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 Write equilibrium constant expressions for both solutions and gas phase reactions Deduce relationship between K c and K p Deduce relationship between K c and K p Use reaction quotients to predict direction of reaction Use reaction quotients to predict direction of reaction Apply LeChatelier’s principle to predict consequences of changing equilibrium conditions Apply LeChatelier’s principle to predict consequences of changing equilibrium conditions

Equilibrium Chemical equilibrium is: 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 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 Not all reactions proceed to completion – reactants completely converted into products As reactants convert into products, the products themselves convert back into reactants 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 In the reaction The same final concentrations of NO 2 and N 2 O 4 are obtained regardless of the initial conditions – pure NO 2 or pure N 2 O 4 The reactions don’t stop, the processes become equal in both directions 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 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 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 As the concentration of reactant (product) decreases, the rate of disappearance also decreases The equilibrium point is reached when the rates are equal 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 K c is used, where concentrations are in mol/L Reactions usually take place in solution or in the gas phase. For solution reactions, the equilibrium constant K c is used, where concentrations are in mol/L For the equilibrium For the equilibrium aA +bB = cC + dD Products Reactants Concentration M Coefficients from equation

Notes about K c K c is a constant at a given temperature, regardless of the concentrations of the reactants used K c is a constant at a given temperature, regardless of the concentrations of the reactants used Substances may be gases or solutions Substances may be gases or solutions K c has no units: each concentration is considered as a ratio to the standard state (1 M) K c has no units: each concentration is considered as a ratio to the standard state (1 M)

Equilibrium constant K p For reactions in the gas phase, the partial pressure can be used instead of molarity For reactions in the gas phase, the partial pressure can be used instead of molarity K p is unitless because the ratio with respect to the standard state (1 atm) is used K p is unitless because the ratio with respect to the standard state (1 atm) is used

Relationship between K c and K p P A V = n A RT so P A = n A /V●RT = [A]RT Δn = (c+d)-(a+b)

Heterogeneous equilibria Reactions often involve solid or liquid phases in addition to gas and solution Reactions often involve solid or liquid phases in addition to gas and solution Concentrations of liquids and solids are constants – independent of the amount Concentrations of liquids and solids are constants – independent of the amount Since they are constant they become folded into K c Since they are constant they become folded into K c

Solids and liquids are ignored CaCO 3 (s) = CaO(s) + CO 2 (g) Include only gas or solution entities in K c Include only gas or solution entities in K c Solid concentrations are constant

Using equilibrium constants The value of K c or K p indicates the extent of a reaction The value of K c or K p indicates the extent of a reaction Generally: Generally:  K c > 10 3, reaction goes to completion  K c < 10 -3, reaction does not proceed  10 3 > K c > reactants and products all present

Reaction Quotient Reaction Quotient is the instanteous value obtained for K c for a combination of reactants and products not yet at equilibrium Reaction Quotient is the instanteous value obtained for K c 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 It can be used to predict the direction the reaction will take from that set of conditions

K c and Q c In the reaction In the reaction A mixture made up with [H 2 ] = 0.1 M, [I 2 ] = 0.2 M and [HI] = 0.4 M A mixture made up with [H 2 ] = 0.1 M, [I 2 ] = 0.2 M and [HI] = 0.4 M K c > Q c so reaction will go towards HI K c > Q c so reaction will go towards HI

Predicting reactions with Q c  Q c < K c, reaction goes towards products  Q c > K c, reaction goes towards reactants  Q c = K c, reaction is at equilibrium

Calculations with K c Simple calculations: Simple calculations: K c and all equilibrium concentrations but one are given. Use K c to calculate concentration of unknown Complex calculations: Complex calculations: K c 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 The ICE man cometh: it is widely used in equilibrium problems Given K c = 57 and initial concentrations of [H 2 ] = [I 2 ] = 0.1 M, find equilibrium concentrations of H 2, I 2 and HI Given K c = 57 and initial concentrations of [H 2 ] = [I 2 ] = 0.1 M, find equilibrium concentrations of H 2, I 2 and HI H2H2H2H2 I2I2I2I2HI Initial conc Change -x-x2x Equilibrium conc x 2x

Solve for x X = > 0.1 so is physically unreasonable X = > 0.1 so is physically unreasonable X =0.0791: [H 2 ] = [I 2 ] = M; [HI] = M X =0.0791: [H 2 ] = [I 2 ] = M; [HI] = M

Upsetting the applecart Conditions of reactions must often be manipulated to optimize yield of products 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: 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 NH 3 from the elements: N 2 (g) + 3H 2 (g) = 2NH 3 (g) One of the most important industrial processes is the synthesis of NH 3 from the elements: N 2 (g) + 3H 2 (g) = 2NH 3 (g) At 700 K, K c = 0.29 At 700 K, K c = 0.29 Altering reactant concentrations: 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 Pressure is only important if there is an overall change in the number of gas moles N 2 (g) + 3H 2 (g) = 2NH 3 (g) In the Haber process there are 4 moles of reactants vs 2 moles of products 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 K c depends on temperature. Increasing or decreasing temperature will cause mixture to adjust to new value of K c. K c depends on temperature. Increasing or decreasing temperature will cause mixture to adjust to new value of K c. Treat the ΔH of a reaction as a reactant/product Treat the ΔH of a reaction as a reactant/product Raising T causes heat input into reaction Raising T causes heat input into reaction Lowering T causes withdrawal of heat Lowering T causes withdrawal of heat

The Haber process as Function of T The process is exothermic: heat is a product The process is exothermic: heat is a product Raising T puts heat into reaction: Raising T puts heat into reaction:  Equilibrium adjusts to reduce heat output – moves towards reactants Lowering T removes heat: Lowering T removes heat:  Equilibrium adjusts to increase heat output – moves towards products Endothermic reactions will show the opposite T- dependence Endothermic reactions will show the opposite T- dependence N 2 (g) + 3H 2 (g) = 2NH 3 (g) kJ

Increasing T in Haber process reduces yield

Catalysts and equilibrium Equilibrium depends on the initial and final states Equilibrium depends on the initial and final states Catalyst lowers the transition state Catalyst lowers the transition state Equilibrium is unaffected by addition of a catalyst 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 catalyst increases the forward reaction rate by lowering the energy barrier The rate of the backward reaction is lowered by the same amount The rate of the backward reaction is lowered by the same amount

Linking rate equations with K c For the general reaction: For the general reaction: A + B = C + D Assume single bimolecular steps Assume single bimolecular steps  Rate of forward reaction = k f [A][B]  Rate of backward reaction = k r [C][D] At equilibrium At equilibrium