Lecture 16.1

• Chapter 16: Chemical Equilibria

All chemical reactions are reversible, at least in principle.

Equilibrium is a dynamic situation. It appears that no change is occurring. However, reactants are combining together to from products and the products are combining to reform the reactions. The two reactions, the forward one and the reverse one, occur at the same rate so there is no NET change in the concentrations.

H2O(g) + CO(g) CO2(g) + H 2(g)

Dynamite exploding-- equilibrium?

The equilibrium position of a reaction– left right, or somewhere in between is determined by many factors: the initial concentrations, the relative energies of the products and reactants, and the relative degree of “organization” of the reactants and products. Energy and organization come into play because nature tries to achieve minimum energy and maximum disorder. (Chapter 20)

The Equilibrium Constant

The Law of Mass ActionTwo Norwegian chemist, Cato Maximilian Guildberg (1836-1902)

and Peter Waage (1833-1900) proposed in 1864 a general description of the equilibrium condition (called the Law of Mass Action). They proposed for the rxn of the type

a A + b B c C + d DThe equilibrium concentrations of rxn and products can

be represented by the equilibrium constant expressionEquilibrium Constant = K = [C]c[D]d PRODUCTS

[A]a[B]b REACTANTS[ ] represent concentration at equilibriumA, B, C, and D represent chemical species and a,b, c, and

d are their coefficients in the balanced equation.

Write the equilibrium expression for the rxn:2NH3(g) N2(g) + 3H2(g)

Keq at a given T can be calculated if equilibrium concentrations of reaction components are known.

NOTE: Keq constants are without units. The reason is beyond this course, but involves corrections for nonideal behavior of substances taking part in the reaction. When corrections are made, the units cancel out and the corrected K has no units. So, we will NOT use units for K.

Keq = [N2][H2]3 PRODUCTS

[NH3]2 REACTANTS

Writing Equilibrium Constant ExpressionsRule for Rxn Involving Solids R.O.T. Keq is in same phase

In a heterogeneous rxn., equilibrium does NOT depend on amounts of pure solids or liquids present. The concentration of pure liquids and solids does NOT change. (C = constant)

Keq =CCaO[CO2(g)] /CCaCO3 = [CO2(g)]

Rules for Rxns Involving WaterR.O.T. Keq is in same phase

However, if the rxn were carried out under conditions where the water is a gas rather than a liquid, that is then it is included in Keq b/c the concentration OR pressure of water vapor can change.

If pure solids or pure liquids are involved in a chem. rxn, their concentrations are not included in the equilibrium expression. This simplification occurs ONLY with pure solids or liquids, not with solutions or gases, since the last two cases the concentrations vary.

2H2O(l) 2 H2(g) + O2(g) Keq = [H2(g)]2[O2(g)]

2H2O(g) 2 H2(g)+ O2(g) Keq =[H2(g)]2[O2(g)]/[H2O(g)]

Equilibrium Expressions Involving Pressures

The relationship b/t P and concentration

PV= nRT or P = (n/V)RT or P = CRT

Write the equilibrium expression in terms of partial pressures and the equilibrium expression

in terms of concentration for the rxn:2NH3(g) N2(g) + 3H2(g)

Kp = PN2PH23

PNH32

Keq = [N2][H2]3

[NH3]2

Write the expressions for K and Kp for the following processes:

PCl5(s) PCl3(l) + Cl2(g)

CuSO4 5H2O(s) CuSO4(s) + 5 H2O(g)

Keq = [Cl2] Kp = PCl2

Keq = [H2O]5 Kp = PH2O5

Calculating Kp values

The reaction for the formation of nitrosyl chloride

2NO(g) + Cl2(g) 2 NOCl(g)

was studied at 25oC. The pressures at equilibrium were found to be

PNOCl = 1.2 atm PNO= 0.050 PCl2 = 0.30 atm. Calculate the value of Kp for the reaction.

Kp = PNOCl2 /(PNO)2(PCl2) = (1.2)2/(0.05)2(0.3)

= 1.9 x 10 3

The relationship between K and Kp

Kp = K(RT)n

For the derivation read A Closer Look p. 753 in text. Remember P = CRT or C = P/RT and must be substituted in equilibrium expression.

The relationship is Kp = K(RT)n where n is the difference in the sums of the coefficients for the gaseous products and reactants.

NOTE: Kp = Kc when n = 0

Example: The value of Kp was 1.9 x 103 in the previous example. Calculate the value of K at 25oC for the reaction

2NO (g) + Cl2(g) 2NOCl(g)

1.9 x 103 = K((0.0821 Latm/mol K)(273 + 25))(2-3)

1.9 x 103 = K (24 –1)

K = 45600 = 4.6 x 10 4

NOTE: If n = 0, then Kp = Kc

Kp = K(RT)n

Manipulating Equilibrium Expressions

2NO (g+ Cl2(g) 2NOCl(g) K = 4.6 x 10 4

Kforward = [NOCl]2/[NO]2[Cl2] = 4.6 x 10 4

Kreverse = [NO]2[Cl2]/[NOCl]2= 1/4.6 x 10 4

If stoichiometric coefficients of balanced equations are multiplied by some factor, n, the equilibrium constant for new equation is raised to the power of the new factor K new = (Kold)n

Kforward = [NOCl]6/[NO]6[Cl2]3 = (4.6 x 10 4) 3

Forward and reverse equilibrium expressions

3 (2 NO (g) + Cl2(g) 2 NOCl(g) )

Write the equilibrium expression for the reverse direction for the following reactionBr2(g) 2 Br(g) K = 2.2 x 10 –15

Keq = [Br2]/[Br]2 = 1/ 2.2 x 10 –15

Write the equilibrium expression for the reverse direction for the following reaction½ (Br2(g) 2 Br(g)) K = 2.2 x 10 –15

K new = (Kold)n note: n is multiplication factor

Keq = [Br2] 1/2/[Br] = 1/(2.2 x 10 –15)1/2

In general, when two or more equations are added to produce a net equation, K for the net equation is the product of the K for added equations.

AgCl(s) is dissolved in water (to a small extent). Ammonia is then added to form the complex Ag(NH3)2

+

AgCl(s) Ag+ (aq) + Cl- (aq) K1 = [Ag+][Cl-] = 1.8 x 10 –10

Ag+(aq)+ 2 NH3(aq)Ag(NH3)2

+ (aq) K2 =[Ag(NH3)2

+(aq)] = 1.6 x 107

[Ag+][NH3]2

AgCl (s) + 2 NH3(aq) Ag(NH3)2+

(aq) + Cl -(aq)

Knet=[Ag(NH3)2+][Cl-] =K1K2=(1.6 x 107)(1.8 x 10 –10 )=2.9x 10 -3

[NH3 ]2

NET

Exercise 16.3 p. 756 Manipulating Equilibrium Constant Expressions

The following equilibrium constants are given at 500 K. H2(g) + Br2(g) 2 HBr(g) K = 7.9 x 10 11

H2(g) 2 H(g) K = 4.8 x 10 –41

Br2(g) 2 Br(g) K = 2.2 x 10 –15

Calculate K for the reaction of H and Br atoms to give HBrH(g) + Br(g) HBr (g) K = ?

H2(g) + Br2(g) 2 HBr(g) K1 = 7.9 x 10 11

2 H(g) H2(g) K2 = 1/4.8 x 10 –41

2 Br(g) Br2(g) K3 = 1/2.2 x 10 –15

2 H(g) + 2 Br(g) 2 HBr Knet = [HBr]2/[H]2[Br]2

Want Knet = [HBr]/[H][Br] so…Knet=(K1K2K3 )½=((7.9 x10 11)(1/4.8 x10 –41)(1/2.2 x10 –15)) ½

= (7.5 x 10 66 )½ = 2.7 x 1033

Work on HW

• ↔

H2O + CO CO2 + H2

(a) H2O and CO are mixed in equal numbers and begin to react (b) to from CO2 and H2. After time has passed, equilibrium is reached (c) and the number of reactant and product molecules then remain constant over time (d)

a. b. c. d.

Demonstration: Limewater and CO2

Saturated solution of limewater

Ca(OH)2(s) Ca(OH)2(aq)

CO2 + Ca(OH)2(aq)

Add MORE CO2(g) to the CaCO3 (s)

CO2 + H2O + CaCO3(s)

Add CO2(g)

CaCO3(s) + H2O

Ca(HCO3)2(aq)

Equilibria in CO2/Ca2+/H2O System

CaCl2+ 2NaHCO3

Add CO2(s)

Ca2++ HCO3 – CaCO3(s) + H2O + CO2

2NaCl + Ca(HCO3)2 CaCO3(s) + 2 H2O + 2 CO2

Net:Ca2++ HCO3

- CaCO3(s) + H2O +CO2