Equilibrium, Acids, and Bases
Equilibrium
 Equilibrium Constant Expressions
Homogeneous equilibria
Heterogeneous equilibria
 Applications of Equilibrium Constants
 LeChatelier’s Principle
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.
Chemical Equilibrium
Molar Concentration
Consider the reaction to produce
ammonia:
N2 (g) + 3 H2 (g)
2 NH3 (g)
Hydrogen
Nitrogen
Ammonia
Time
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)
2 NH3 (g)
2 NH3 (g)
N2 (g) + 3 H2 (g)
Chemical Equilibrium
 The reaction has reached chemical equilibrium
and is best represented by the equation:
N2 (g) + 3 H2 (g)
2 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.
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)
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
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.
Chemical Equilibrium
 For a balanced, general equilibrium
reaction:
aA +bB
pP + qQ
the equilibrium condition is expressed by
the equation:
Kc = [P]p [Q]q
Equilibrium-constant
[A]a [B]b
expression
where Kc = equilibrium constant obtained
when concentrations are
expressed in molarity
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 .
Chemical Equilibrium
 The equilibrium constant expression for the
following reaction is:
Ag+ (aq) + 2 NH3 (aq)
Kc = [Ag(NH3)2+ ]
[Ag+] [NH3]2
Ag(NH3)2+ (aq)
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)
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]
Chemical Equilibrium
Example: Write the equilibrium constant
expression, Kc, for the following reactions:
Cd2+ (aq) + 4 Br- (aq)
CH4 (g) + 2 H2S (g)
CdBr42- (aq)
CS2 (g) + 4 H2 (g)
Chemical Equilibrium
Example: Write the equilibrium constant
expression, Kc, for the following reactions:
Ca3(PO4)2 (s)
3 Ca2+ (aq) + 2 PO43- (aq)
Ti (s) + 2 Cl2 (g)
TiCl4 (l)
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
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.
Chemical Equilibrium
 The numerical values of Kc and Kp are different
for most reactions.
Kp = Kc (RT)Dn
where R = 0.0821 atm.L
mol.K
T = temperature in K
Dn = change in # of moles
= # mol products - # mol reactants
Chemical Equilibrium
Example: Write the equilibrium constant
expression, Kp, for the following reaction:
CH4 (g) + 2 H2S (g)
CS2 (g) + 4 H2 (g)
Chemical Equilibrium
Example: Write the equilibrium constant
expression, Kp, for the following equilibrium:
CO2 (g) + H2 (g)
CO (g) + H2O (l)
Chemical Equilibrium
Example: Write the equilibrium constant
expression, Kp, for the following reaction:
Ti (s) + 2 Cl2 (g)
TiCl4 (l)
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)
Ksp = [Ca2+] [F-]2
Ca2+ (aq) + 2 F- (aq)
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.
Chemical Equilibrium
Example: Write the solubility product constant
expression for the dissolution of silver
chromate.
Magnitude of Equilibrium Constants
 Kc, Kp, and Ksp can have a wide range of
values.
N2 (g) + O2 (g)
2 NO (g)
Kc =
[NO]2 = 1 x 10-30
[N2] [O2]
CO (g) + Cl2 (g)
Kc =
COCl2 (g)
[COCl2] = 4.57 x 109
[CO] [Cl2]
Magnitude of Equilibrium Constants
 When Kc (or Kp or Ksp) < 1, more reactants than
products are present at equilibrium.
N2 (g) + O2 (g)
Kc =
2 NO (g)
[NO]2 = 1 x 10-30
[N2] [O2]
Equilibrium lies to the left.
Reactants are favored.
Magnitude of Equilibrium Constants
 When Kc (or Kp or Ksp) is > 1, more products
than reactants are present at equilibrium.
CO (g) + Cl2 (g)
Kc =
COCl2 (g)
[COCl2] = 4.57 x 109
[CO] [Cl2]
Equilibrium lies to the right.
Products are favored.
Magnitude of Equilibrium Constants
Example: Are reactants or products favored in
the following reaction?
H2 (g) + I2 (g)
2 HI (g) Kc = 50.5
Magnitude of Equilibrium Constants
 Equilibrium can be approached from either
direction.
N2O4 (g)
2 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.
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.
Magnitude of Equilibrium Constants
 For the reaction,
N2O4 (g)
2 NO2 (g)
the equilibrium constant expression is:
Kc = [NO2]2 = 0.212 at 100oC
[N2O4]
 For the reaction,
2 NO2 (g)
N2O4 (g)
the equilibrium constant expression is:
Kc = [N2O4] = 4.72 at 100oC
[NO2]2
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
B
A
Kc = [B]
[A]
Kc = [A]
[B]
Kc (forward) =
1
Kc (reverse)
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
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)
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.
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 = 0.124 atm, PCl2 = 0.157
atm, and PPCl5 = 1.30 atm?
PCl3 (g) + Cl2 (g)
PCl5 (g)
Calculating Equilibrium Constants
 Write the expression for Kp
 Substitute the pressure of each reactant or
product:
Calculating Equilibrium Constants
Example: Calculate the Kc for the following
reaction. At equilibrium, the reaction mixture
contained 0.0360 mol H2, 0.0570 mol N2, 0.414
mol H2O, and 0.186 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
Calculating Equilibrium Constants
Next, calculate all concentrations:
[H2] =
[N2] =
[H2O] =
[NO] =
Finally, plug concentrations into expression for
Kc
Kc = 654
Calculating Equilibrium Constants
Example: A mixture of 0.678 mol of H2 and 0.440
mole of Br2 is heated in a 2.00-L reactor at 700 K.
At equilibrium, 0.283 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)
2 HBr (g)
Write the expression for Kc:
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 =
Calculating Equilibrium Constants
Set up a table showing initial conc., change
in concentration, equilibrium conc. of all
reactants and products.
H2 (g)
Initial
0.339 M
Change
Equil.
0.1415 M
+
Br2 (g)
0.220 M
2 HBr
0.000 M
Calculating Equilibrium Constants
Calculating Equilibrium Constants
Calculating Equilibrium Constants
Calculating Equilibrium Constants
 Use the equilibrium concentrations of the
reactants and products to determine the value
of Kc.
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
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.
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)
Applications of Equilibrium Constants
Example: At 1000 K, the value of Kc for the
reaction 2 SO3 (g)
2 SO2 (g) + O2 (g) is 4.08 x
10-3. 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.
Applications of Equilibrium Constants
 Kc =
Q=