Chapter 13 Chemical Equilibrium

13.1 Describing Chemical Equilibrium Reactants  Product Reactants  Products When substances react, they eventually form a mixture of reactants and products in dynamic equilibrium forward reverse For a general reversible reaction: c C + d Da A + b B Double arrows show reversible reaction

The Equilibrium State Many reactions do not go to completion instead of reaching Chemical Equilibrium: -The state reached when the concentrations of reactants and products remain constant over time. -The rate forward and reverse have become equal 2NO 2 (g)N2O4(g)N2O4(g) Brown Colorless

The Equilibrium State 2NO 2 (g)N2O4(g)N2O4(g)

13.2 The Equilibrium Constant K c cC + dDaA + bB Consider the reaction K c = [A] a [B] b [C] c [D] d Equilibrium constant expression when concentrations are used Equilibrium constant Reactants Products Equilibrium equation: Coefficient = K c is temperature dependent

The Equilibrium Constant K c

2NO 2 (g)N2O4(g)N2O4(g) [N 2 O 4 ] [NO 2 ] 2 K c = = 4.63 x (0.0141) 2 [N 2 O 4 ] [NO 2 ] 2 K c == 4.64 x (0.0125) 2 Experiment 2 Experiment 5 =

The Equilibrium Constant K c K c = The equilibrium constant and the equilibrium constant expression are for the chemical equation as written. N 2 (g) + 3H 2 (g)2NH 3 (g) [NH 3 ] 2 [N 2 ][H 2 ] 3 = 1 KcKc 2NH 3 (g)N 2 (g) + 3H 2 (g) [N 2 ][H 2 ] 3 [NH 3 ] 2 K c = ´ 4NH 3 (g)2N 2 (g) + 6H 2 (g) [N 2 ] 2 [H 2 ] 6 [NH 3 ] 4 = K c ´´ K c = 2

13.3The Equilibrium Constant K p When writing an equilibrium expression for a gaseous reaction in terms of partially pressure, we call it equilibrium constant, Kp 2NO 2 (g)N2O4(g)N2O4(g) K p = N2O4N2O4 P NO 2 P 2 P is the partial pressure of that component

Examples Write the equilibrium constant, K c and K p for the following reactions: a.CH 4 (g) + H 2 O(g) CO(g) + 3 H 2 (g) b.CO(g) + 3 H 2 (g) CH 4 (g) + H 2 O(g) c. What is the K’c expression for question b

Relating the Equilibrium Constant K p and K c n K p = K c (RT)  n K mol L atm R is the gas constant, T is the absolute temperature (Kelvin). is the number of moles of gaseous products minus the number of moles of gaseous reactants.

Example Phosphorous pentachloride dissociate on heating PCl 5 (g) PCl 3 (g) + Cl 2 (g) If K c equals 3.26 x at 191 o C, what is K p at this temperature?

Heterogeneous Equilibria

13.4Heterogeneous Equilibria CaO(s) + CO 2 (g)CaCO 3 (s) LimeLimestone (1) (1)[CO 2 ] = [CO 2 ] [CaCO 3 ] [CaO][CO 2 ] = Pure solids and pure liquids are not included. K c = K c = [CO 2 ]K p = P CO 2

Example In the industrial synthesis of hydrogen, mixtures of CO and H 2 are enriched in H 2 by allowing the CO to react with steam. The chemical equation for this so-called water-gas shift reaction is CO(g) + H 2 O(g) CO 2 (g) + H 2 (g) What is the value of K p at 700K if the partial pressures in an equilibrium mixture at 700K are 1.31 atm of CO, 10.0 atm of H 2 O, 6.12 atm of CO 2, and 20.3 atm of H 2 ?

Examples Consider the following unbalanced reaction (NH 4 ) 2 S(s) 2NH 3 (g) + H 2 S(g) An equilibrium mixture of this mixture at a certain temperature was found to have [NH 3 ] = M and [H 2 S] = M. What is the value of the equilibrium constant (K c ) at this temperature?

13.5Using the Equilibrium Constant K c = 4.2 x H 2 (g) + O 2 (g)2H 2 O(g) (at 500 K) K c = 2.4 x H 2 O(g)2H 2 (g) + O 2 (g) (at 500 K) K c = H I (g)H 2 (g) + I 2 (g) (at 500 K)

Predicting the Direction of Reaction For a chemical system whether in equilibrium or not, we can calculate the value given by the law of mass action We called it reaction quotient, Qc cC + dDaA + bB Qc =Qc = [A] t a [B] t b [C] t c [D] t d Reaction quotient: The reaction quotient, Q c, is defined in the same way as the equilibrium constant, K c, except that the concentrations in Q c are not necessarily equilibrium values.

Using the Equilibrium Constant If Q c = K c no net reaction occurs. If Q c < K c net reaction goes from left to right (reactants to products). If Q c > K c net reaction goes from right to left (products to reactants). The equilibrium between reactant A and product B: A B

Finding Equilibrium concentrations from Initial Concentrations Steps to follow in calculating equilibirium concentrations from initial concentration Write a balance equation for the reaction Make an ICE (Initial, Change, Equilibrium) table, involves The initial concentrations The change in concentration on going to equilibrium, defined as x The equilibrium concentration Substitute the equilibrium concentrations into the equilibrium equation for the reaction and solve for x Calculate the equilibrium concentrations form the calculated value of x Check your answers

Calculating Equilibrium Concentrations Sometimes you must use quadratic equation to solve for x, choose the mathematical solution that makes chemical sense Quadratic equation ax 2 + bx + c = 0

Finding Equilibrium concentrations from Initial Concentrations For Homogeneous Mixture aA(g) bB(g) + cC(g) Initial concentration (M) [A] initial [B] initial [C] initial Change (M) - ax + bx + cx Equilibrium (M) [A] initial – ax [B] initial + bx [C] initial + cx K c = [products] [reactants]

Finding Equilibrium concentrations from Initial Concentrations For Heterogenous Mixture aA(g) bB(g) + cC(s) Initial concentration (M) [A] initial [B] initial …….. Change (M) - ax + bx …….. Equilibrium (M) [A] initial – ax [B] initial + bx ………. K c = [products] [reactants]

Examples The value of K c for the reaction is 3.0 x Determine the equilibrium concentration if the initial concentration of water is 8.75 M C(s) + H 2 O(g) CO(g) + H 2 (g)

Using the Equilibrium Constant At 700 K, mol of H I is added to a 2.00 L container and allowed to come to equilibrium. Calculate the equilibrium concentrations of H 2, I 2, and H I. K c is 57.0 at 700 K. 2H I (g)H 2 (g) + I 2 (g)

Examples Consider the following reaction I 2 (g) + Cl 2 (g) 2ICl(g) K p = 81.9 (at 25 o C) A reaction mixture at 25 o C intially contains P I2 = atm, P Cl2 = atm, and P ICl = atm. Find the equilibrium pressure of I 2, Cl 2 and ICl at this temperature. In which direction does the reaction favored?

13.6 Le Châtelier’s Principle Le Châtelier’s Principle: If a stress is applied to a reaction mixture at equilibrium, net reaction occurs in the direction that relieves the stress. The concentration of reactants or products can be changed. The pressure and volume can be changed. The temperature can be changed.

13.7Altering an Equilibrium Mixture: Concentration 2NH 3 (g)N 2 (g) + 3H 2 (g)

Altering an Equilibrium Mixture: Concentration

the concentration stress of an added reactant or product is relieved by net reaction in the direction that consumes the added substance. the concentration stress of a removed reactant or product is relieved by net reaction in the direction that replenishes the removed substance. In general, when an equilibrium is disturbed by the addition or removal of any reactant or product, Le Châtelier’s principle predicts that

Altering an Equilibrium Mixture: Concentration Add reactant – denominator in Qc expression becomes larger ◦ Q c < K c ◦ To return to equilibrium, Qc must be increases ◦ More product must be made => reaction shifts to the right Remove reactant – denominator in Qc expression becomes smaller ◦ Q c > K c ◦ To return to equilibrium, Qc must be decreases ◦ Less product must be made => reaction shifts to the left

Altering an Equilibrium Mixture: Concentration

An equilibrium mixture of 0.50 M N 2, 3.00 M H 2, and 1.98 M NH 3 is disturbed by increasing the N 2 concentration to 1.50 M. Which direction will the net reaction shift to re-establish the equilibrium? 2NH 3 (g)N 2 (g) + 3H 2 (g) at 700 K, K c = 0.291

Example The reaction of iron (III) oxide with carbon monoxide occurs in a blast furnace when iron ore is reduced to iron metal: Fe 2 O 3 (s) + 3 CO(g) 2 Fe(l) + 3CO 2 (g) Use Le Chatellier’s principle to predict the direction of net reaction when an equilibrium mixture is disturbed by: a.adding Fe 2 O 3 b.Removing CO 2 c.Removing CO; also account for the change using the reaction quotient Q c

Example Consider the following reaction at equilibrium CO(g) + Cl 2 (g) COCl 2 (g) Predict whether the reaction will shift left, shift right, or remain unchanged upon each of the following reaction mixture a.COCl 2 is added to the reaction mixture b.Cl 2 is added to the reaction mixture c.COCl 2 is removed from the reaction mixture: also account for the change using the reaction quotient Q c

Altering an Equilibrium Mixture: Pressure and Volume 2NH 3 (g)N 2 (g) + 3H 2 (g)

13.8 Altering an Equilibrium Mixture: Changes in Pressure and Volume 2NH 3 (g)N 2 (g) + 3H 2 (g) at 700 K, K c = An equilibrium mixture of 0.50 M N 2, 3.00 M H 2, and 1.98 M NH 3 is disturbed by reducing the volume by a factor of 2. Which direction will the net reaction shift?

Altering an Equilibrium Mixture: Pressure and Volume an increase in pressure by reducing the volume will bring about net reaction in the direction that decreases the number of moles of gas. a decrease in pressure by enlarging the volume will bring about net reaction in the direction that increases the number of moles of gas. In general, when an equilibrium is disturbed by a change in volume which results in a corresponding change in pressure, Le Châtelier’s principle predicts that

Altering an Equilibrium Mixture: Pressure and Volume If reactant side has more moles of gas ◦ Denominator will be larger  Q c < K c  To return to equilibrium, Qc must be increased  Reaction shifts toward fewer moles of gas (to the product) If product side has more moles of gas ◦ Numerator will be larger  Q c > K c  To return to equilibrium, Q c must be decreases  Reaction shifts toward fewer moles of gas (to the reactant)

Altering an Equilibrium Mixture: Pressure and Volume Reaction involves no change in the number moles of gas ◦ No effect on composition of equilibrium mixture For heterogenous equilibrium mixture ◦ Effect of pressure changes on solids and liquids can be ignored  Volume is nearly independent of pressure Change in pressure due to addition of inert gas ◦ No change in the molar concentration of reactants or products ◦ No effect on composition

Example Consider the following reaction at chemical equilibrium 2 KClO 3 (s) 2 KCl(s) + 3O 2 (g) a.What is the effect of decreasing the volume of the reaction mixture? b.Increasing the volume of the reaction mixture? c.Adding inert gas at constant volume?

Examples Does the number moles of products increases, decreases or remain the same when each of the following equilibria is subjected to a increase in pressure by decreasing the volume? ◦ PCl 5 (g) PCl 3 (g) + Cl 2 (g) ◦ CaO(s) + CO 2 (g) CaCO 3 (s) ◦ 3 Fe(s) + 4H 2 O(g) Fe 3 O 4 (s) + 4 H 2 (g)

13.9 Altering an Equilibrium Mixture: Temperature 2NH 3 (g)N 2 (g) + 3H 2 (g)  H° = kJ (exothermic ) As the temperature increases, the equilibrium shifts from products to reactants.

Altering an Equilibrium Mixture: Temperature

the equilibrium constant for an exothermic reaction (negative  H°) decreases as the temperature increases. Contains more reactant than product Kc decreases with increasing temperature the equilibrium constant for an endothermic reaction (positive  H°) increases as the temperature increases. Contains more product than reactant Kc increases with increasing temperature In general, when an equilibrium is disturbed by a change in temperature, Le Châtelier’s principle predicts that

Example The following reaction is endothermic CaCO 3 (s) CaO(s) + CO 2 (g) a.What is the effect of increasing the temperature of the reaction mixture? b.Decreasing the temperature?

Examples In the first step of Ostwald process for the synthesis of nitric acid, ammonia is oxidized to nitric oxide by the reaction: 2 NH 3 (g) + 5 O 2 (g) 4 NO(g) + 6 H 2 O(l) ΔH o = -905 kJ How does the temperature amount of NO vary with an increases in temperature?

The Effect of a Catalyst on Equilibrium

Catalyst increases the rate of a chemical reaction ◦ Provide a new, lower energy pathway ◦ Forward and reverse reactions pass through the same transition state ◦ Rate for forward and reverse reactions increase by the same factor ◦ Does not affect the composition of the equilibrium mixture ◦ Does not appear in the balance chemical equation ◦ Can influence choice of optimum condition for a reaction