Chemical Equilibrium

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Chemical Equilibrium

• Chapter 15

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Introduction
Many chemical reactions can under the proper
conditions be made to go predominantly in one
direction or the other.
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Lets consider the catalytic methanation reaction
Start with 1.000 mol CO and 3.000 mol H2 in a
10.00 L vessel at 1200 K.
The rate of the reaction will depend on the
concentrations of the reagents.
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Applying Stoichiometry to an equilibrium mixture
When heated, PCl5 forms PCl3 and Cl2 as follows
When 1.00 mol PCl5 in a 1.00-L container is
allowed to come to equilibrium at a certain
temperature, the mixture is found to contain
0.135 mol PCl3.
How many moles of each substance are present at
equilibrium?
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This problem, may conveniently be solved with the
aid of the following table
Initial
?
Equilibrium
Were given that the equilibrium mixture contains
0.135 mol PCl3
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The Equilibrium Constant
Following a number of experiments it was observed
that all of the equilibrium compositions for a
reaction at a given temperature are related by a
quantity called the equilibrium constant.
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Definition of the equilibrium constant, Kc
Consider the general reaction
The equilibrium constant is the value obtained
for the equilibrium-constant expression when
equilibrium concentrations are substituted.
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Some equilibrium compositions for the methanation
reaction
Starting Concs
Equilibrium Concs
Kc
Experiment 1
0.1000 M HCl 0.300 M H2
0.0613 M CO 0.1839 M H2 0.0387 M CH4 0.0387 M H2O
3.93
Experiment 2
0.2000 M HCl 0.300 M H2
0.1522 M CO 0.1566 M H2 0.0478 M CH4 0.0478 M H2O
3.91
Experiment 3
0.1000 M HCl 0.100 M H2
0.0613 M CO 0.1839 M H2 0.0387 M CH4 0.0387 M H2O
3.93
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Example
Write the equilibrium-constant expression for the
following reaction
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The Law of Mass Action
The Law of Mass Action is a relation that
states the values of the equilibrium-constant
expression Kc are constant for a particular
reaction at a given temperature, whatever
equilibrium concentrations are substituted.
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The manipulation rules of equilibrium constants
Equilibrium constant for a reverse reaction
K1 1/K
cC dD ? aA bB
If the reaction is halved, the new equilibrium
constant is the square root of the original K.
If the reaction is doubled, then the new
equilibrium constant is the square of the
original K.
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If two reversible reactions are added together,
then the equilibrium constant of the resulting
reaction will be the product of the two original
K-values.
Equilibrium constant for two reactions added K3
K1 x K2
HA ? H A-
H C ? CH
HA C ? CH A-
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Example
The equilibrium constant for reaction (1) is K.
What is the equilibrium constant for equation (2)?
(1) 1/3 N2(g) H2(g) 2/3 NH3(g)
(2) 2 NH3(g) N2(g) 3 H2(g)
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Heterogeneous Equilibria
A homogeneous equilibrium is an equilibrium that
involves reactants and products in a single phase
only.
A heterogeneous equilibrium is an equilibrium
involving reactants and products in more that one
phase
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Example
Write the equilibrium-constant expression for the
following reaction
3Fe (s) 4H2O (g) Fe3O4 (s) 4H2 (g)
Note
When writing the equilibrium-constant expression
for heterogeneous equilibria, the concentration
terms for pure solids and liquids are omitted.
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Calculating Equilibrium Constants
See p570, 8th Ed.
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Example
Determining the equilibrium constant given
equilibrium concentrations.
Haber mixed some nitrogen and hydrogen and
allowed it to react at 500 K until the mixture
reached equilibrium with the product, ammonia.
When he analysed the equilibrium mixture, he
found it to consist of 0.796 M NH3, 0.305 M N2
and 0.324 M H2
What is the equilibrium constant for the reaction?
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Example
Determining the equilibrium constant given
equilibrium concentrations.
Carbon dioxide decomposes at elevated
temperatures to carbon monoxide and oxygen
2CO2(g) 2CO(g) O2(g)
At 3000 K, 2.00 mol CO2 is placed into a 1.00 L
container and allowed to come to equilibrium. At
equilibrium, 0.90 mol CO2 remains. What is the Kc
at this temperature?
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USING THE EQUILIBRIUM CONSTANT
So far

• we described how a chemical reaction reaches
  equilibrium.
• how this equilibrium can be characterised by the
  equilibrium constant.

We now look at the following uses of the
equilibrium constant

• Qualitatively interpreting the equilibrium
  constant.
• Predicting the direction of reaction.
• Calculating equilibrium concentrations.

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Applications of Equilibrium Constants
Rule of Thumb
If the equilibrium constant is large, then the
products are favoured at equilibrium.
N2 (g) 3H2 (g) 2 NH3 (g)
Eg.
For this reaction Kc 4.1 x 108
Conversely, if the equilibrium constant is small
then the reactants will be favoured at
equilibrium.
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Predicting the direction of Reaction.
Suppose a gaseous mixture from an industrial
plant has the following composition at 1200 K
0.0200 M CO 0.0200 M H2 0.00100 M CH4 0.00100 M
H2O
Would the following reaction go forward or in
reverse?
To answer this question we need to calculate the
reaction quotient, and compare its value to that
of Kc
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The reaction quotient (Qc) is an expression that
has the same form as the equilibrium constant
expression but whose concentration values are not
necessarily those at equilibrium.
6.25
Remember that Kc 3.93 for this reaction at 1200
K.
Thus we have that Qc gt Kc
For Qc to become equal to Kc the reaction must
shift to the left.
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Calculating Equilibrium Concentrations
In general

• If Qc gt Kc, the reaction will go left
• If Qc lt Kc, the reaction will go right
• If Qc Kc, the reaction is at equilibrium

Know This !!
Once you have determined the equilibrium constant
for a reaction, you can use it to calculate the
concentrations of substances in an equilibrium
mixture.
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Example
Obtaining one equilibrium concentration given the
others.
Nitrogen and oxygen form nitric oxide
N2(g) O2(g) 2NO(g)
If an equilibrium mixture at 25C contains 0.040
M of N2 and 0.010 M of O2, what is the
concentration of NO in this mixture? Kc at 25C
is 1 x 10-30.
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Example
Solving an equilibrium problem (involving a
linear equation)
Hydrogen iodide decomposes to hydrogen gas and
iodine gas.
At 800 K, the equilibrium constant for this
reaction is 0.016. If 0.50 mol is placed in a
5.0-L flask, what will be the composition of the
equilibrium mixture?
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Three steps in solving equilibrium concentrations
Remember

• Set up a table of concentrations.
• Substitute the expressions in x for equilibrium
  concentrations into the equilibrium constant
  expression.
• Solve the equilibrium constant expression for the
  values of the equilibrium concentrations.

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Changing the Reaction ConditionsLe Chateliers
Principle
By changing the reaction conditions, you can
increase or decrease the yield of product.
Three ways to alter the equilibrium composition
of a gaseous reaction mixture

• Changing the concentrations by removing products
  or adding reactants to the reaction vessel.
• Changing the partial pressure of gaseous
  reactants and products by changing the volume.
• Changing the temperature.

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Change in Reactant or Product Concentrations
Le Chateliers Principle states that
when a system in chemical equilibrium is
disturbed (by a change of temperature, pressure,
or a concentration) the system shifts in
equilibrium composition in a way that tends to
counteract this change.
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Applying Le Chateliers Principle When a
Concentration is altered.
The Fischer-Tropsch process for the synthesis of
gasoline consists of passing a mixture of carbon
monoxide and hydrogen over an iron-cobalt
catalyst.
A typical reaction that occurs in the process is
as follows
Suppose the reaction mixture comes to equilibrium
at 200C, then is suddenly cooled to room
temperature where octane liquifies. The remaining
gases are then reheated to 200C.
What is the direction of the reaction as
equilibrium is attained?
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Effects of Volume and Pressure Changes
In General
If the pressure is increased by decreasing the
volume of a reaction mixture, the reaction shifts
in the direction of fewer moles of gas.
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Applying Le Chateliers Principle When the
Pressure is Altered
Lets consider the same reaction in the
Fischer-Tropsch process
8CO(g) 17H2(g) C8H18(g) 8H2O(g)
Would you expect more or less of the product
octane, C8H18, as the pressure increases?
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Effect of Temperature Change
For an exothermic reaction (?H negative), the
amounts of products are decreased at equilibrium
by an increase in temperature.
A B C D heat
For an endothermic reaction (?H positive), the
amounts of products are increased by a increase
in temperature.
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Example
Applying Le Chateliers Principle When
Temperature is altered.
One stage in the manufacture of sulfuric acid is
the formation of sulfur trioxide by the reaction
of SO2 with O2. Predict how the equilibrium
composition of the reaction mixture will change
when the temperature is raised.
2SO2(g) O2(g) 2 SO3(g) ?H -198 kJ
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The Effect of Catalyst
A catalyst is a substance that increases the rate
of a reaction but is not consumed by it.
A catalyst has no effect on the equilibrium
composition of a reaction mixture. A catalyst
merely speeds up the reaction to achieve
equilibrium.