Suppose human’s memory decays exponentially as a first order reaction and the half life is one day. Three days have passed since you came to class last Friday. If you have not reviewed what you learned, what is the percentage of chemistry you remember from last Friday? IF you need the equations for first order reaction, here they are r = k [A]

Chapter 14 Chemical Equilibrium

Liquid Gas phase equilibrium

Two opposite processes have reached the same rate. Equilibrium Note: equilibrium is dynamic!

Reactants  Products Reactants  Products Reactants ⇌ Products Reversible Reaction

N 2 O 4 (g) ⇌ 2NO 2 (g) kfkf krkr Both directions are elementary reactions r r = k r [NO 2 ] 2 r f = k f [N 2 O 4 ] What are the differential rate laws?

At equilibrium, the forward and reverse reactions are proceeding at the same rate. r f = r r Suppose we start with a flask of pure N 2 O 4 gas N 2 O 4 (g) ⇌ 2NO 2 (g) kfkf krkr r r = k r [NO 2 ] 2 r f = k f [N 2 O 4 ]

Once equilibrium is achieved, the concentration of each reactant and product remains constant. N 2 O 4 (g) ⇌ 2NO 2 (g) kfkf krkr r f = k f [N 2 O 4 ] = r r = k r [NO 2 ] 2

N 2 O 4 (g) ⇌ 2NO 2 (g) kfkf krkr r r = k r [NO 2 ] 2 r f = k f [N 2 O 4 ] k f [N 2 O 4 ] = k r [NO 2 ] 2 K =

a A + b B ⇌ c C + d D K: equilibrium constant. [ ]: concentration at equilibrium! K: independent of concentration, dependent upon temperature. K: no unit. recall d=m/V

Write the equilibrium expression for K for the following reactions: (a) 2O 3 (g) ⇌ 3O 2 (g) (b) 2NO(g) + Cl 2 (g) ⇌ 2NOCl(g) (c) Ag + (aq) + 2NH 3 (aq) ⇌ Ag(NH 3 ) 2 + (aq) a A + b B ⇌ c C + d D

At one temperature: one K, infinite number of equilibrium concentrations. K is independent of concentrations. Recall d = m/V.

What Does the Value of K Mean?

If K>>1, the reaction is product-favored; product predominates at equilibrium. If K<<1, the reaction is reactant-favored; reactant predominates at equilibrium. a A + b B ⇌ c C + d D

N 2 (g) + 3H 2 (g) ⇌ 2NH 3 (g) Haber process

Anhydrous Ammonia is Injected into the Solid to Act as a Fertilizer

Haber process: N 2 (g) + 3H 2 (g) ⇌ 2NH 3 (g) The following equilibrium concentrations were observed for the Haber process at 127 °C: [NH 3 ] = 3.1 x 10 −2 mol/L, [N 2 ] = 8.5 x 10 −1 mol/L, [H 2 ] = 3.1 x 10 −3 mol/L. a)Calculate the value of K at 127 °C for this reaction. b)Calculate the value of the equilibrium constant at 127 °C for the reaction 2NH 3 (g) ⇌ N 2 (g) + 3H 2 (g) c) Calculate the value of the equilibrium constant at 127 °C for the reaction given by the equation ⇌ NH 3 (g)

a A + b B ⇌ c C + d Dc C + d D ⇌ a A + b B na A + nb B ⇌ nc C + nd D reverse x n

Consider the following chemical equation and equilibrium constant at 25 °C: 2COF 2 (g) ⇌ CO 2 (g) + CF 4 (g)K = 2.2 x 10 6 Compute the equilibrium constant for the following reaction At 25 °C: 2CO 2 (g) + 2CF 4 (g) ⇌ 4COF 2 (g)K’ = ? For practice 14.2, page 622

2 NOBr (g) ⇌ 2 NO (g) + Br 2 (g) Br 2 (g) + Cl 2 (g) ⇌ 2 BrCl (g) + 2NOBr (g) + Cl 2 (g) ⇌ 2NO (g) + 2BrCl (g) Sum of reactions  Product of equilibrium constants Equilibrium constant of a composite reaction

HF (aq) ⇌ H + (aq) + F − (aq) K 1 = 6.8 x 10 −4 H 2 C 2 O 4 (aq) ⇌ 2H + (aq) + C 2 O 4 2− (aq) K 2 = 3.8 x 10 −6 2HF (aq) + C 2 O 4 2− (aq) ⇌ 2F − (aq) + H 2 C 2 O 4 (aq) Determine the equilibrium constant for Method: take linear combination of known reactions to construct target reaction. K 3 = 0.12

2NO(g) + O 2 (g) ⇌ 2NO 2 (g)K = 5.0 x NO 2 (g) ⇌ NO(g) + ½ O 2 (g) What is the equilibrium constant for

N 2 (g) + 3H 2 (g) ⇌ 2NH 3 (g) = K c a A (g) + b B (g) ⇌ c C (g) + d D (g) ∆n = Sum of the coefficients of gaseous products − Sum of the coefficients of gaseous reactants

K p for the following reaction is 2.2 x at 25 °C, calculate the value of K c. 2NO(g) + O 2 (g) ⇌ 2NO 2 (g) Example 14.3, page 624 Try For Practice 14.3 on the same page

Consider the equilibrium Calculate the equilibrium constant K p for this reaction, given The following information (at 298 K): N 2 (g) + O 2 (g) + Br 2 (g) ⇌ 2NOBr(g) 2NO (g) + Br 2 (g) ⇌ 2NOBr(g)K c, 1 = 2.0 2NO(g) ⇌ N 2 (g) + O 2 (g)K c, 2 = 2.1 x Answer: K p = 4.3 x 10 28

Equilibrium Category based on Phase

Homogeneous Equilibrium Heterogeneous Equilibrium N 2 (g) + 3H 2 (g) ⇌ 2NH 3 (g) 2CO(g) ⇌ CO 2 (g) + C(s) K c, K p All species have the same phase Not all species have the same phase

The concentration of pure solid or liquid is not included in the equilibrium constant expression for heterogeneous equilibria.

2H 2 O(l) ⇌ 2H 2 (g) + O 2 (g) 2H 2 O(g) ⇌ 2H 2 (g) + O 2 (g)

Write the expression for K and K p for the following processes: a) PCl 5 (s) ⇌ PCl 3 (l) + Cl 2 (g) b) CuSO 4 5H 2 O (s) ⇌ CuSO 4 (s) + 5H 2 O(g) bluewhite

Hydrated Copper (II) Sulfate on the Left. Water Applied to Anhydrous Copper (II) Sulfate, on the Right, Forms the Hydrated Compound

a A + b B ⇌ c C + d D [ ]: concentration at equilibrium! reaction quotient [ ]: concentration at a particular moment.

Q = K, system (mixture) is at equilibrium, r r = r f Q > K → r r > r f → system will shift to left to reach equilibrium Q < K → r r < r f → system will shift to right to reach equilibrium a A + b B ⇌ c C + d D

Haber process: N 2 (g) + 3H 2 (g) ⇌ 2NH 3 (g) At 500 °C, K = 6.01 x 10 −2. Predict the direction in which the system will shift to reach equilibrium in each of the following cases: a)[NH 3 ] 0 =1.0 x 10 −3 M; [N 2 ] 0 = 1.0 x 10 −5 M; [H 2 ] 0 = 2.0 x10 −3 M b)[NH 3 ] 0 =2.00 x 10 −4 M; [N 2 ] 0 = 1.50 x 10 −5 M; [H 2 ] 0 =3.54 x10 −1 M c)[NH 3 ] 0 =1.0 x 10 −4 M; [N 2 ] 0 = 5.0 M; [H 2 ] 0 = 1.0 x10 −2 M a) Q = 1.3 x 10 7 b) Q = 6.01 x 10 −2 c) Q = 2.0 x 10 −3

value of K c or K p equilibrium concentrations or pressures

N 2 O 4 (g) ⇌ 2NO 2 (g) N 2 O 4 was placed in a flask and allowed to reach equilibrium at a temperature where K p = At equilibrium, the pressure of N 2 O 4 was found to be 2.71 atm. Calculate the equilibrium pressure of NO 2 (g) atm

Try Example 14.8 and For Practice 14.8 on page 632

CO(g) + H 2 O(g) ⇌ CO 2 (g) + H 2 (g) At 700 K the equilibrium constant is Calculate the equilibrium concentrations of all species if mol of each component is mixed in a L flask. x = (M)

Consider the following reaction: A reaction mixture at 25  C initially contains P I 2  atm, P C1 2  atm, and P ICl = atm. Find the equilibrium partial pressures of I 2, Cl 2, and ICl at this temperature. I 2 (g) + Cl 2 (g) ⇌ 2ICl(g)K p = 81.9 Example 14.11, page 636

Try Example 14.9 and For Practice 14.9 on page 634.

H 2 (g) + F 2 (g) ⇌ 2HF(g) mol H 2 and mol F 2 are mixed in a L flask. K at this temperature is 115. Calculate the equilibrium concentration of each component. x = 2.14 (M) or (M)

N 2 O 4 (g) ⇌ 2NO 2 (g) K c = 0.36 at 100 °C. A reaction mixture at 100 °C initially contains [NO 2 ] = M. Find the equilibrium concentration of NO 2 and N 2 O 4 at this temperature. Example 14.10, page 634

H 2 (g) + I 2 (g) ⇌ 2HI(g) K p = 1.00 x Suppose HI at x 10 −1 atm, H 2 at x 10 −2 atm, and I 2 at x 10 −3 atm are mixed in a L flask. Calculate the equilibrium pressure of each component. x = 3.55 x 10 −2 (atm) or −7.19 x 10 −2 (atm)

2H 2 S(g) ⇌ 2H 2 (g) + S 2 (g) A L reaction vessel initially contains mol of H 2 S at 800 °C. Find the equilibrium concentration of H 2 and S 2. K c = 1.67 x10 −7 at 800 °C Example 14.12, page 638

If K>>1, the reaction is product-favored; product predominates at equilibrium. If K<<1, the reaction is reactant-favored; reactant predominates at equilibrium. a A + b B ⇌ c C + d D

Try Example on page 638.

value of K c or K p equilibrium concentrations or pressures

Consider the following reaction: CO(g) + 2H 2 (g) ⇌ CH 3 OH(g) A reaction mixture at 780  C initially contains [CO] = M and [H 2 ] = 1.00 M. At equilibrium, the CO concentration is found to be 0.15 M. What is the value of the equilibrium constant? Example 14.5, page 628

Consider the following reaction: 2CH 4 (g) ⇌ C 2 H 2 (g) + 3H 2 (g) A reaction mixture at 1700  C initially contains [CH 4 ] = M. At equilibrium, the mixture contains [C 2 H 2 ] = M. What is the value of the equilibrium constant? Example 14.6, page 628

Try For Practice 14.5 and 14.6 on page 629.

Q = K, system (mixture) is at equilibrium. Q > K → r r > r f → system will shift to left to reach equilibrium Q < K → r r < r f → system will shift to right to reach equilibrium a A + b B ⇌ c C + d D

Effect of a change in concentration add reactants → reactant concentrations ↑ → Q < K → system shifts to right remove reactants → reactant concentrations ↓ → Q > K → system shifts to left a A + b B ⇌ c C + d D

add products → product concentrations ↑ → Q > K → system shifts to left remove products → product concentrations ↓ → Q < K → system shifts to right Effect of a change in concentration a A + b B ⇌ c C + d D

Haber process: N 2 (g) + 3H 2 (g) ⇌ 2NH 3 (g) concentration

As 4 O 6 (s) + 6C(s) ⇌ As 4 (g) + 6CO(g) Predict the direction of the shift of the equilibrium position in response to each of the following changes in conditions. a)Addition of CO b)Addition or removal of C or As 4 O 6 c)Removal of As 4

Try Example and For Practice on page 644.

Effect of a change in pressure 1) Add or remove a gaseous reactant or product.

Haber process: N 2 (g) + 3H 2 (g) ⇌ 2NH 3 (g)

Effect of a change in pressure 1) Add or remove a gaseous reactant or product. 2) Add an inert gas (one not involved in the reaction). Equilibrium does not shift 3) Change the volume of the container.

(a) A Mixture of NH 3 (g), N 2 (g), and H 2 (g) at Equilibrium (b) The Volume is Suddenly Decreased (c) The New Equilibrium Position for the System Containing More NH 3 and Less N 2 and H 2 compared to the old equilibrium (a) N 2 (g) + 3H 2 (g) ⇌ 2NH 3 (g)

Effect of a change in pressure 1) Add or remove a gaseous reactant or product. 2) Add an inert gas (one not involved in the reaction). Equilibrium does not shift 3) Change the volume of the container. decrease volume → equilibrium shifts to the direction with less moles of gases increase volume → equilibrium shifts to the direction with more moles of gases

Predict the shift of equilibrium position that will occur for each of the following processes when the volume is reduced. a) P 4 (s) + 6Cl 2 (g) ⇌ 4PCl 3 (l) b) PCl 3 (g) + Cl 2 (g) ⇌ PCl 5 (g) c) PCl 3 (g) + 3NH 3 (g) ⇌ P(NH 2 ) 3 (g) + 3HCl(g)

Try Example and For Practice on page 645.

a A + b B ⇌ c C + d D

Effect of a change in temperature K is a function of temperature Do experiments

(brown) 2NO 2 ⇌ N 2 O 4 (colorless) 100 °C 0 °C decrease T → shifts to right → K increases increase T → shifts to left → K decreases ∆H = − 58 kJ ∆H < 0, exothermic ∆H > 0, endothermic

decrease T → shifts to right → K increases increase T → shifts to left → K decreases Exothermic reactions Endothermic reactions decrease T → shifts to left → K decreases increase T → shifts to right → K increases

For each of the following reactions, predict how the value of K changes as the temperature is increased. a)N 2 (g) + O 2 (g) ⇌ 2NO(g) ∆H = 181 kJ b)2SO 2 (g) + O 2 (g) ⇌ 2SO 3 (g) ∆H = −198 kJ

Try Example and For Practice on page 648.

Le Châtelier's Principle If a change is imposed on a system at equilibrium, the position of the equilibrium will shift in a direction that tends to reduce that change.

Does catalyst shift an equilibrium?

A ⇌ B

∆Ea∆Ea Ef’Ef’ Er’Er’ Catalyst does not shift equilibrium

For the reaction PCl 5 (g) ⇌ PCl 3 (g) + Cl 2 (g)∆H = 87.9 kJ In which direction will the equilibrium shift when a) Cl 2 (g) is removed, b) The temperature is decreased, c) The volume of the system is increased, d) PCl 3 (g) is added? In b), will the equilibrium constant increase or decrease? In d), will the concentration of Cl 2 and PCl 5 increase or decrease?