Download Document

Chapter 13
Chemical Equilibrium
13.1 Describing Chemical Equilibrium
Reactants

Product
forward
Reactants

Products
reverse
When substances react, they eventually form a mixture of
reactants and products in dynamic equilibrium
For a general reversible reaction:
aA+bB
cC+dD
Double arrows show reversible reaction
The Equilibrium State
Many reactions do not go to completion instead of reaching
Chemical Equilibrium:
- The state reached when the concentrations of reactants and
products remain constant over time.
- The rate forward and reverse have become equal
N2O4(g)
Colorless
2NO2(g)
Brown
The Equilibrium State
N2O4(g)
2NO2(g)
13.2 The Equilibrium Constant Kc
For a homogeneous reaction
aA + bB
cC + dD
Coefficient
[C]c[D]d
Equilibrium equation:
Equilibrium constant
Kc is temperature dependent
Kc =
=
[A]a[B]b
Products
Reactants
Equilibrium constant expression
when concentrations are used
13.3The Equilibrium Constant Kp

When writing an equilibrium expression for a gaseous reaction in
terms of partially pressure, we call it equilibrium constant, Kp
N2O4(g)
Kp =
2NO2(g)
P NO
2
2
PN O
2 4
P is the partial pressure of that component
The Equilibrium Constant Kc
The equilibrium constant and the equilibrium constant expression are for
the chemical equation as written.
N2(g) + 3H2(g)
2NH3(g)
2N2(g) + 6H2(g)
2NH3(g)
N2(g) + 3H2(g)
4NH3(g)
Kc =
Kc´ =
[NH3]2
[N2][H2]3
[N2][H2]3
[NH3]2
K´´c = ??????
=
1
Kc
Examples

Write the equilibrium constant, Kc and K’c for the following
reactions:
a. CH4(g) + H2O(g)
CO(g) + 3 H2(g)
Write Kp and K’p for the following reactions:
CO(g)+ 2H2(g)
CH3OH(g)

Relating the Equilibrium
Constant Kp and Kc
Kp = Kc(RT)Dn
R is the gas constant,
0.082058
L atm
K mol
T is the absolute temperature (Kelvin).
Δn is the number of moles of gaseous products minus the
number of moles of gaseous reactants.
Example
Phosphorous pentachloride dissociate on heating
PCl5(g)
PCl3(g) + Cl2(g)
If Kc equals 3.26 x 10-2 at 191oC, what is Kp at this temperature?

Example
Consider the following reaction
2NO (g) + O2 (g)
2NO2 (g)
If Kp = 1.48 x 104 at 184 C, what is Kc?

13.4Heterogeneous Equilibria
CaCO3(s)
CaO(s) + CO2(g)
Limestone
Kc =
[CaO][CO2]
[CaCO3]
Lime
=
(1)[CO2]
= [CO2]
(1)
Pure solids and pure liquids are not included.
Kc = [CO2]
Kp = P
CO2
Heterogeneous Equilibria
Example
In the industrial synthesis of hydrogen, mixtures of CO and H2 are enriched
in H2 by allowing the CO to react with steam. The chemical equation for this
so-called water-gas shift reaction is
CO(g) + H2O(g)
CO2(g) + H2(g)
What is the value of Kp at 700K if the partial pressures in an equilibrium
mixture at 700K are 1.31 atm of CO, 10.0 atm of H2O, 6.12 atm of CO2, and
20.3 atm of H2?

Examples
Consider the following balanced reaction
(NH4)2S(s)
2NH3(g) + H2S(g)
An equilibrium mixture of this mixture at a certain temperature was
found to have [NH3] = 0.278 M and [H2S] = 0.355 M. What is the
value of the equilibrium constant (Kc) at this temperature?

13.5 Using the Equilibrium
Constant
When we know the numerical value of the equilibrium
constant, we can make certain judgments about the
extent of the chemical reaction
Predicting the Direction of
Reaction


For a chemical system whether in equilibrium or not, we can
calculate the value given by the law of mass action
We called it reaction quotient, Qc
aA + bB
Reaction quotient:
cC + dD
Qc =
[C]tc[D]td
[A]ta[B]tb
The reaction quotient, Qc, is defined in the same way as the equilibrium
constant, Kc, except that the concentrations in Qc are not necessarily
equilibrium values.
Using the Equilibrium
Constant
•
If Qc < Kc
net reaction goes from left to
right (reactants to products).
If Qc > Kc
•
net reaction goes from right to
left (products to reactants).
•
If Qc = Kc
no net reaction occurs.
The equilibrium between reactant A
and product B:
A
B
Finding Equilibrium concentrations from
Initial Concentrations

Steps to follow in calculating equilibrium concentrations from initial
concentration
 Write a balance equation for the reaction
 Make an ICE (Initial, Change, Equilibrium) table, involves
 The initial concentrations
 The change in concentration on going to equilibrium, defined as x
 The equilibrium concentration
 Substitute the equilibrium concentrations into the equilibrium
equation for the reaction and solve for x
 Calculate the equilibrium concentrations form the calculated value of
x
 Check your answers
Calculating Equilibrium
Concentrations

Sometimes you must use quadratic equation to solve for x, choose the
mathematical solution that makes chemical sense
Quadratic equation
ax2 + bx + c = 0
Finding Equilibrium
concentrations from Initial
Concentrations
For Homogeneous Mixture
aA(g)
Initial concentration (M)
Change (M)
Equilibrium (M)
Kc =
[products]
[reactants]
bB(g)
+
cC(g)
[A]initial
[B]initial
[C]initial
- ax
+ bx
+ cx
[A]initial – ax
[B]initial + bx
[C]initial + cx
Finding Equilibrium
concentrations from Initial
Concentrations
Kc =
For Heterogenous Mixture
aA(g)
Initial concentration (M)
[products]
bB(g)
[A]initial
[B]initial
Change (M)
- ax
+ bx
Equilibrium (M)
[A]initial – ax
[reactants]
+
[B]initial + bx
cC(s)
……..
……..
……….
Example

The value of Kc for the reaction is 3.0 x 10-2. Determine the equilibrium
concentration if the initial concentration of water is 8.75 M
C(s) + H2O(g)
CO(g) + H2(g)
Using the Equilibrium Constant
At 700 K, 0.500 mol of HI is added to a 2.00 L container and
allowed to come to equilibrium. Calculate the equilibrium
concentrations of H2, I2, and HI . Kc is 57.0 at 700 K.
H2(g) + I2(g)
2HI(g)
Examples

Consider the following reaction
I2(g) + Cl2(g)
2ICl(g)
Kp = 81.9 (at 25oC)
A reaction mixture at 25oC initially contains PI2 = 0.100 atm,
PCl2 = 0.100 atm, and PICl = 0.100 atm. Find the
equilibrium pressure of I2, Cl2 and ICl at this temperature.
Using the value of Kp, predict in which direction does the
reaction favored?
Example

A flask initially contained hydrogen sulfide at a pressure of 5.00
atm at 313 K. When the reaction reached equilibrium, the partial
pressure of sulfur vapor was found to be 0.15 atm. What is the Kp
for the reaction?
2H2S(g)
2H2(g) + S2(g)
13.6 Le Châtelier’s Principle
Le Châtelier’s Principle: If a stress is applied to a reaction
mixture at equilibrium, net reaction occurs in the direction
that relieves the stress.
•
The concentration of reactants or products can be
changed.
•
The pressure and volume can be changed.
•
The temperature can be changed.
13.7Altering an Equilibrium
Mixture: Concentration
N2(g) + 3H2(g)
2NH3(g)
Altering an Equilibrium Mixture:
Concentration
In general, when an equilibrium is disturbed by the addition or
removal of any reactant or product, Le Châtelier’s principle
predicts that
•
the concentration stress of an added reactant or product is
relieved by net reaction in the direction that consumes the
added substance.
•
the concentration stress of a removed reactant or product is
relieved by net reaction in the direction that replenishes the
removed substance.
Altering an Equilibrium Mixture:
Concentration

Add reactant – denominator in Qc expression becomes larger
◦ Q c < Kc
◦ To return to equilibrium, Qc must be increases
◦ More product must be made => reaction shifts to the right

Remove reactant – denominator in Qc expression becomes smaller
◦ Q c > Kc
◦ To return to equilibrium, Qc must be decreases
◦ Less product must be made => reaction shifts to the left
Altering an Equilibrium
Mixture: Concentration

An equilibrium mixture of 0.50 M N2, 3.00 M H2, and 1.98 M NH3 is
disturbed by increasing the N2 concentration to 1.50 M.
N2(g) + 3H2(g)
2NH3(g)
at 700 K, Kc = 0.291
Which direction will the net reaction shift to re-establish the
equilibrium?
Example
The reaction of iron (III) oxide with carbon monoxide occurs in a blast
furnace when iron ore is reduced to iron metal:
Fe2O3(s) + 3 CO(g)
2 Fe(l) + 3CO2(g)
Use Le Chatellier’s principle to predict the direction of net reaction when an
equilibrium mixture is disturbed by:
a.
adding Fe2O3

b.
Removing CO2
c.
Removing CO; also account for the change using the reaction
quotient Qc
Example
Consider the following reaction at equilibrium
CO(g) + Cl2(g)
COCl2(g)
Predict whether the reaction will shift left, shift right, or remain unchanged
upon each of the following reaction mixture
a.
COCl2 is added to the reaction mixture

b.
Cl2 is added to the reaction mixture
c.
COCl2 is removed from the reaction mixture: also account for the
change using the reaction quotient Qc
13.8 Altering an Equilibrium Mixture:
Changes in Pressure and Volume
N2(g) + 3H2(g)
2NH3(g)
at 700 K, Kc = 0.291
An equilibrium mixture of 0.50 M N2, 3.00 M H2, and 1.98 M NH3 is
disturbed by reducing the volume by a factor of 2. Which direction
will the net reaction shift?
Altering an Equilibrium Mixture:
Pressure and Volume
In general, when an equilibrium is disturbed by a change in
volume which results in a corresponding change in pressure, Le
Châtelier’s principle predicts that
•
an increase in pressure by reducing the volume will bring
about net reaction in the direction that decreases the
number of moles of gas.
•
a decrease in pressure by enlarging the volume will bring
about net reaction in the direction that increases the
number of moles of gas.
Altering an Equilibrium Mixture:
Pressure and Volume


If reactant side has more moles of gas
◦ Denominator will be larger
 Qc < K c
 To return to equilibrium, Qc must be increased
 Reaction shifts toward fewer moles of gas (to the product)
If product side has more moles of gas
◦ Numerator will be larger
 Qc > K c
 To return to equilibrium, Qc must be decreases
 Reaction shifts toward fewer moles of gas (to the reactant)
Altering an Equilibrium Mixture:
Pressure and Volume
Reaction involves no change in the number moles of gas
◦ No effect on composition of equilibrium mixture
 For heterogenous equilibrium mixture
◦ Effect of pressure changes on solids and liquids can be ignored
 Volume is nearly independent of pressure
 Change in pressure due to addition of inert gas
◦ No change in the molar concentration of reactants or products
◦ No effect on composition

Example

Consider the following reaction at chemical equilibrium
2 KClO3(s)
2 KCl(s) + 3O2(g)
a.
What is the effect of decreasing the volume of the reaction
mixture?
b.
Increasing the volume of the reaction mixture?
c.
Adding inert gas at constant volume?
Example

Does the number moles of products increases, decreases or remain the
same when each of the following equilibria is subjected to a increase in
pressure by decreasing the volume?
◦ PCl5(g)
PCl3(g) + Cl2(g)
◦ CaO(s) + CO2(g)
CaCO3(s)
◦ 3 Fe(s) + 4H2O(g)
Fe3O4(s) + 4 H2(g)
Altering an Equilibrium Mixture:
Temperature
In general, when an equilibrium is disturbed by a change in
temperature, Le Châtelier’s principle predicts that
•
the equilibrium constant for an exothermic reaction
(negative DH°) decreases as the temperature increases.
• Contains more reactant than product
• Kc decreases with increasing temperature
•
the equilibrium constant for an endothermic reaction
(positive DH°) increases as the temperature increases.
• Contains more product than reactant
• Kc increases with increasing temperature
13.9 Altering an Equilibrium
Mixture: Temperature
N2(g) + 3H2(g)
2NH3(g)
DH° = -2043 kJ (exothermic )
As the
temperature
increases, the
equilibrium shifts
from products to
reactants.
Example

The following reaction is endothermic
CaCO3(s)
CaO(s) + CO2(g)
a.
What is the effect of increasing the temperature of the reaction
mixture?
b.
Decreasing the temperature?
Examples
In the first step of Ostwald process for the synthesis of nitric acid,
ammonia is oxidized to nitric oxide by the reaction:
2 NH3(g) + 5 O2(g)
4 NO(g) + 6 H2O(l)
ΔHo = -905 kJ
How does the temperature amount of NO vary with an increases in
temperature?

The Effect of a Catalyst on
Equilibrium

Catalyst increases the rate of a chemical reaction
◦ Provide a new, lower energy pathway
◦ Forward and reverse reactions pass through the same transition state
◦ Rate for forward and reverse reactions increase by the same factor
◦ Does not affect the composition of the equilibrium mixture
◦ Does not appear in the balance chemical equation
◦ Can influence choice of optimum condition for a reaction
The Effect of a Catalyst on
Equilibrium