AP Chemistry
Chapter 15 Equilibrium
Chapter 15. Chemical Equilibrium
15.1 The Concept of Equilibrium
•
Chemical equilibrium is the point at which the concentrations of all species are constant.
•
A dynamic equilibrium exists when the rates of the forward and reverse reactions are equal.
•
The double arrow  implies that the process is dynamic.
15.2 The Equilibrium Constant
Equilibrium-Constant Expression
•
law of mass action.
aA + bB  dD + eE
•
For a general reaction
•
The equilibrium-constant expression is given by:
[ D d ][ E ] e
Kc 
[ A] a [ B]b
•
•
•
Where Kc is the equilibrium constant.
The subscript “c” indicates that molar concentrations were used to evaluate the constant.
Note that the equilibrium constant expression has products in the numerator and reactants in the
denominator.
Equilibrium Constants in Terms of Pressure, Kp
•
When the reactants and products are gases the equilibrium constant is Kp where “p” stands for
pressure.
•
For the reaction:
aA + bB  dD + eE
Kp 
( PD ) d ( PE ) e
•
( PA ) a ( PB ) b
They can be interconverted using the ideal gas equation and our definition of molarity:
PV = nRT thus P = (n/V)RT
•
If we express volume in liters the quantity (n/V) is equivalent to molarity.
•
Thus the partial pressure of a substance, A, is given as:
PA =(nA/V)RT = [A]RT
•
We can use this to obtain a general expression relating Kc and Kp:
Kp = Kc(RT)∆n
• Where ∆n = (moles of gaseous products) – (moles of gaseous reactants).
• The numerical values of Kc and Kp will not differ if ∆n = 0.
(Note: See p. 635 in textbook for info about why we do not use units for K)
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AP Chemistry
Chapter 15 Equilibrium
Sample Exercise 15.1 (p. 634)
Write the equilibrium expression for Keq for these three reactions:
a) 2 O3(g)  3 O2(g)
b) 2 NO(g) + Cl2(g)  2 NOCl(g)
c) Ag+(aq) + 2 NH3(g)  Ag(NH3)2+(aq)
Practice Exercise 1 (15.1)
For the reaction 2 SO2(g) + O2(g)  2 SO3(g) which of the following is the correct equilibrium-constant
expression:
a)
Kp = PSO22 PO2
PSO32
b) Kp = 2 PSO2 PO2
2 PSO3
c) Kp = PSO32
PSO22 PO2
d) Kc = 2 PSO3
2 PSO2 PO2
Practice Exercise 2 (15.1)
Write the equilibrium expression for Keq for these two reactions:
a) H2(g) + I2(g)  2 HI(g)
b) Cd2+(aq) + 4 Br-(aq)  CdBr42-(aq
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AP Chemistry
Chapter 15 Equilibrium
Evaluating Kc
•
The value of Keq does not depend on initial concentrations of products or reactants.
•
The equilibrium expression depends on stoichiometry.
• It does not depend on the reaction mechanism.
• The value of Keq varies with temperature.
•
We generally omit the units of the equilibrium constant.
15.3 Interpreting and Working with Equilibrium Constants
The Magnitude of Equilibrium Constants
• The larger Keq the more products are present at equilibrium.
• The smaller Keq the more reactants are present at equilibrium.
• If Keq >> 1, then products dominate at equilibrium and equilibrium lies to the right.
• If Keq << 1, then reactants dominate at equilibrium and the equilibrium lies to the left.
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AP Chemistry
Chapter 15 Equilibrium
Sample Exercise 15.3 (p. 638)
The following diagrams represent three different systems at equilibrium, all in the same size containers.
a) Without doing any calculations, rank the three systems in order of increasing equilibrium
constant, Kc.
b) If the volume of the containers is 1.0 L and each sphere represents 0.10 mol, calculate Kc for each
system.
Practice Exercise 2 (15.3)
The equilibrium constant for the reaction H2(g) + I2(g)  2 HI(g) varies with temperature as follows:
Kp = 792 at 298 K; Kp = 54 at 700 K.
Is the formation of HI favored more at the higher or lower temperature?
Relating Chemical Equations and Equilibrium Constants
•
The equilibrium constant of a reaction in the reverse direction is the inverse of the equilibrium
constant of the reaction in the forward direction.
•
The equilibrium constant of a reaction that has been multiplied by a number is the equilibrium
constant raised to a power equal to that number.
•
The equilibrium constant for a net reaction made up of two or more steps is the product of the
equilibrium constants for the individual steps.
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AP Chemistry
Chapter 15 Equilibrium
Sample Exercise 15.4 (p. 640)
Given the following information,
HF(aq)  H+(aq) + F-(aq)
H2C2O4(aq)  2 H+(aq) + C2O42-(aq)
Kc = 6.8 x 10-4
Kc = 3.8 x 10-6
determine the value of Kc for the following reaction:
2 HF(aq) + C2O42-(aq)  2 F-(aq) + H2C2O4(aq)
(0.12)
Practice Exercise 1 (15.4)
Given the equilibrium constants for the following two reactions in aqueous solution at 25oC,
HNO2(aq)  H+(aq) + NO2-(aq)
Kc = 4.5 x 10-4
H2SO3(aq)  2 H+(aq) + SO32-(aq)
Kc = 1.1 x 10-9
What is the value of Kc for the following reaction?
2 HNO2(aq) + SO32-(aq) H2SO3(aq) + 2 NO2-(aq)
a)
b)
c)
d)
e)
4.9 x 10-13
4.1 x 105
8.2 x 105
1.8 x 102
5.4 x 10-3
Practice Exercise 2 (15.4)
Given the following information at 700 K,
H2(g) + I2(g)  2HI(g)
N2(g) + 3 H2(g)  2 NH3(g)
Kp = 54.0
Kp = 1.04 x 10-4
determine the value of Kp (at 700 K)
2 NH3(g) + 3 I2(g)  6 HI(g) + N2(g)
(1.51 x 109)
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AP Chemistry
Chapter 15 Equilibrium
15.4 Heterogeneous Equilibria
•
Equilibria in which one or more reactants or products are present in a different phase are called
heterogeneous equilibria.
•
If a pure solid or pure liquid is involved in a heterogeneous equilibrium, its concentration is not
included in the equilibrium constant expression.
•
Note: Although the concentrations of these species are not included in the equilibrium expression,
they do participate in the reaction and must be present for an equilibrium to be established!
•
systems where the solvent is involved as a reactant or product and the solutes are present at low
concentrations.
• Example: H2O(l) + CO32–(aq)  OH–(aq) + HCO3–(aq)
Kc = [OH–][HCO3–] / [CO32–]
• Here the concentration of water is essentially constant and we can think of it as a pure
liquid.
Sample Exercise 15.5 (p. 643)
Write the equilibrium-constant Keq for each of the following reactions:
a) CO2(g) + H2(g)  CO(g) + H2O(l)
Keq =
b) SnO2(s) + 2 CO(g)  Sn(s) + 2 CO2(g)
Keq =
Practice Exercise 1 (15.5)
Consider the equilibrium that is established in a saturated solution of silver chloride,
Ag+(aq) + Cl-(aq) AgCl(s).
If more solid AgCl is added to this solution, what will happen to the concentration of Ag+ and Cl- ions in
solution?
a) [Ag+] and [Cl-] will both increase.
b) [Ag+] and [Cl-] will both decrease.
c) [Ag+] will increase and [Cl-] will decrease.
d) [Ag+] will decrease and [Cl-] will increase.
e) Neither [Ag+] nor [Cl-] will change.
Practice Exercise 2 (15.5)
Write the equilibrium-constant expressions for each of the following reactions:
a) Cr(s) + 3 Ag+(aq)  Cr3+(aq) + 3 Ag(s)
Kc =
b) 3 Fe(s) + 4 H2O(g)  Fe3O4(s) + 4 H2(g)
Kp =
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AP Chemistry
Chapter 15 Equilibrium
Sample Exercise 15.6 (p. 643)
Each of the following mixtures was placed in a closed container and allowed to stand. Which of these
mixtures is capable of attaining the equilibrium
CaCO3(s)  CaO(s) + CO2(g)
a) pure CaCO3
b) CaO and a pressure of CO2 greater than the value of Kp
c) Some CaCO3 and a pressure of CO2 greater than the value of Kp
d) CaCO3 and CaO
Practice Exercise 1 (15.6)
If 8.0 g of NH4HS(s) is placed in a sealed vessel with a volume of 1.0 L and heated to 200oC the reaction
NH4HS(s) NH3(g) + H2S(g) will occur. When the system comes to equilibrium, some NH4HS(s) is
still present. Which of the following changes will lead to a reduction in the amount of NH4HS(s) that is
present, assuming in all cases that equilibrium is re-established following the change?
a) Adding more NH3(g) to the vessel
b) Adding more H2S(g) to the vessel
c) Adding more NH4HS(s) to the vessel
d) Increasing the volume of the vessel
e) Decreasing the volume of the vessel
Practice Exercise 2 (15.6)
When added to Fe3O4(s) in a closed container, which one of the following substances – H2(g), H2O(g), O2(g) will allow equilibrium to be established in the reaction
3 Fe(s) + 4 H2O(g)  Fe3O4(s) + 4 H2(g)
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AP Chemistry
Chapter 15 Equilibrium
15.5 Calculating Equilibrium Constants
Sample Exercise 15.7 (p. 644)
A mixture of hydrogen and nitrogen in a reaction vessel is allowed to attain equilibrium at 472oC. The
equilibrium mixture of gases was analyzed and found to contain 7.38 atm H2, 2.46 atm N2, and 0.166 atm
NH3. From these data calculate the equilibrium constant, Kp, for
N2(g) + 3 H2(g)  2 NH3(g)
(2.79 x 10-5)
Practice Exercise 1 (15.7)
A mixture of gaseous sulfur dioxide and oxygen are added to a reaction vessel and heated to 1000 K
where they react to form SO3(g). If the vessel contains 0.669 atm SO2(g), 0.395 atm O2(g), and 0.0851 atm
SO3(g) after the system has reached equilibrium, what is the equilibrium constant Kp for the reaction
2 SO2(g) + O2(g)  2 SO3(g)?
a)
b)
c)
d)
e)
0.0410
0.322
24.4
3.36
3.11
Practice Exercise 2 (15.7)
An aqueous solution of acetic acid is found to have the following equilibrium concentrations at 25oC:
[CH3COOH] = 1.65 x 10-2 M; [H+] = 5.44 x 10-4 M; and [CH3COO-] = 5.44 x 10-4 M. Calculate the
equilibrium constant, Kc, for the ionization of acetic acid at 25oC. The reaction is
CH3COOH (aq)  H+(aq) + CH3COO-(aq)
(1.79 x 10-5)
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AP Chemistry
Chapter 15 Equilibrium
If we do not know the equilibrium concentrations of all species involved in the reaction,
proceed as follows:
1. Tabulate all the known initial and equilibrium concentrations of the species that appear in the
equilibrium-constant expression.
2. For those species for which both the initial and equilibrium concentrations are known, calculate
the change in concentration that occurs as the system reaches equilibrium.
3. Use the stoichiometry of the reaction (that is, use the coefficients in the balanced chemical
equation) to calculate the changes in concentration of all the other species in the equilibrium.
4. From the initial concentrations and the changes in concentration, calculate the equilibrium
concentrations. These are then used to evaluate the equilibrium constant.
Sample Exercise 15.8 (p. 645)
A closed system initially containing 1.000 x 10-3 M H2 and 2.000 x 10-3 M I2 at 448oC is allowed to reach
equilibrium, and at equilibrium the concentration of HI is 1.87 x 10-3 M. Calculate Kc at 448oC for the
reaction taking place, which is
(1.81 x 10-5)
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AP Chemistry
Chapter 15 Equilibrium
Practice Exercise 1 (15.8)
In Section 15.1, we discussed the equilibrium between N2O4(g) and NO2(g). Let’s return to that equation in
a quantitative example. When 9.2 g of frozen N2O4(g) is added to a 0.50 L reaction vessel and the vessel is
heated to 400 K and allowed to come to equilibrium, the concentration of N2O4 is determined to be 0.057
M. Given this information, what is the value of Kc for the reaction N2O4(g)  2 NO2(g) at 400 K?
a) 0.23
b) 0.36
c) 0.13
d) 1.4
e) 2.5
Practice Exercise 2 (15.8)
Sulfur trioxide decomposes at high temperature in a sealed container:
2 SO3(g)  2 SO2(g) + O2(g)
Initially the vessel is charged at 1000 K with SO3(g) at a partial pressure of 0.500 atm. At equilibrium the
SO3 partial pressure is 0.200 atm. Calculate the value of Kp at 1000 K.
(0.338)
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AP Chemistry
Chapter 15 Equilibrium
15.6 Applications of Equilibrium Constants
Predicting the Direction of Reaction
aA + bB  cC + dD
•
For a general reaction:
•
We define Q, the reaction quotient, as:
c
d

C D
Q
Aa Bb
•
Where [A], [B], [C], and [D] are molarities (for substances in solution) or partial pressures (for
gases) at any given time.
Note: Q = Keq only at equilibrium.
• If Q < Keq then the forward reaction must occur to reach equilibrium.
• If Q > Keq then the reverse reaction must occur to reach equilibrium.
• Products are consumed, reactants are formed.
• Q decreases until it equals Keq.
•
Calculating Equilibrium Concentrations
•
The same steps used to calculate equilibrium constants are used to calculate equilibrium
concentrations.
•
Generally, we do not have a number for the change in concentration.
• Therefore, we need to assume that x mol/L of a species is produced (or used).
•
The equilibrium concentrations are given as algebraic expressions.
Sample Exercise 15.9 (p. 647)
At 448 C the equilibrium constant, Kc, for the reaction
H2(g) + I2(g)  2 HI(g) is 51.
o
Predict how the reaction will proceed to reach equilibrium at 448oC if we start with 2.0 x 10-2 mol of HI,
1.0 x 10-2 mole of H2, and 3.0 x 10-2 mol of I2 in a 2.00-L container.
(Q = 1.3, so reaction must proceed from left to right)
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AP Chemistry
Chapter 15 Equilibrium
Practice Exercise 1 (15.9)
Which of the following statements accurately describes what would happen to the direction of the
reaction described in the sample exercise above, if the size of the container were different from 2.00 L?
a)
The reaction would proceed in the opposite direction (from right to left) if the container volume
were reduced sufficiently.
b) The reaction would proceed in the opposite direction if the container volume were expanded
sufficiently.
c) The direction of this reaction does not depend on the volume of the container.
Practice Exercise 2 (15.9)
At 1000 K the value of Kp for the reaction 2 SO3(g)  2 SO2(g) + O2(g) is 0.338. Calculate the value for
Qp, and predict the direction in which the reaction proceeds toward equilibrium if the initial partial
pressures are PSO3 = 0.16 atm; PSO2 = 0.41 atm; PO2 = 2.5 atm.
(Qp = 16; Qp > Kp, so reaction will proceed from right to left)
Sample Exercise 15.10 (p. 648)
For the Haber process, N2(g) + 3 H2(g)  2 NH3(g), Kp = 1.45 x 10-5 at 500oC. In an equilibrium mixture of
the three gases at 500oC, the partial pressure of H2 is 0.928 atm and that of N2 is 0.432 atm. What is the
partial pressure of NH3 in this equilibrium mixture?
(2.24 x 10-3 atm)
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AP Chemistry
Chapter 15 Equilibrium
Practice Exercise 1 (15.10)
At 500 K, the reaction 2 NO(g) + Cl2(g)  2 NOCl(g) has Kp = 51. In an equilibrium mixture at 500 K, the
partial pressure of NO is 0.125 atm and that of PCl3 is 0.165 atm. What is the partial pressure of NOCl in
the equilibrium mixture?
a) 0.13 atm
b) 0.36 atm
c) 1.0 atm
d) 5.1 x 10-5 atm
e) 0.125 atm
Practice Exercise 2 (15.10)
At 500 K the reaction PCl5(g)  PCl3(g) + Cl2(g) has Kp = 0.497. In an equilibrium mixture at 500 K, the
partial pressure of PCl5 is 0.860 atm and that of PCl3 is 0.350 atm. What is the partial pressure of Cl2 in
the equilibrium mixture?
(1.22 atm)
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AP Chemistry
Chapter 15 Equilibrium
15.7 Le Châtelier’s Principle
•
If a system at equilibrium is disturbed by a change in temperature, a change in pressure, or a change
in the concentration of one or more components, the system will shift its equilibrium position in such
a way as to counteract the effects of the disturbance.
Change in Reactant or Product Concentration
•
If a chemical system is at equilibrium and we add or remove a product or reactant, the reaction will
shift so as to reestablish equilibrium.
Effects of Volume and Pressure Changes
•
•
•
An increase in pressure favors the direction that has fewer moles of gas.
In a reaction with the same number of moles of gas in the products and reactants, changing the
pressure has no effect on the equilibrium.
In addition, no change will occur if we increase the total gas pressure by the addition of a gas that is
not involved in the reaction.
Effect of Temperature Changes
•
The equilibrium constant is temperature dependent, and dependent on the particular reaction.
Sample Exercise 15.13 (p. 656)
Consider the following equilibrium:
N2O4(g)  2 NO2(g)
Ho = 58.0 kJ
In what direction will the equilibrium shift when
a) N2O4 is added,
b) NO2 is removed,
c) the pressure is increased by adding N2(g),
d) the volume is increased,
e) the temperature is decreased?
Practice Exercise 1 (15.12)
For the reaction 4 NH3(g) + 5 O2(g)  4 NO(g) + 6 H2O(g)
Ho = -904 kJ
which of the following changes will shift the equilibrium to the right, toward the formation of more
products?
a) adding more water vapor,
b) increasing the temperature,
c) increasing the volume of the reaction vessel,
d) removing O2(g),
e) adding 1 atm Ne(g) to the reaction vessel.
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AP Chemistry
Chapter 15 Equilibrium
Practice Exercise 2 (15.12)
For the reaction
PCl5(g)  PCl3(g) + Cl2(g)
Ho = 87.9 kJ
in which direction will the equilibrium shift when
a) Cl2(g) is removed,
b) the temperature is decreased,
c) the volume of the reaction system is increased,
d) PCl3(g) is added?
The Effect of Catalysts
•
A catalyst lowers the activation energy barrier for the reaction.
• Therefore, a catalyst will decrease the time taken to reach equilibrium.
• A catalyst does not affect the composition of the equilibrium mixture.
Sample Integrative Exercise 15 (p. 658)
At temperatures near 800oC, steam passed over hot coke (a form of carbon obtained from coal) reacts to
form CO and H2:
C(s) + H2O(g)  CO(g) + H2(g)
The mixture of gases that results is an important industrial fuel called water gas.
a) At 800oC the equilibrium constant for this reaction is Kp = 14.1. What are the equilibrium partial
pressures of H2O, CO, and H2 in the equilibrium mixture at this temperature if we start with solid
carbon and 0.100 mol of H2O in a 1.00-L vessel?
b) What is the minimum amount of carbon required to achieve equilibrium under these conditions?
c) What is the total pressure in the vessel at equilibrium?
d) At 25oC the value of Keq for this reaction is 1.7 x 10-21. Is the reaction exothermic or
endothermic?
e) To produce the maximum amount of CO and H2 at equilibrium, should the pressure of the system
be increased or decreased?
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