1. Equilibrium, Acids, and Bases
Equilibrium Constant Expressions
Homogeneous equilibria
Heterogeneous equilibria
Applications of Equilibrium Constants
LeChatelier’s Principle

2. Chemical Equilibrium
One of the challenges that industrial chemists face is to maximize the yield of product obtained in a reaction.
Many reactions do not go to completion.
The reaction stops short of the theoretical yield.
Unreacted starting materials are still present.

3. Chemical Equilibrium Consider the reaction to produce ammonia:
N2 (g) + 3 H2 (g) NH3 (g)

4. Chemical Equilibrium
After a period of time, the composition of the reaction mixture stays the same even though most of the reactants are still present.
Although it is not apparent, chemical reactions are still occurring within the reaction mixture.
N2 (g) + 3 H2 (g) NH3 (g)
2 NH3 (g) N2 (g) + 3 H2 (g)

5. Chemical Equilibrium
The reaction has reached chemical equilibrium and is best represented by the equation:
N2 (g) + 3 H2 (g) NH3 (g)
The double arrow is used to indicate that the reaction is an equilibrium reaction.
It indicates that the reaction occurs in both directions simultaneously.

6. Chemical Equilibrium Chemical equilibrium:
A state of dynamic balance in which the opposing reactions are occurring at equal rates
Rate of forward reaction (reactants to products) = rate of reverse reaction (products decomposing to reactants)

7. Chemical Equilibrium Consider a simple system at equilibrium:
Forward: A B Rate = kf[A]
Reverse: B A Rate = kr[B]
At equilibrium, the rate for the forward reaction equals the rate of the reverse reaction.
kf[A] = kr[B]
Rearranging: [B] = kf = a constant
[A] kr

8. Chemical Equilibrium
At chemical equilibrium, the concentrations of the reactants and products do not change.
ratio of products over reactants is constant
Note: This does not mean that the concentrations of the reactants and products are identical to each other.

9. Equilibrium-constant expression
Chemical Equilibrium
For a balanced, general equilibrium reaction:
a A + b B p P + q Q
the equilibrium condition is expressed by the equation:
Kc = [P]p [Q]q
[A]a [B]b
where Kc = equilibrium constant obtained
when concentrations are
expressed in molarity
Equilibrium-constant expression

10. Chemical Equilibrium
The equilibrium constant, Kc, is the numerical value obtained when the actual equilibrium concentrations (in M) of reactants and products are substituted into the equilibrium constant expression.
Kc is unitless.
The subscript c indicates that all concentrations used to calculate the value of Kc were expressed in M .

11. Chemical Equilibrium
The equilibrium constant expression for the following reaction is:
Kc = [Ag(NH3)2+ ]
[Ag+] [NH3]2
Ag+ (aq) + 2 NH3 (aq) Ag(NH3)2+ (aq)

12. Chemical Equilibrium
Some equilibrium reactions involve reactants and products that are all in the same phase.
Homogeneous equilibrium
Example: N2 (g) + 3 H2 (g)  2 NH3 (g)
Some equilibrium reactions involve reactants and/or products that are in different phases
heterogeneous equilibrium
Example: Ag+ (aq) + Cl- (aq)  AgCl (s)

13. CO2 (g) + H2 (g) CO (g) + H2O (l)
Chemical Equilibrium
An example of a heterogeneous equilibrium:
CO2 (g) + H2 (g) CO (g) + H2O (l)
If a solid or liquid is involved in a heterogeneous equilibrium, its concentration is constant and is not included in the equilibrium constant expression.
For this example:
Kc = [CO]
[CO2][H2]

14. Chemical Equilibrium
Example: Write the equilibrium constant expression, Kc, for the following reactions:
Cd2+ (aq) + 4 Br- (aq) CdBr42- (aq)
CH4 (g) + 2 H2S (g) CS2 (g) + 4 H2 (g)

15. Ca3(PO4)2 (s) 3 Ca2+ (aq) + 2 PO43- (aq)
Chemical Equilibrium
Example: Write the equilibrium constant expression, Kc, for the following reactions:
Ca3(PO4)2 (s) Ca2+ (aq) PO43- (aq)
Ti (s) + 2 Cl2 (g) TiCl4 (l)

16. Chemical Equilibrium
When all reactants and products in a chemical equilibrium are gases, the equilibrium constant expression can also be written in terms of the partial pressure of gases.
Kp = the equilibrium constant in terms of partial pressures
Partial pressure:
the pressure exerted by a particular gas in a mixture of gases

17. a A (g) + b B (g) d D (g) + e E (g)
Chemical Equilibrium
For the general chemical equation:
a A (g) + b B (g) d D (g) + e E (g)
the equilibrium constant expression is:
Kp = Pd Pe
D E
Pa Pb
A B
where Kp = equilibrium constant in terms of
pressure
PD = partial pressure of D in atm.

18. Chemical Equilibrium
The numerical values of Kc and Kp are different for most reactions.
Kp = Kc (RT)Dn
where R = atm.L
mol.K
T = temperature in K
Dn = change in # of moles
= # mol products - # mol reactants

19. Chemical Equilibrium
Example: Write the equilibrium constant expression, Kp, for the following reaction:
CH4 (g) + 2 H2S (g) CS2 (g) + 4 H2 (g)

20. CO2 (g) + H2 (g) CO (g) + H2O (l)
Chemical Equilibrium
Example: Write the equilibrium constant expression, Kp, for the following equilibrium:
CO2 (g) + H2 (g) CO (g) + H2O (l)

21. Chemical Equilibrium
Example: Write the equilibrium constant expression, Kp, for the following reaction:
Ti (s) + 2 Cl2 (g) TiCl4 (l)

22. CaF2 (s) Ca2+ (aq) + 2 F- (aq)
Chemical Equilibrium
The solubility-product constant (Ksp) describes the equilibrium that is established between an undissolved solid and its hydrated ions in aqueous solution.
For the dissolution of CaF2:
CaF2 (s) Ca2+ (aq) + 2 F- (aq)
Ksp = [Ca2+] [F-]2

23. Chemical Equilibrium Dissolution:
The process of dissolving a substance in a solvent
Notes:
The expression for Ksp excludes solids (just like other heterogeneous equilibria)
The value for Ksp is calculated using the concentrations (in M) of the ions.

24. Chemical Equilibrium
Example: Write the solubility product constant expression for the dissolution of silver chromate.

25. Magnitude of Equilibrium Constants
Kc, Kp, and Ksp can have a wide range of values.
N2 (g) + O2 (g) NO (g)
Kc = [NO]2 = 1 x 10-30
[N2] [O2]
CO (g) + Cl2 (g) COCl2 (g)
Kc = [COCl2] = 4.57 x 109
[CO] [Cl2]

26. Magnitude of Equilibrium Constants
When Kc (or Kp or Ksp) < 1, more reactants than products are present at equilibrium.
N2 (g) + O2 (g) NO (g)
Kc = [NO]2 = 1 x 10-30
[N2] [O2]
Equilibrium lies to the left.
Reactants are favored.

27. Magnitude of Equilibrium Constants
When Kc (or Kp or Ksp) is > 1, more products than reactants are present at equilibrium.
CO (g) + Cl2 (g) COCl2 (g)
Kc = [COCl2] = 4.57 x 109
[CO] [Cl2]
Equilibrium lies to the right.
Products are favored.

28. Magnitude of Equilibrium Constants
Example: Are reactants or products favored in the following reaction?
H2 (g) + I2 (g) HI (g) Kc = 50.5

29. Magnitude of Equilibrium Constants
Equilibrium can be approached from either direction.
N2O4 (g) NO2 (g)
If N2O4 (g) is placed in a reactor at 100oC, N2O4 will decompose to form NO2 (g).
If NO2(g) is placed in a reactor at 100oC, NO2 will react to form N2O4.

30. Magnitude of Equilibrium Constants
For an equilibrium reaction, the direction that we write the chemical equation is arbitrary.
Influences the way we write the equilibrium constant expression and the value of the equilibrium constant.

31. Magnitude of Equilibrium Constants
For the reaction,
N2O4 (g) NO2 (g)
the equilibrium constant expression is:
Kc = [NO2]2 = at 100oC
[N2O4]
2 NO2 (g) N2O4 (g)
Kc = [N2O4] = 4.72 at 100oC
[NO2]2

32. Magnitude of Equilibrium Constants
The equilibrium constant expression and the value of the equilibrium constant for a reaction written in one direction is the reciprocal of the one written in the opposite direction.
A B Kc = [B]
[A]
B A Kc = [A]
[B]
Kc (forward) = 1
Kc (reverse)

33. Magnitude of Equilibrium Constants
Example: Given the information below, what is the value of Kc for the reaction:
COCl2 (g) CO (g) + Cl2 (g) Kc = ?
CO (g) + Cl2 (g) COCl2 (g) Kc = 4.57 x 109

34. Calculating Equilibrium Constants
In order to calculate the value of an equilibrium constant, you must know either
concentrations of reactants and products at equilibrium (for Kc or Ksp)
partial pressures of reactants and products at equilibrium (for Kp)

35. Calculating Equilibrium Constants
On the exam, you must be able to calculate the value of equilibrium constant
given equilibrium concentrations or partial pressures of reactants and products
given equilibrium # moles (or grams) of reactants and products and the volume of the reactor
given initial quantity of reactant(s) present and the quantity of one reactant (or product) at equilibrium.

36. Calculating Equilibrium Constants
Example: PCl5 is prepared at 450 K according to the following reaction. What is the value of Kp if the partial pressure of the three gases at equilibrium are: PPCl3 = atm, PCl2 = atm, and PPCl5 = 1.30 atm?
PCl3 (g) + Cl2 (g) PCl5 (g)

37. Calculating Equilibrium Constants
Write the expression for Kp
Substitute the pressure of each reactant or product:

38. Calculating Equilibrium Constants
Example: Calculate the Kc for the following reaction. At equilibrium, the reaction mixture contained mol H2, mol N2, mol H2O, and mol NO in a 3.00 liter reactor.
2 NO (g) + 2 H2 (g) N2 (g) + 2 H2O (g)
First, write the expression for Kc

39. Calculating Equilibrium Constants
Next, calculate all concentrations:
[H2] =
[N2] =
[H2O] =
[NO] =
Finally, plug concentrations into expression for Kc
Kc = 654

40. Calculating Equilibrium Constants
Example: A mixture of mol of H2 and mole of Br2 is heated in a 2.00-L reactor at 700 K. At equilibrium, mol of H2 are present in the reactor. What are the equilibrium concentrations of H2, Br2, and HBr? Calculate Kc for the reaction.
H2 (g) + Br2 (g) HBr (g)
Write the expression for Kc:

41. Calculating Equilibrium Constants
Determine the initial concentrations of the reactants and products as well as the equilibrium concentration of the reactant (H2) given in the problem.
[H2]initial =
[Br2]initial =
[HBr]initial =
[H2]equil =

42. Calculating Equilibrium Constants
Set up a table showing initial conc., change in concentration, equilibrium conc. of all reactants and products.
H2 (g) Br2 (g) HBr

43. Calculating Equilibrium Constants

44. Calculating Equilibrium Constants

45. Calculating Equilibrium Constants

46. Calculating Equilibrium Constants
Use the equilibrium concentrations of the reactants and products to determine the value of Kc.

47. Applications of Equilibrium Constants
The magnitude of Kc, Kp, or Ksp indicates the extent to which a reaction will proceed.
Products favored (Kc >> 1)
Reactants favored (Kc << 1)
Kc can also be used to predict
the direction a reaction mixture must go to reach equilibrium
equilibrium concentrations of reactants and products

48. Applications of Equilibrium Constants
In order to use Kc to predict the direction in which a reaction mixture must go in order to reach equilibrium, we must calculate the reaction quotient (Q).
The value obtained when the concentrations of reactants and products are substituted into the equilibrium constant expression.

49. Applications of Equilibrium Constants
The value of the reaction quotient can be compared to the value of Kc or Kp in order to determine the direction the reaction must proceed to reach equilibrium.
If Q = K
reaction mixture is at equilibrium
If Q < K
reaction must proceed toward products (toward the right)
If Q > K
reaction must proceed toward reactants (toward the left)

50. Applications of Equilibrium Constants
Example: At 1000 K, the value of Kc for the reaction 2 SO3 (g) SO2 (g) + O2 (g) is 4.08 x Calculate the reaction quotient and predict the direction in which the reaction will proceed to reach equilibrium if the initial concentrations of reactants are [SO3] = 2 x 10-3 M,
[SO2] = 5 x 10-3 M, and [O2] = 3 x 10-2 M.

51. Applications of Equilibrium Constants
Kc =
Q =