to completion? a. HS (aq) H + (aq) + S 2 (aq) Kc = 1.0 10 19 b. 2 CO(g) + O2(g) 2 CO2(g) Kc = 2.2 10 22 c. N2(g) + 3 H2(g) 2 NH3(g) Kc = 1.2 The Reaction Quotient, Q Q gives the ratio of product concentrations to reactant concentrations at any point in a reaction For the general reaction aa + bb cc + dd, Q = c d [ C] [ D] [ A] a [ B] b [products] [reactants] K = c d [ C] @ equilibrium [ D] @ equilibrium a [ A] [ ] b @ equilibrium B @ equilibriu m [products] at [reactants] at Determining the Direction of Reaction Comparison of Q vs K indicates which direction the reaction must proceed to reach equilibrium If Q < K then more products will be formed as rxn approaches equilibrium We say the reaction proceeds to the right If Q > K then more products will be formed as rxn approaches equilibrium We say the reaction proceeds to the left We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 4 of 22

For the reaction N2O4(g) 2NO2(g), KC = 0.21 at 100 C. At a point during the reaction, [N2O4] = 0.12 M and [NO2] = 0.55 M. Is the reaction at equilibrium? If not, in which direction will it progress towards equilibrium? not at equilibrium, reaction will proceed to the left towards equilibrium Special notes: For an overall reaction that is the sum of two more individual reactions Q overall = Q1 Q2 Q3... and Koverall = K1 K2 K3... The form of Q and K depend on the direction in which the balanced equation is written 1 1 Q c(rev) = and K c(rev) = Q K c(fwd) If the coefficients of a balanced equation are multiplied by a common factor, n Q c [ C] [ D] a [ A] [ B] d n n = Q = b and c(fwd) n K = K We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 5 of 22

Nitrogen dioxide is a toxic pollutant that contributes to photochemical smog. One way it forms is through the following sequence (1) N2(g) + O2(g) 2 NO(g) Kc1= 4.3 10 25 (2) 2 NO(g) + O2(g) 2 NO2(g) Kc2= 6.4 10 9 Show that the overall Qc for this reaction sequence is the same as the product of the Qc's of the individual reactions Given that both reactions occur at the same temperature, find Kc for the overall reaction Kc,overall= 2.8 10 15 For the ammonia formation reaction, the reference equation is N2(g) + 3H2(g) 2 NH3(g) Kc is 2.4 10 3 at 1000 K. What is the value of Kc for 1/3 N2(g) + H2(g) 2/3 NH3(g) What is the value of Kc for NH3(g) ½ N2(g) + 3/2 H2(g) Kc = 0.13 Kc = 2.0 10 1 Concept Check The equilibrium constant, Kc, for the decomposition of COBr2 is 0.190 COBr2(g) CO(g) + Br2(g) What is Kc for the following reaction? 2CO(g) + 2Br2(g) 2COBr2(g) a. 0.0361 b. 2.63 c. 5.62 d. 10.5 e. 27.7 We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 6 of 22

K and Q for hetereogeneous equilibrium A hetereogeneous equilibrium involves reactants and/or products in different phases The expressions for Q and K include only species whose concentrations change Pure solids and liquids are omitted from the expression for Q or K For the reaction below Qc= [CO2] and Kc= [CO2]eq CaCO3(s) CaO(s) + CO2(g) Consider an equilibrium mixture of solid CaCO3, solid CaO, and gaseous CO2, obtained as a result of the endothermic decomposition of CaCO3. What happens when additional solid CaCO3 molecules are added to the system? Expressing Equilibria with Pressure Terms Kc and Kp Consider : CaCO3(s) CaO(s) + CO2(g) n V nrt n n K P = PCO2 = = = V V V ideal gas law P = ( RT) = [ gas]( RT) n, gas General form: ( ) K = K p c ( RT) = ( RT) K ( RT) RT C We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 7 of 22

A chemical engineer injects limestone (CaCO3) into the hot flue gas of a coal-burning power plant for form lime (CaO), which scrubs SO2 from the gas and forms synthetic gypsum CaSO3(s). Find Kc for the following reaction CaO(s) + SO2(g) CaSO3(s) KP=2.1 10 4 at 1000K. Concept Check Under what conditions are the values of Kc and Kp for a given gas-phase equilibrium the same? a. If temperature remains the same b. If the sum of the total coefficients is the same on both sides of the equation c. If the reaction produces no change in number of moles of gas d. All of the above are correct e. None on the above are correct KC=2.6 10 6 We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 8 of 22

Consider a closed container half-filled with water Some liquid phase particles possess sufficient kinetic energy to overcome IMF and enter the gas phase Vapor pressure pressure due to gas phase particles above its liquid Occasionally a gas phase particle impacts the surface and it recaptured by the liquid phase An equilibrium exists between gas phase and liquid phase particles evaporation H2O(l) + heat H2O(g) condensation Consider the same container as it is heated to a higher temperature evaporation H2O(l) + heat condensation H2O(g) Stress: added heat (a reactant) Response: some of added reagent consumed and more product formed (shift right) Le Châtelier s Principle (Shift happens!!) A system is disturbed when a change in conditions forces it temporarily out of equilibrium new equilibrium reached by a net reaction that reduces the effect of the disturbance (stress) Le Châtelier s Principle as applied to this example System stress: For example, adding a reactant (heat) causes the forward reaction to temporarily increase (a shift to the right) for a short time the forward reaction rate is higher than the reverse reaction rate System response: A NEW equilibrium is established by consuming some of the added reactant (relieve stress) We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 9 of 22

Concentration Stress: adding or removing a reactant or product Stress: Response: Stress: Response: Concentration Stress: Stress: Response: We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 10 of 22

Consider the system below at equilibrium. In what direction will the system shift if additional Cl2(g) is added? PCl3(g) + Cl2(g) PCl5(g) Concept Check Shift to the right to consume some of the added Cl2 Nitrogen dioxide, NO2(g), exists in equilibrium with N2O4(g). Suppose a mixture of NO2(g) and N2O4(g) is allowed to come to equilibrium in a sealed vessel. If the volume of the vessel is halved at constant temperature, what direction will the equilibrium shift as it approaches a new equilibrium? a. It will shift to the left b. It will shift to the right c. Neither, the equilibrium is not stressed Concept Check Historically, the reaction of coke (a form of elemental carbon) and superheated steam takes place was of great importance in the generation of a combustible gas known as "water gas", or "synthesis gas". This gas distributed through pipelines to houses in major cities until around 1950 by which time natural gas (methane, CH4 ) replaced it for use as a household fuel. One of the major problems with synthesis gas is that it contains carbon monoxide. Death from carbon monoxide poisoning was not uncommon when synthesis gas was in widespread household use. CO can be removed using the water gas shift reaction CO(g) + H2O(g) CO2(g) + H2(g) A mixture of CO, H2O, CO2 and H2 gases is at equilibrium. If the volume of the reaction vessel is halved at constant temperature, what direction will the equilibrium shift as it approaches a new equilibrium? a. It will shift to the left b. It will shift to the right c. Neither, the equilibrium is not stressed Concept Check Crystals of iodine, I2(s), are placed in a closed container and allowed to sublime until they come to equilibrium with I2(g). If more I2(s) is added to the vessel, the partial pressure of I2(g) will: a. Stay the same b. Increase c. Decrease We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 11 of 22

Important Note: Only substances that appear in the expression for Q can cause a stress Adding an inert gas has no effect on equilibrium Adding a solid (or liquid) to a system at equilibrium does not affect the value of Q. The system remains at equilibrium To improve air quality and obtain a useful product, chemists often remove sulfur from coal and natural gas by treating the contaminant hydrogen sulfide with O2: 2H2S(g) + O2(g) 2S(s) + 2H2O(g) What happens to [H2O] if O2 is added? What happens to [H2S] if O2 is added? What happens to [O2] if H2S is removed? What happens to [H2S] if sulfur is added? Concept Check Consider the following reactions at equilibrium. Which one of these reactions will remain at equilibrium despite a volume increase due to a decrease in pressure? a. N2O4(g) 2 NO2(g) b. 2 CO(g) C(s) + CO2(g) c. 2 Fe(s) + 3 H2O(g) Fe2O3(s) + 3 H2(g) d. 2 NO(g) + O2(g) 2 NO2(g) e. None of the above Would an increase in pressure by decreasing volume increase or decrease the yield of the following CaCO3(s) CaO(s) + CO2(g) S(s) + 3 F2(g) SF6(g) We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 12 of 22

Temperature as a stress Temperature is the only stress factor that actually changes the value of K An increase in temperature will cause K to increase for an endothermic reaction Note: rxns that are endothermic in forward direction are exothermic in reverse direction endothermic reaction Endothermic rxn Heat + reactants products exothermic reaction exothermic reaction Exothermic rxn reactants products + heat endothermic reaction Consider the following reaction at equilibrium. Concept Check 2 NO(g) + Cl2(g) 2 NOCl(g); Hº = 77.07 kj A temperature increase will cause the reaction to proceed in (the) direction; while a pressure increase due to a volume decrease will cause the reaction to proceed in (the) direction to regain equilibrium. a. forward; reverse b. forward; forward c. reverse; reverse d. reverse; forward e. forward; neither. We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 13 of 22

Solving Equilibrium Problems If all equilibrium quantities are given, we plug them into Kc If not all equilibrium quantities are given, we use a reaction (ICE) table A reaction (ICE) table shows the balanced equation the initial quantities of reactants and products (concentrations or partial pressure) the changes in these quantities during the reaction, and the equilibrium quantities In a study of carbon oxidation, an evacuated vessel containing a small amount of powdered graphite (a form of solid carbon) is heated to 1080 K. Gaseous CO2 is added to a pressure of 0.458 atm and CO forms. At equilibrium, the total pressure is 0.757 atm. Calculate Kp. Kp= 2.25 To study hydrogen halide decomposition, a researcher fills an evacuated 2.00-L flask with 0.200 moles of HI gas and allows the reaction to proceed at 453 C. At equilibrium, [HI] = 0.078 M. Calculate Kc. 2 HI(g) H2 (g) + I2(g) Kc=0.020 We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 14 of 22

In a study of the conversion of methane to other fuels, a chemical engineer mixes gaseous CH4 and H2O in a 0.32-L flask at 1200 K. At equilibrium the flask contains 0.26 mol of CO, 0.091 mol of H2, and 0.041 mol of CH4. What is the [H2O] at equilibrium? Kc = 0.26 for this process at 1200 K CH4(g) + H2O(g) CO(g) + 3H2(g) [H2O]eq = 0.56 M Fuel engineers use the extent of the change from CO and H2O to CO2 and H2 to regulate the proportions of synthetic fuel mixtures. If 0.250 mol of CO and 0.250 mol of H2O are placed in a 125- ml flask at 900 K, what is the composition of the equilibrium mixture? At this temperature, Kc is 1.56 CO(g) + H2O(g) CO2(g) + H2(g) [CO]eq=[H2O]eq= 0.89 M [CO2]eq= [H2]eq = x = 1.11 M We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 15 of 22

Concept Check The following pictures represent reaction mixtures that contain A2 molecules (shaded) and B2 molecules (unshaded), and AB molecules. Which reaction mixture is at equilibrium? A2 + B2 2 AB Kc = 1.8 The research and development unit of a chemical company is studying the reaction of CH4 and H2S, two components of natural gas as shown below. In one experiment, 1.00 mol of CH4, 1.00 mol of CS2, 2.00 mol of H2S, and 2.00 mol of H2 are mixed in a 250-mL vessel at 960 C. CH4(g) + 2H2S(g) CS2(g) + 4H2(g) At this temperature, Kc = 0.036 If [CH4] = 5.56 M at equilibrium, what are the equilibrium concentrations of the other substances? [H2S]eq = 11.1 M [CS2]eq = 2.44 M [H2]eq = 1.76 M We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 16 of 22

What are the partial pressures of reactants and products when the system achieves equilibrium? Initial H2 = 1.00 atm; Initial I2 = 1.03 atm; Initial HI(g) = 0.0 atm H2(g) + I2(g) 2 HI(g) KP = 50.2 [H2]eq = 0.21 atm [I2]eq = 0.24 atm [HI]eq = 1.58 atm The Simplifying Assumption [A]eq = [A]initial [A]reacting or [A]eq = [A]initial x We try assumption that [A]initial [A]reacting [A]initial this is justified if.. Kc is relatively small and/or [A]initial is relatively large o General rule If K 1000 < [A]initial then the simplifying assumption is OK We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 17 of 22

Phosgene is a potent chemical warfare agent that is now outlawed by international agreement. It decomposes by the reaction shown below. Calculate [CO], [Cl2], and [COCl2] when the 5.00 moles of phosgene gas decompose and reach equilibrium in a 10.0-L flask. COCl2(g) CO(g) + Cl2(g) Kc = 8.3 10 4 at 360 C [COCl2] = 0.480 M [CO]=[Cl2] = x = 0.020 M We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 18 of 22

Steps in solving equilibrium problems Preliminary Construct the ICE table Write the balanced equation. Write the reaction quotient, Q (or K as appropriate) Convert all amounts into the correct units (M or atm) Construct a reaction table Solving for x and equilibrium quantities Substitute the quantities into Q (or K as appropriate) Solve for x. (The tricky part) Look for perfect square Method of Successive approximation Quadratic equation Simplifying assumption (only if justified) Find the equilibrium quantities (plug x into reaction table) Sanity check Consider the theoretical equilibrium shown below. The equilibrium concentration of B is 2.20 M. Determine the numerical value of KC 2 A(aq) + B(aq) 3 C Initial 1.00 2.00 5.00 change equilibrium KC = 19.8 We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 19 of 22

Consider the equilibrium shown below. What is the equilibrium concentration of O2(g), if initially only 0.300 M NO(g) was present? N2(g) + O2(g) 2 NO(g) KC = 81.0 [O2]eq = 0.0273 M Consider the reaction shown below. What is the equilibrium partial pressure of SO2 if the equilibrium partial pressures of O2 and SO3 are 0.43 atm and 1.56 atm respectively 2 SO2(g) + O2(g)(g) 2 SO3(g) KP = 48.2 PSO2 = 0.34 atm We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 20 of 22

Phosgene COCl2, is a potent chemical warfare agent that is now outlawed by international agreement. Calculate the equilibrium partial pressures of the three gases when the initial partial pressure of both CO and Cl2 is 0.210 atm. CO(g) + Cl2(g) COCl2(g) KC = 5.0 at 600K [COCl2] = 0.0043 atm [CO]=[Cl2] = 0.206 M We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 21 of 22

Determine the equilibrium partial pressure of NH3 in a reaction vessel that initially contained 1.50 atm of H2 and 1.90 atm of N2. 3 H2(g) + N2(g) 2 NH3(g) KP= 4.3 10 4 PNH3 = 2x = 6.96 10 3 atm We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 22 of 22