1. 17
Chemical Equilibrium

2. Chapter Goals Basic Concepts The Equilibrium Constant
Variation of Kc with the Form of the Balanced Equation
The Reaction Quotient
Uses of the Equilibrium Constant, Kc
Disturbing a System at Equilibrium: Predictions

3. Chapter Goals
The Haber Process: A Commercial Application of Equilibrium
Disturbing a System at Equilibrium: Calculations
Partial Pressures and the Equilibrium Constant
Relationship between Kp and Kc
Heterogeneous Equilibria

4. Chapter Goals Relationship between Gorxn and the Equilibrium Constant
Evaluation of Equilibrium Constants at Different Temperatures

5. Basic Concepts Reversible reactions do not go to completion.
They can occur in either direction
Symbolically, this is represented as:

6. Basic Concepts
Chemical equilibrium exists when two opposing reactions occur simultaneously at the same rate.
A chemical equilibrium is a reversible reaction that the forward reaction rate is equal to the reverse reaction rate.
Chemical equilibria are dynamic equilibria.
Molecules are continually reacting, even though the overall composition of the reaction mixture does not change.

7. Basic Concepts
One example of a dynamic equilibrium can be shown using radioactive 131I as a tracer in a saturated PbI2 solution.

8. Basic Concepts
This movie depicts a dynamic equilibrium.

9. Basic Concepts
Graphically, this is a representation of the rates for the forward and reverse reactions for this general reaction.

10. Basic Concepts
One of the fundamental ideas of chemical equilibrium is that equilibrium can be established from either the forward or reverse direction.

11. Basic Concepts

12. Basic Concepts

13. The Equilibrium Constant
For a simple one-step mechanism reversible reaction such as:
The rates of the forward and reverse reactions can be represented as:

14. The Equilibrium Constant
When system is at equilibrium:
Ratef = Rater

15. The Equilibrium Constant
Because the ratio of two constants is a constant we can define a new constant as follows :

16. The Equilibrium Constant
Similarly, for the general reaction:
we can define a constant

17. The Equilibrium Constant
Kc is the equilibrium constant .
Kc is defined for a reversible reaction at a given temperature as the product of the equilibrium concentrations (in M) of the products, each raised to a power equal to its stoichiometric coefficient in the balanced equation, divided by the product of the equilibrium concentrations (in M) of the reactants, each raised to a power equal to its stoichiometric coefficient in the balanced equation.

18. The Equilibrium Constant
Example 17-1: Write equilibrium constant expressions for the following reactions at 500oC. All reactants and products are gases at 500oC.

19. The Equilibrium Constant

20. The Equilibrium Constant

21. The Equilibrium Constant

22. The Equilibrium Constant

23. The Equilibrium Constant
Equilibrium constants are dimensionless because they actually involve a thermodynamic quantity called activity.
Activities are directly related to molarity

24. The Equilibrium Constant
Example 17-2: One liter of equilibrium mixture from the following system at a high temperature was found to contain mole of phosphorus trichloride, mole of chlorine, and mole of phosphorus pentachloride. Calculate Kc for the reaction.
Equil []’s M M M
You do it!

25. The Equilibrium Constant

26. The Equilibrium Constant
Example 17-3: The decomposition of PCl5 was studied at another temperature. One mole of PCl5 was introduced into an evacuated 1.00 liter container. The system was allowed to reach equilibrium at the new temperature. At equilibrium 0.60 mole of PCl3 was present in the container. Calculate the equilibrium constant at this temperature.

27. The Equilibrium Constant

28. The Equilibrium Constant

29. The Equilibrium Constant

30. The Equilibrium Constant

31. The Equilibrium Constant
Example 17-4: At a given temperature 0.80 mole of N2 and 0.90 mole of H2 were placed in an evacuated 1.00-liter container. At equilibrium 0.20 mole of NH3 was present. Calculate Kc for the reaction.
You do it!

32. The Equilibrium Constant

33. Variation of Kc with the Form of the Balanced Equation
The value of Kc depends upon how the balanced equation is written.
From example 17-2 we have this reaction:
This reaction has a Kc=[PCl3][Cl2]/[PCl5]=0.53

34. Variation of Kc with the Form of the Balanced Equation
Example 17-5: Calculate the equilibrium constant for the reverse reaction by two methods, i.e, the equilibrium constant for this reaction.
Equil. []’s M M M
The concentrations are from Example 17-2.

35. Variation of Kc with the Form of the Balanced Equation

36. Variation of Kc with the Form of the Balanced Equation

37. Variation of Kc with the Form of the Balanced Equation
Large equilibrium constants indicate that most of the reactants are converted to products.
Small equilibrium constants indicate that only small amounts of products are formed.

38. The Reaction Quotient

39. The Reaction Quotient

40. The Reaction Quotient
The mass action expression or reaction quotient has the symbol Q.
Q has the same form as Kc
The major difference between Q and Kc is that the concentrations used in Q are not necessarily equilibrium values.

41. The Reaction Quotient
Why do we need another “equilibrium constant” that does not use equilibrium concentrations?
Q will help us predict how the equilibrium will respond to an applied stress.
To make this prediction we compare Q with Kc.

42. The Reaction Quotient

43. The Reaction Quotient
Example 17-6: The equilibrium constant for the following reaction is 49 at 450oC. If 0.22 mole of I2, 0.22 mole of H2, and 0.66 mole of HI were put into an evacuated 1.00-liter container, would the system be at equilibrium? If not, what must occur to establish equilibrium?

44. Uses of the Equilibrium Constant, Kc
Example 17-7: The equilibrium constant, Kc, is 3.00 for the following reaction at a given temperature. If 1.00 mole of SO2 and 1.00 mole of NO2 are put into an evacuated 2.00 L container and allowed to reach equilibrium, what will be the concentration of each compound at equilibrium?

45. Uses of the Equilibrium Constant, Kc

46. Uses of the Equilibrium Constant, Kc

47. Uses of the Equilibrium Constant, Kc

48. Uses of the Equilibrium Constant, Kc

49. Uses of the Equilibrium Constant, Kc

50. Uses of the Equilibrium Constant, Kc
Example 17-8: The equilibrium constant is 49 for the following reaction at 450oC. If 1.00 mole of HI is put into an evacuated 1.00-liter container and allowed to reach equilibrium, what will be the equilibrium concentration of each substance?

51. Uses of the Equilibrium Constant, Kc

52. Disturbing a System at Equlibrium: Predictions
LeChatelier’s Principle - If a change of conditions (stress) is applied to a system in equilibrium, the system responds in the way that best tends to reduce the stress in reaching a new state of equilibrium.
We first encountered LeChatelier’s Principle in Chapter 14.
Some possible stresses to a system at equilibrium are:
Changes in concentration of reactants or products.
Changes in pressure or volume (for gaseous reactions)
Changes in temperature.

53. Disturbing a System at Equlibrium: Predictions
For convenience we may express the amount of a gas in terms of its partial pressure rather than its concentration.
To derive this relationship, we must solve the ideal gas equation.

54. Disturbing a System at Equlibrium: Predictions
Changes in Concentration of Reactants and/or Products
Also true for changes in pressure for reactions involving gases.
Look at the following system at equilibrium at 450oC.

55. Disturbing a System at Equlibrium: Predictions
Changes in Concentration of Reactants and/or Products
Also true for changes in pressure for reactions involving gases.
Look at the following system at equilibrium at 450oC.

56. Disturbing a System at Equlibrium: Predictions
Changes in Concentration of Reactants and/or Products
Also true for changes in pressure for reactions involving gases.
Look at the following system at equilibrium at 450oC.

57. Disturbing a System at Equlibrium: Predictions
Changes in Volume
(and pressure for reactions involving gases)
Predict what will happen if the volume of this system at equilibrium is changed by changing the pressure at constant temperature:

58. Disturbing a System at Equlibrium: Predictions

59. Disturbing a System at Equlibrium: Predictions

60. Disturbing a System at Equlibrium: Predictions

61. Disturbing a System at Equlibrium: Predictions
Changing the Temperature

62. Disturbing a System at Equlibrium: Predictions
Changing the Reaction Temperature
Consider the following reaction at equilibrium:

63. Disturbing a System at Equlibrium: Predictions
Introduction of a Catalyst
Catalysts decrease the activation energy of both the forward and reverse reaction equally.
Catalysts do not affect the position of equilibrium.
The concentrations of the products and reactants will be the same whether a catalyst is introduced or not.
Equilibrium will be established faster with a catalyst.

64. Disturbing a System at Equlibrium: Predictions

65. Disturbing a System at Equlibrium: Predictions
Example 17-9: Given the reaction below at equilibrium in a closed container at 500oC. How would the equilibrium be influenced by the following?

66. Disturbing a System at Equlibrium: Predictions
Example 17-10: How will an increase in pressure (caused by decreasing the volume) affect the equilibrium in each of the following reactions?

67. Disturbing a System at Equlibrium: Predictions
Example 17-11: How will an increase in temperature affect each of the following reactions?

68. The Haber Process: A Practical Application of Equilibrium
The Haber process is used for the commercial production of ammonia.
This is an enormous industrial process in the US and many other countries.
Ammonia is the starting material for fertilizer production.
Look at Example What conditions did we predict would be most favorable for the production of ammonia?

69. The Haber Process: A Practical Application of Equilibrium

70. The Haber Process: A Practical Application of Equilibrium

71. The Haber Process: A Practical Application of Equilibrium
This diagram illustrates the commercial system devised for the Haber process.

72. Disturbing a System at Equilibrium: Calculations
To help with the calculations, we must determine the direction that the equilibrium will shift by comparing Q with Kc.
Example 17-12: An equilibrium mixture from the following reaction was found to contain 0.20 mol/L of A, 0.30 mol/L of B, and 0.30 mol/L of C. What is the value of Kc for this reaction?

73. Disturbing a System at Equilibrium: Calculations

74. Disturbing a System at Equilibrium: Calculations
If the volume of the reaction vessel were suddenly doubled while the temperature remained constant, what would be the new equilibrium concentrations?
Calculate Q, after the volume has been doubled

75. Disturbing a System at Equilibrium: Calculations
Since Q<Kc the reaction will shift to the right to re-establish the equilibrium.
Use algebra to represent the new concentrations.

76. Disturbing a System at Equilibrium: Calculations
Since Q<Kc the reaction will shift to the right to re-establish the equilibrium.
Use algebra to represent the new concentrations.

77. Disturbing a System at Equilibrium: Calculations
Since Q<Kc the reaction will shift to the right to re-establish the equilibrium.
Use algebra to represent the new concentrations.

78. Disturbing a System at Equilibrium: Calculations
Since Q<Kc the reaction will shift to the right to re-establish the equilibrium.
Use algebra to represent the new concentrations.

79. Disturbing a System at Equilibrium: Calculations

80. Disturbing a System at Equilibrium: Calculations

81. Disturbing a System at Equilibrium: Calculations

82. Disturbing a System at Equilibrium: Calculations
Example 17-13: Refer to example If the initial volume of the reaction vessel were halved, while the temperature remains constant, what will the new equilibrium concentrations be? Recall that the original concentrations were: [A]=0.20 M, [B]=0.30 M, and [C]=0.30 M.
You do it!

83. Disturbing a System at Equilibrium: Calculations

84. Disturbing a System at Equilibrium: Calculations

85. Disturbing a System at Equilibrium: Calculations

86. Disturbing a System at Equilibrium: Calculations
Example 17-14: A 2.00 liter vessel in which the following system is in equilibrium contains 1.20 moles of COCl2, 0.60 moles of CO and 0.20 mole of Cl2. Calculate the equilibrium constant.
You do it!

87. Disturbing a System at Equilibrium: Calculations

88. Disturbing a System at Equilibrium: Calculations
An additional 0.80 mole of Cl2 is added to the vessel at the same temperature. Calculate the molar concentrations of CO, Cl2, and COCl2 when the new equilibrium is established.
You do it!

89. Disturbing a System at Equilibrium: Calculations

90. Disturbing a System at Equilibrium: Calculations

91. Partial Pressures and the Equilibrium Constant
For gas phase reactions the equilibrium constants can be expressed in partial pressures rather than concentrations.
For gases, the pressure is proportional to the concentration.
We can see this by looking at the ideal gas law.
PV = nRT
P = nRT/V
n/V = M
P= MRT and M = P/RT

92. Partial Pressures and the Equilibrium Constant
Consider this system at equilibrium at 5000C.

93. Partial Pressures and the Equilibrium Constant

94. Relationship Between Kp and Kc
From the previous slide we can see that the relationship between Kp and Kc is:

95. Relationship Between Kp and Kc
Example 17-15: Nitrosyl bromide, NOBr, is 34% dissociated by the following reaction at 25oC, in a vessel in which the total pressure is 0.25 atmosphere. What is the value of Kp?

96. Relationship Between Kp and Kc

97. Relationship Between Kp and Kc

98. Relationship Between Kp and Kc

99. Relationship Between Kp and Kc
The numerical value of Kc for this reaction can be determined from the relationship of Kp and Kc.

100. Relationship Between Kp and Kc
Example 17-16: Kc is 49 for the following reaction at 450oC. If 1.0 mole of H2 and 1.0 mole of I2 are allowed to reach equilibrium in a 3.0-liter vessel,
(a) How many moles of I2 remain unreacted at equilibrium?
You do it!

101. Relationship Between Kp and Kc

102. Relationship Between Kp and Kc
(b) What are the equilibrium partial pressures of H2, I2 and HI?
You do it!

103. Relationship Between Kp and Kc

104. Relationship Between Kp and Kc
(c) What is the total pressure in the reaction vessel?
You do it!

105. Relationship Between Kp and Kc

106. Heterogeneous Equlibria
Heterogeneous equilibria have more than one phase present.
For example, a gas and a solid or a liquid and a gas.
How does the equilibrium constant differ for heterogeneous equilibria?
Pure solids and liquids have activities of unity.
Solvents in very dilute solutions have activities that are essentially unity.
The Kc and Kp for the reaction shown above are:

107. Heterogeneous Equlibria

108. Heterogeneous Equlibria
What are Kc and Kp for this reaction?
You do it!

109. Heterogeneous Equlibria
What are Kc and Kp for this reaction?

110. Relationship Between DGorxn and the Equilibrium Constant
DGorxn is the standard free energy change.
DGorxn is defined for the complete conversion of all reactants to all products.
DG is the free energy change at nonstandard conditions
For example, concentrations other than 1 M or pressures other than 1 atm.
DG is related to DGo by the following relationship.

111. Relationship Between DGorxn and the Equilibrium Constant
At equilibrium, DG=0 and Q=Kc.
Then we can derive this relationship:

112. Relationship Between DGorxn and the Equilibrium Constant
For the following generalized reaction, the thermodynamic equilibrium constant is defined as follows:

113. Relationship Between DGorxn and the Equilibrium Constant
The relationships among DGorxn, K, and the spontaneity of a reaction are:
Gorxn K
Spontaneity at unit concentration
< 0
> 1
Forward reaction spontaneous
= 0
= 1
System at equilibrium
> 0
< 1
Reverse reaction spontaneous

114. Relationship Between DGorxn and the Equilibrium Constant

115. Relationship Between DGorxn and the Equilibrium Constant
Example 17-17: Calculate the equilibrium constant, Kp, for the following reaction at 25oC from thermodynamic data in Appendix K.
Note: this is a gas phase reaction.

116. Relationship Between DGorxn and the Equilibrium Constant

117. Relationship Between DGorxn and the Equilibrium Constant

118. Relationship Between DGorxn and the Equilibrium Constant
Kp for the reverse reaction at 25oC can be calculated easily, it is the reciprocal of the above reaction.

119. Relationship Between Gorxn and the Equilibrium Constant
Example 17-18: At 25oC and 1.00 atmosphere, Kp = 4.3 x for the decomposition of NO2. Calculate Gorxn at 25oC.
You do it.

120. Relationship Between Gorxn and the Equilibrium Constant

121. Relationship Between Gorxn and the Equilibrium Constant
The relationship for K at conditions other than thermodynamic standard state conditions is derived from this equation.

122. Evaluation of Equilibrium Constants at Different Temperatures
From the value of Ho and K at one temperature, T1, we can use the van’t Hoff equation to estimate the value of K at another temperature, T2.

123. Evaluation of Equilibrium Constants at Different Temperatures
Example 17-19: For the reaction in example 17-18, DHo = 114 kJ/mol and Kp = 4.3 x at 25oC. Estimate Kp at 250oC.

124. Evaluation of Equilibrium Constants at Different Temperatures

125. Evaluation of Equilibrium Constants at Different Temperatures

126. 17
Chemical Equilibrium