Chemical Equilibrium
Foundation of equilibrium
Expressing equilibrium:
Equilibrium constants
Upsetting equilibrium – Le
Chatelier
Learning objectives
• Write equilibrium constant expressions for
both solutions and gas phase reactions
• Deduce relationship between Kc and Kp
• Use reaction quotients to predict direction
of reaction
• Apply LeChatelier’s principle to predict
consequences of changing equilibrium
conditions
Equilibrium
• Chemical equilibrium is:
The state reached when the concentrations
of reactants and products remain constant
over time
• Equilibrium is evident in physical
processes: vapour pressure over a liquid,
solid and liquid coexisting at the freezing
point
Equilibrium in a chemical change
• Not all reactions proceed to completion –
•
reactants completely converted into products
As reactants convert into products, the products
themselves convert back into reactants
As reactant concentration declines, the forward rate
decreases
As product concentration increases, the backward
rate increases
Dynamic equilibrium
• In the reaction N O ( g )  NO ( g )
2 4
2
The same final concentrations of NO2 and N2O4 are
obtained regardless of the initial conditions –
pure NO2 or pure N2O4
• The reactions don’t stop, the processes become
equal in both directions
Reactants and products no more
• In an equilibrium mixture, there is a
constant, dynamic cycling of materials and
the identities of reactant and product are
lost
• By convention, the substance(s) used
initially are called the reactants
Rate perspective
• As the concentration of reactant (product)
•
decreases, the rate of disappearance also
decreases
The equilibrium point is reached when the rates
are equal
Equilibrium constant
• Reactions usually take place in solution or
in the gas phase. For solution reactions,
the equilibrium constant Kc is used, where
concentrations are in mol/L
Concentration M
• For the equilibrium
Products
aA +bB = cC + dD
c
d
[C ] [ D]
Kc 
a
b
[ A] [ B]
Coefficients from equation
Reactants
Notes about Kc
• Kc is a constant at a given temperature,
regardless of the concentrations of the
reactants used
• Substances may be gases or solutions
• Kc has no units: each concentration is
considered as a ratio to the standard state
(1 M)
Equilibrium constant Kp
• For reactions in the gas phase, the partial
pressure can be used instead of molarity
c
d
PC PD
Kp  a b
PA PB
• Kp is unitless because the ratio with
respect to the standard state (1 atm) is
used
Relationship between Kc and Kp
PAV = nART so PA = nA/V●RT = [A]RT
c
d
[C ] [ D]
( c  d ) ( a b )
Kp 
( RT )
a
b
[ A] [ B]
K p  K c ( RT )
n
Δn = (c+d)-(a+b)
Heterogeneous equilibria
• Reactions often involve solid or liquid
phases in addition to gas and solution
• Concentrations of liquids and solids are
constants – independent of the amount
• Since they are constant they become
folded into Kc
Solids and liquids are ignored
CaCO3(s) = CaO(s) + CO2(g)
[CaO][CO2 ]
Kc 
[CaCO3 ]
[CaCO3 ]
Kc x
 [CO2 ]
[CaO]
Solid concentrations
are constant
• Include only gas or solution entities in Kc
Using equilibrium constants
• The value of Kc or Kp indicates the extent
of a reaction
• Generally:
Kc > 103, reaction goes to completion
Kc < 10-3, reaction does not proceed
103 > Kc > 10-3 reactants and products all
present
Reaction Quotient
• Reaction Quotient is the instanteous
value obtained for Kc for a combination of
reactants and products not yet at
equilibrium
• It can be used to predict the direction the
reaction will take from that set of
conditions
Kc and Qc
• In the reaction
H 2 ( g )  I 2 ( g )  2HI ( g ), K c  57
• A mixture made up with [H2] = 0.1 M, [I2] = 0.2
M and [HI] = 0.4 M
2
2
[ HI ]
0.4
Qc 

 8.0
[ H 2 ][ I 2 ] 0.1  0.2
• Kc > Qc so reaction will go towards HI
Predicting reactions with Qc
Qc < Kc, reaction goes towards products
Qc > Kc, reaction goes towards reactants
Qc = Kc, reaction is at equilibrium
Calculations with Kc
• Simple calculations:
Kc and all equilibrium concentrations but one
are given. Use Kc to calculate
concentration of unknown
• Complex calculations:
Kc and initial concentrations are given,
calculate equilibrium concentrations
I.C.E. – It’s pretty cool
• The ICE man cometh: it is widely used in
equilibrium problems
• Given Kc = 57 and initial concentrations of
[H2] = [I2] = 0.1 M, find equilibrium
concentrations of H2, I2 and HI
Initial
conc
Change
Equilibrium
conc
H2
I2
HI
0.1
0.1
0.0
-x
-x
2x
0.1 - x
0.1 - x
2x
Solve for x
2
2
[ HI ]
( 2 x)
K c  57 

[ H 2 ][ I 2 ] (0.1  x)  (0.1  x)
2
4x
 57
2
(0.1  x)
x  0.0791M , or 0.136M
• X = 0.136 > 0.1 so is physically unreasonable
• X =0.0791: [H2] = [I2] = 0.0209 M; [HI] =
0.158 M
Upsetting the applecart
• Conditions of reactions must often be
manipulated to optimize yield of products
Concentrations of reactants or products
Temperature
Pressure and volume
• Le Chatelier’s Principle:
If a stress is applied to a reaction mixture at
equilibrium, the system adjusts to relieve the
stress
The Haber process
• One of the most important industrial
processes is the synthesis of NH3 from the
elements: N2(g) + 3H2(g) = 2NH3(g)
• At 700 K, Kc = 0.29
• Altering reactant concentrations:
Increasing [reactant]: reactants → products
Increasing [product]: products → reactants
Effects of pressure
• Pressure is only important if there is an overall
•
change in the number of gas moles
N2(g) + 3H2(g) = 2NH3(g)
In the Haber process there are 4 moles of
reactants vs 2 moles of products
Increasing pressure: converts reactants to products
(fewer moles)
Decreasing pressure: converts products to reactants
(more moles)
Effects of temperature
• Kc depends on temperature. Increasing or
decreasing temperature will cause mixture
to adjust to new value of Kc.
• Treat the ΔH of a reaction as a
reactant/product
• Raising T causes heat input into reaction
• Lowering T causes withdrawal of heat
The Haber process as Function of T
• The process is exothermic: heat is a product
•
N2(g) + 3H2(g) = 2NH3(g) + 92.2 kJ
Raising T puts heat into reaction:
Equilibrium adjusts to reduce heat output – moves
towards reactants
• Lowering T removes heat:
Equilibrium adjusts to increase heat output – moves
towards products
• Endothermic reactions will show the opposite Tdependence
Increasing T in Haber process
reduces yield
Catalysts and equilibrium
• Equilibrium depends on the initial and final
states
• Catalyst lowers the transition state
• Equilibrium is unaffected by addition of a
catalyst
From the rate perspective
• The catalyst increases the forward
reaction rate by lowering the energy
barrier
• The rate of the backward reaction is
lowered by the same amount
Linking rate equations with Kc
• For the general reaction:
•
A+B=C+D
Assume single bimolecular steps
 Rate of forward reaction = kf[A][B]
 Rate of backward reaction = kr[C][D]
• At equilibrium
k f [ A][ B]  k r [C ][ D]
kf
[C ][ D]

 Kc
k r [ A][ B]