Chemical Equilibrium Foundation of equilibrium Expressing equilibrium: Equilibrium constants Upsetting equilibrium – Le Chatelier Learning objectives • Write equilibrium constant expressions for both solutions and gas phase reactions • Deduce relationship between Kc and Kp • Use reaction quotients to predict direction of reaction • Apply LeChatelier’s principle to predict consequences of changing equilibrium conditions Equilibrium • Chemical equilibrium is: The state reached when the concentrations of reactants and products remain constant over time • Equilibrium is evident in physical processes: vapour pressure over a liquid, solid and liquid coexisting at the freezing point Equilibrium in a chemical change • Not all reactions proceed to completion – • reactants completely converted into products As reactants convert into products, the products themselves convert back into reactants As reactant concentration declines, the forward rate decreases As product concentration increases, the backward rate increases Dynamic equilibrium • In the reaction N O ( g ) NO ( g ) 2 4 2 The same final concentrations of NO2 and N2O4 are obtained regardless of the initial conditions – pure NO2 or pure N2O4 • The reactions don’t stop, the processes become equal in both directions Reactants and products no more • In an equilibrium mixture, there is a constant, dynamic cycling of materials and the identities of reactant and product are lost • By convention, the substance(s) used initially are called the reactants Rate perspective • As the concentration of reactant (product) • decreases, the rate of disappearance also decreases The equilibrium point is reached when the rates are equal Equilibrium constant • Reactions usually take place in solution or in the gas phase. For solution reactions, the equilibrium constant Kc is used, where concentrations are in mol/L Concentration M • For the equilibrium Products aA +bB = cC + dD c d [C ] [ D] Kc a b [ A] [ B] Coefficients from equation Reactants Notes about Kc • Kc is a constant at a given temperature, regardless of the concentrations of the reactants used • Substances may be gases or solutions • Kc has no units: each concentration is considered as a ratio to the standard state (1 M) Equilibrium constant Kp • For reactions in the gas phase, the partial pressure can be used instead of molarity c d PC PD Kp a b PA PB • Kp is unitless because the ratio with respect to the standard state (1 atm) is used Relationship between Kc and Kp PAV = nART so PA = nA/V●RT = [A]RT c d [C ] [ D] ( c d ) ( a b ) Kp ( RT ) a b [ A] [ B] K p K c ( RT ) n Δn = (c+d)-(a+b) Heterogeneous equilibria • Reactions often involve solid or liquid phases in addition to gas and solution • Concentrations of liquids and solids are constants – independent of the amount • Since they are constant they become folded into Kc Solids and liquids are ignored CaCO3(s) = CaO(s) + CO2(g) [CaO][CO2 ] Kc [CaCO3 ] [CaCO3 ] Kc x [CO2 ] [CaO] Solid concentrations are constant • Include only gas or solution entities in Kc Using equilibrium constants • The value of Kc or Kp indicates the extent of a reaction • Generally: Kc > 103, reaction goes to completion Kc < 10-3, reaction does not proceed 103 > Kc > 10-3 reactants and products all present Reaction Quotient • Reaction Quotient is the instanteous value obtained for Kc for a combination of reactants and products not yet at equilibrium • It can be used to predict the direction the reaction will take from that set of conditions Kc and Qc • In the reaction H 2 ( g ) I 2 ( g ) 2HI ( g ), K c 57 • A mixture made up with [H2] = 0.1 M, [I2] = 0.2 M and [HI] = 0.4 M 2 2 [ HI ] 0.4 Qc 8.0 [ H 2 ][ I 2 ] 0.1 0.2 • Kc > Qc so reaction will go towards HI Predicting reactions with Qc Qc < Kc, reaction goes towards products Qc > Kc, reaction goes towards reactants Qc = Kc, reaction is at equilibrium Calculations with Kc • Simple calculations: Kc and all equilibrium concentrations but one are given. Use Kc to calculate concentration of unknown • Complex calculations: Kc and initial concentrations are given, calculate equilibrium concentrations I.C.E. – It’s pretty cool • The ICE man cometh: it is widely used in equilibrium problems • Given Kc = 57 and initial concentrations of [H2] = [I2] = 0.1 M, find equilibrium concentrations of H2, I2 and HI Initial conc Change Equilibrium conc H2 I2 HI 0.1 0.1 0.0 -x -x 2x 0.1 - x 0.1 - x 2x Solve for x 2 2 [ HI ] ( 2 x) K c 57 [ H 2 ][ I 2 ] (0.1 x) (0.1 x) 2 4x 57 2 (0.1 x) x 0.0791M , or 0.136M • X = 0.136 > 0.1 so is physically unreasonable • X =0.0791: [H2] = [I2] = 0.0209 M; [HI] = 0.158 M Upsetting the applecart • Conditions of reactions must often be manipulated to optimize yield of products Concentrations of reactants or products Temperature Pressure and volume • Le Chatelier’s Principle: If a stress is applied to a reaction mixture at equilibrium, the system adjusts to relieve the stress The Haber process • One of the most important industrial processes is the synthesis of NH3 from the elements: N2(g) + 3H2(g) = 2NH3(g) • At 700 K, Kc = 0.29 • Altering reactant concentrations: Increasing [reactant]: reactants → products Increasing [product]: products → reactants Effects of pressure • Pressure is only important if there is an overall • change in the number of gas moles N2(g) + 3H2(g) = 2NH3(g) In the Haber process there are 4 moles of reactants vs 2 moles of products Increasing pressure: converts reactants to products (fewer moles) Decreasing pressure: converts products to reactants (more moles) Effects of temperature • Kc depends on temperature. Increasing or decreasing temperature will cause mixture to adjust to new value of Kc. • Treat the ΔH of a reaction as a reactant/product • Raising T causes heat input into reaction • Lowering T causes withdrawal of heat The Haber process as Function of T • The process is exothermic: heat is a product • N2(g) + 3H2(g) = 2NH3(g) + 92.2 kJ Raising T puts heat into reaction: Equilibrium adjusts to reduce heat output – moves towards reactants • Lowering T removes heat: Equilibrium adjusts to increase heat output – moves towards products • Endothermic reactions will show the opposite Tdependence Increasing T in Haber process reduces yield Catalysts and equilibrium • Equilibrium depends on the initial and final states • Catalyst lowers the transition state • Equilibrium is unaffected by addition of a catalyst From the rate perspective • The catalyst increases the forward reaction rate by lowering the energy barrier • The rate of the backward reaction is lowered by the same amount Linking rate equations with Kc • For the general reaction: • A+B=C+D Assume single bimolecular steps Rate of forward reaction = kf[A][B] Rate of backward reaction = kr[C][D] • At equilibrium k f [ A][ B] k r [C ][ D] kf [C ][ D] Kc k r [ A][ B]