Chemical Equilibrium Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1
Equilibrium is a state in which there are no observable changes as time goes by. Chemical equilibrium is achieved when: the rates of the forward and reverse reactions are equal and the concentrations of the reactants and products remain constant Physical equilibrium H 2 O (l) H 2 O (g) NO 2 Chemical equilibrium N 2 O 4 (g) 2NO 2 (g) 2
N 2 O 4 (g) 2NO 2 (g) equilibrium equilibrium equilibrium Start with NO 2 Start with N 2 O 4 Start with NO 2 & N 2 O 4 3
constant 4
N 2 O 4 (g) 2NO 2 (g) K = [NO 2 ]2 = 4.63 x 10-3 [N 2 O 4 ] aa + bb K = [C]c [D] d [A] a [B] b cc + dd Law of Mass Action 5
K = [C]c [D] d [A] a [B] b aa + bb cc + dd Equilibrium Will K >> 1 K << 1 Lie to the right Lie to the left Favor products Favor reactants 6
Homogenous equilibrium applies to reactions in which all reacting species are in the same phase. N 2 O 4 (g) 2NO 2 (g) K c = [NO 2 ]2 [N 2 O 4 ] In most cases K c K p K p = P NO 2 2 P N 2 O 4 aa (g) + bb (g) cc (g) + dd (g) K p = K c (RT) Δn Δn = moles of gaseous products moles of gaseous reactants = (c + d) (a + b) 7
Homogeneous Equilibrium CH 3 COOH (aq) + H 2 O (l) CH 3 COO - (aq) + H 3 O + (aq) K c = [CH 3 COO - ][H 3 O + ] [CH 3 COOH][H 2 O] [H 2 O] = constant K c = [CH 3 COO- ][H 3 O + ] [CH 3 COOH] = K c [H 2 O] General practice not to include units for the equilibrium constant. 8
The equilibrium constant K p for the reaction 2NO 2 (g) 2NO (g) + O 2 (g) is 158 at 1000K. What is the equilibrium pressure of O 2 if the P NO = 0.400 atm and P NO = 0.270 atm? 2 K p = 2 P NO P O 2 P NO 2 2 P O 2 = K P 2 NO p 2 2 P NO P O 2 = 158 x (0.400) 2 /(0.270) 2 = 347 atm 9
Heterogenous equilibrium applies to reactions in which reactants and products are in different phases. CaCO 3 (s) CaO (s) + CO 2 (g) K c = [CaO][CO 2 ] [CaCO 3 ] [CaCO 3 ] = constant [CaO] = constant [CaCO K c = [CO 2 ] = 3 ] K c x K p = P [CaO] CO 2 The concentration of solids and pure liquids are not included in the expression for the equilibrium constant. 10
CaCO 3 (s) CaO (s) + CO 2 (g) P CO 2 = K p P CO 2 does not depend on the amount of CaCO 3 or CaO 11
Consider the following equilibrium at 295 K: NH 4 HS (s) NH 3 (g) + H 2 S (g) The partial pressure of each gas is 0.265 atm. Calculate K p and K c for the reaction? K p = P NH3 P H 2 S = 0.265 x 0.265 = 0.0702 K p = K c (RT) Δn K c = K p (RT) - Δn Δn = 2 0 = 2 T = 295 K K c = 0.0702 x (0.0821 x 295) -2 = 1.20 x 10-4 12
N 2 O 4 (g) 2NO 2 (g) 2NO 2 (g) N 2 O 4 (g) K = [NO 2 ]2 = 4.63 x 10-3 [N 2 O 4 ] K = [N 2 O 4 ] = 1 [NO 2 ] 2 K = 216 When the equation for a reversible reaction is written in the opposite direction, the equilibrium constant becomes the reciprocal of the original equilibrium constant. 13
Writing Equilibrium Constant Expressions 1. The concentrations of the reacting species in the condensed phase are expressed in M. In the gaseous phase, the concentrations can be expressed in M or in atm. 2. The concentrations of pure solids, pure liquids and solvents do not appear in the equilibrium constant expressions. 3. The equilibrium constant is a dimensionless quantity. 4. In quoting a value for the equilibrium constant, you must specify the balanced equation and the temperature. 14
The reaction quotient (Q c ) is calculated by substituting the initial concentrations of the reactants and products into the equilibrium constant (K c ) expression. IF Q c > K c system proceeds from right to left to reach equilibrium Q c = K c the system is at equilibrium Q c < K c system proceeds from left to right to reach equilibrium 15
Calculating Equilibrium Concentrations 1. Express the equilibrium concentrations of all species in terms of the initial concentrations and a single unknown x, which represents the change in concentration. 2. Write the equilibrium constant expression in terms of the equilibrium concentrations. Knowing the value of the equilibrium constant, solve for x. 3. Having solved for x, calculate the equilibrium concentrations of all species. 16
At 1280 o C the equilibrium constant (K c ) for the reaction Br 2 (g) 2Br (g) Is 1.1 x 10-3. If the initial concentrations are [Br 2 ] = 0.063 M and [Br] = 0.012 M, calculate the concentrations of these species at equilibrium. Let x be the change in concentration of Br 2 Initial (M) Change (M) Equilibrium (M) Br 2 (g) 2Br (g) 0.063 0.012 -x +2x 0.063 - x 0.012 + 2x [Br] K 2 c = K [Br 2 ] c = (0.012 + 2x)2 0.063 - x = 1.1 x 10-3 Solve for x 17
(0.012 + 2x)2 K c = = 1.1 x 10 0.063 - x -3 4x 2 + 0.048x + 0.000144 = 0.0000693 0.0011x 4x 2 + 0.0491x + 0.0000747 = 0 Initial (M) Change (M) Equilibrium (M) ax 2 + bx + c =0 Br 2 (g) x = 2Br (g) 0.063 0.012 -x +2x -b ± b 2 4ac 2a x = -0.0105 0.063 - x 0.012 + 2x x = -0.00178 At equilibrium, [Br] = 0.012 + 2x = -0.009 M or 0.00844 M At equilibrium, [Br 2 ] = 0.062 x = 0.0648 M 18
Le Châtelier s Principle If an external stress is applied to a system at equilibrium, the system adjusts in such a way that the stress is partially offset as the system reaches a new equilibrium position. A different mechanism is operating depending on what parameter is changed 19
van t Hoff s law dlnk = ΔH dt RT 2 The temperature is the only parameter that change the equilibrium situation by variation of the K. The other quantities will operate a change by the need to keep constant K 20
Changes in Temperature Le Châtelier s Principle Change Increase temperature Decrease temperature Exothermic Rx K decreases K increases Endothermic Rx K increases K decreases N 2 O 4 (g) 2NO 2 (g) colder hotter 21
Le Châtelier s Principle If an external stress is applied to a system at equilibrium, the system adjusts in such a way that the stress is partially offset as the system reaches a new equilibrium position. Changes in Concentration N 2 (g) + 3H 2 (g) Equilibrium shifts left to offset stress 2NH 3 (g) Add NH 3 22
Le Châtelier s Principle Changes in Concentration continued Remove Add Add Remove aa + bb cc + dd Change Shifts the Equilibrium Increase concentration of product(s) Decrease concentration of product(s) Increase concentration of reactant(s) Decrease concentration of reactant(s) left right right left 23
Le Châtelier s Principle Changes in Volume and Pressure A (g) + B (g) C (g) Change Increase pressure Decrease pressure Increase volume Decrease volume Shifts the Equilibrium Side with fewest moles of gas Side with most moles of gas Side with most moles of gas Side with fewest moles of gas 24
Le Châtelier s Principle Adding a Catalyst does not change K does not shift the position of an equilibrium system system will reach equilibrium sooner Catalyst lowers E a for both forward and reverse reactions. Catalyst does not change equilibrium constant or shift equilibrium. 25
Le Châtelier s Principle - Summary Change Shift Equilibrium Change Equilibrium Constant Concentration yes no Pressure yes* no Volume yes* no Temperature yes yes Catalyst no no *Dependent on relative moles of gaseous reactants and products 26