chemistry ch09 chemical equilibria
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99ChemicalChemical
equilibriaequilibria
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9.1 Chemical equilibrium9.1 Chemical equilibrium
N2(g) + 3H2(g) 2NH3(g)
Rates of the forward and reverse
reactions are equal There is no net change in the overall
composition of the reaction mixture
Dynamic equilibrium Reactants substances on the left
Products substances on the right
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9.2 The equilibrium constant,9.2 The equilibrium constant, K,K,
and the reaction quotient,and the reaction quotient, QQ
N2O4(g) 2NO2(g)
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For a given OVERALL system
composition equilibrium concentrations
are independent of direction of approach
9.2 The equilibrium constant,9.2 The equilibrium constant, K,K,
and the reaction quotient,and the reaction quotient, QQ
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9.2 The equilibrium constant,9.2 The equilibrium constant, K,K,
and the reaction quotient,and the reaction quotient, QQ
aA + bB cC + dD
The following holds when equilibrium
is established:
Equilibrium constant expression
Kc equilibrium constant
Kcdependent on temperature, always
specify temperature when Kcreported
? A ? A
? A ? A bea
e
de
ce
c
c
B
c
A
c
D
c
C
K
!
UU
UU
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9.2 The equilibrium constant,9.2 The equilibrium constant, K,K,
and the reaction quotient,and the reaction quotient, QQ
aA + bB cC + dD
The following holds when equilibrium
is established:
Equilibrium constant expression
Kc equilibrium constant
Kcdependent on temperature, always
specify temperature when Kcreported
? A ? A? A ? Aba
dc
cBA
DCK !
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9.2 The equilibrium constant,9.2 The equilibrium constant, K,K,
and the reaction quotient,and the reaction quotient, QQ
aA + bB cC + dD
Qc reaction quotient
Expression for systems not necessarily
at equilibrium
Kccan have only one positive value at
a specific temperature
Qccan have any positive value
? A ? A? A ? Aba
dc
cBA
DCQ !
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9.2 The equilibrium constant,9.2 The equilibrium constant, K,K,
and the reaction quotient,and the reaction quotient, QQ
Qc= Kcat equilibrium
Qc> Kcsystem reacts to use up
products and generate more reactants Qc< Kcsystem reacts to use up
reactants and generate more products
c d
p a b
p p
p pK
p p
p p
U U
U U
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9.2 The equilibrium constant,9.2 The equilibrium constant, K,K,
and the reaction quotient,and the reaction quotient, QQ
The relationship between K and Kc
ng= (number of moles ofgaseous products)
(number of moles ofgaseous reactants)
Important to use correct units in this
equation Equilibrium concentrations in mol m-3
Equilibrium pressures in Pa
gn
cRT
KK
(
U
13 Lmol1000mmol ( v cc
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9.2 The equilibrium constant,9.2 The equilibrium constant, K,K,
and the reaction quotient,and the reaction quotient, QQ
Manipulating equilibrium constant
expressions
When the direction of an equation isreversed, the new equilibrium constant is
the reciprocal of the original
cc KK
1'
!
? A
? A? A235
ClCl
Cl!c
? A? A? Ac
' 3 2
5
PCl Cl
PCl!
PCl3 + Cl2 PCl5
PCl5 PCl3 + Cl2
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9.2 The equilibrium constant,9.2 The equilibrium constant, K,K,
and the reaction quotient,and the reaction quotient, QQ
Manipulating equilibrium constant
expressions
When the coefficients in an equation aremultiplied by a factor, the equilibrium
constant is raised to a power equal to
that factor.? A
? A? A235
ClPCl
PCl!cPCl3 + Cl2 PCl5
? A? A ? A
cK
2" 5
2 23 2
PCl
PCl Cl!2PCl3 + 2Cl2 2PCl5
2'' cc !
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9.2 The equilibrium constant,9.2 The equilibrium constant, K,K,
and the reaction quotient,and the reaction quotient, QQ
Manipulating equilibrium constant
expressions
When chemical equilibria are added,their equilibrium constants are multiplied.? A
? A ? A222
22
1ON
ON!cK
? A
? A ? AcK
42
2 2 32 2
NO
N O O!
? A? A ? A
c
42
3 2 42 2
NO
N O
!
2N2 + O2 2N2O
2N2O + 3O2 4NO2
2N2 + 4O2 4NO2
? A
? A ? A
? A
? A ? A
? A
? A ? A4222
42
32
22
42
22
2
22
ON
NO
OON
NO
ON
ON
!v 321 ccc !v
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9.2 The equilibrium constant,9.2 The equilibrium constant, K,K,
and the reaction quotient,and the reaction quotient, QQ
The magnitude of the equilibrium
constant
Product concentrations are in thenumerator ofKc
The size ofKcgives a measure of how
far the reaction proceeds towardscompletion when equilibrium is reached
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The magnitude of the equilibrium
constant
reactant product
9.2 The equilibrium constant,9.2 The equilibrium constant, K,K,
and the reaction quotient,and the reaction quotient, QQ
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9.2 The equilibrium constant,9.2 The equilibrium constant, K,K,
and the reaction quotient,and the reaction quotient, QQ
Equilibrium constant expressions for
heterogeneous systems
Homogeneous reaction, all reactants andproducts are in the same phase
Heterogeneous reaction, more than one
phase exists in reaction mixture
2NaHCO3(s) Na2CO3(s) + H2O(g) + CO2(g)Kc= [H2O(g)][CO2(g)]
Do not include the concentrations of pure
solids or pure liquids
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Equilibrium constant
expressions for
heterogeneous systems
For any pure liquid or solid at
constant temperature, the
ratio of amount of substance
to volume of substance isconstant
9.2 The equilibrium constant,9.2 The equilibrium constant, K,K,
and the reaction quotient,and the reaction quotient, QQ
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9.3 Equilibrium and Gibbs9.3 Equilibrium and Gibbs
free energyfree energy
Free energy diagrams
Phase changes
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Free energy diagrams
Chemical reactions
12
9.3 Equilibrium and Gibbs9.3 Equilibrium and Gibbs
free energyfree energy
4
34
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9.3 Equilibrium and Gibbs9.3 Equilibrium and Gibbsfree energyfree energy
The relationship between G and K
is the gas constant, 8.3141 J K1 mol1 is the temperature in kelvin
lnQ is the natural logarithm of the
reaction quotient
Gaseous reactions: Q is calculated using
partial pressures expressed in Pa
Reactions in solution: Q is calculated from
molar concentrations
QRTGG ln(!( U
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QRTGG ln(!( U
9.3 Equilibrium and Gibbs9.3 Equilibrium and Gibbsfree energyfree energy
The relationship between G and K
The reaction 2NO2(g) N2O4(g) has G
= 5.40kJ mol-1 at 298 K. In a reaction mixture, the partial
pressures of NO2 and N2O4 are 0.25 105 Pa and
0.60 x 105 Pa, respectively. In which direction must
this reaction proceed to reach equilibrium?
2
2
42
!
U
U
p
p
p
p
Q
NO
ON
p
NO
NO
p
pG G RT
p
p
2 4
2
2l
UU
U
( ! (
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9.3 Equilibrium and Gibbs9.3 Equilibrium and Gibbsfree energyfree energy
G5
53 -1 1 -125
5
0.60 10
1 105.40 10 J mol 8.314J K mol 298K ln
0.25 10
1 10
( ! v v
v 12
molJ100.2 v!(G
K298!T
11molKJ314.8 !R
131molJ1040.5molkJ40.5 U v!!(G
Pa1060.0 5ON42
v!p Pa1025.0 5NO2
v!p
Pa101 5v!Up
Gis positive, forward reaction is nonspontaneous
so the reverse reaction occurs
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9.3 Equilibrium and Gibbs9.3 Equilibrium and Gibbsfree energyfree energy
The relationship between G and K
If the system is at equilibrium
G = 0
Q = K
G RT K0 lU! (
QRTGG l(!( U
G RTlU( !
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9.3 Equilibrium and Gibbs9.3 Equilibrium and Gibbsfree energyfree energy
The relationship between G and K
2SO2(g) + O2(g) 2SO3(g)G= -1.40 x 102 kJ mol-1 for this reaction at 25 C.
What is the value ofKp at this temperature?
G RT lnKU( !
RT
GKp
U(!l
p
p
K
K
5 1
-1 1
1.40 10 J molln
8.314J K mol 298K
ln 56.5
v!
!
24
5.56
103 v!
!
p
p
K
eK
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9.3 Equilibrium and Gibbs9.3 Equilibrium and Gibbsfree energyfree energy
The relationship between G and K
Thermodynamic data collected at 25 C
may be used to calculate the values ofequilibrium constants at temperatures
other than 25 C
Values ofHand S do not change
much with temperature
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9.4 How systems at equilibrium9.4 How systems at equilibrium
respond to changerespond to change
Le Chteliers principle
If an outside influence upsets an
equilibrium, the system undergoes achange in a direction that counteracts
the disturbing influence and, if possible,
returns the system to equilibrium
Better to compare equilibrium constant, K,
and reaction quotient, Q, when examining
the effect of perturbation to a chemical
process at equilibrium
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9.4 How systems at equilibrium9.4 How systems at equilibrium
respond to changerespond to change
Adding or removing a product or
reactant
When not a pure solid or liquid removalor addition of a reactant or product
instantaneously alters the concentration
of that species in the reaction mixture
The value ofQ changes so that Q K,
the system is no longer at equilibrium
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9.4 How systems at equilibrium9.4 How systems at equilibrium
respond to changerespond to change
Adding or removing a product or
reactant
Q = K equilibrium
Q < K shift towards products
Q > K shift towards reactants
[Cu(H2O)4]2+(aq) + 4Cl-(aq) [CuCl4]
2-(aq) + 4H2O(l)
Q
- !
- -
24
42
2 4
CuCl
Cu OH Cl
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9.4 How systems at equilibrium9.4 How systems at equilibrium
respond to changerespond to change
Changing the pressure in gaseous
reactions
Two ways of changing the total pressure
Changing the volume of the system
Adding an inert gas
Consider the equilibrium
N2(g) + 3H2(g) 2NH3(g)
3HN
2NH
22
3
!
UU
U
p
p
p
p
p
p
Qp
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9.4 How systems at equilibrium9.4 How systems at equilibrium
respond to changerespond to change
Changing the pressure in gaseous
reactions
Changing the volume of the system
3
HN
2
NH
22
3
!
UU
U
p
p
p
p
p
p
Qp
? A? A? A
cQ !
23
32 2
NH
N H
V
nc!
c
n
VQ
nn
V V
!
v
3
22
2
NH
2
3
HN
3
c
nQ V
n n
! vv
3
2 2
2NH 2
3N H
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9.4 How systems at equilibrium9.4 How systems at equilibrium
respond to changerespond to change
Changing the pressure in gaseous
reactions
Adding an inert gas
Increases total pressure of system
Does not alter the position of equilibrium
Add helium to N2/H2/NH3 equilibrium mixture
Does not react with products or reactants Qp is not changed
3
HN
2
NH
22
3
!
UU
U
p
p
p
p
p
p
Qp
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9.4 How systems at equilibrium9.4 How systems at equilibrium
respond to changerespond to change
Changing the temperature of a
reaction mixture
Value of the equilibrium constant, K, can
only be changed by altering the
temperature
The vant Hoff equation states:
The slope of the plot of lnKversus Thas
the same sign as H
2dlnd
RTH
TK U(!
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9.4 How systems at equilibrium9.4 How systems at equilibriumrespond to changerespond to change
Changing the temperature of a reaction
mixture
H is positive
Endothermic
Q < K
Products are favoured
H is negative
Exothermic
Q > K
Reactants are favoured
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9.4 How systems at equilibrium9.4 How systems at equilibrium
respond to changerespond to change
Changing the temperature of a
reaction mixture
Can use the vant Hoff equation to
calculate the Kat a specifiedtemperature if the value ofKat
another temperature is known
T THK KR T T2 1 1 2
1 1ln ln U ( !
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9.4 How systems at equilibrium9.4 How systems at equilibrium
respond to changerespond to change
Addition of a catalyst
Catalysts affect the rates of chemical
reactions without being used up
Addition of a catalyst may help bring a
system to chemical equilibrium more
rapidly
Addition of a catalyst does not affect the
position of equilibrium
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9.5 Equilibrium calculations9.5 Equilibrium calculations
Calculating Kc from equilibrium
concentrations
Measure the concentrations of reactantsand products after equilibrium reached
Substitute these equilibrium values into
the equilibrium constant expression to
calculate Kc
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9.5 Equilibrium calculations9.5 Equilibrium calculations
At a certain temperature, a mixture of H2 and
I2 was prepared by placing 0.020 mol of H2and 0.020 mol I2 into a 2.00 litre flask. After a
period of time, the equilibrium:H2(g) + I2(g) 2HI(g)
was established. The purple colour of the
I2 vapour was used to monitor the reaction,
and it was determined that, at equilibrium, theI2 concentration had dropped to 0.020 mol L
1.
What is the value of Kc for this reaction at this
temperature?
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9.5 Equilibrium calculations9.5 Equilibrium calculations
? A? A? A22
2
IH
HI!cK
= +equilibrium
concentration
initial
concentration
change in
concentration
H2(g) + I2(g) 2HI(g)
Initial concentration (mol L-1) 0.100 0.100 0.000
Change in concentration (mol L-1) -0.080 -0.080 +2(0.080)
Equilibrium concentration (mol L-1) 0.020 0.020 0.160
c
c
K
K
20.160
0.020 0.020
64
!
!
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9.5 Equilibrium calculations9.5 Equilibrium calculations
The concentration table a summary
1. Only equilibrium concentrations can be
substituted into the equilibrium constant
expression
2. Initial concentrations should be in mol L1.
The initial concentrations are those present
in the reaction mixture when it is prepared3. Changes in concentrations always occur in
the same ratio as the coefficients in the
balanced equation
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9.5 Equilibrium calculations9.5 Equilibrium calculations
The concentration table a summary
4. In constructing the Change in
concentration row reactant concentrations
should all change in the same direction
and have the same sign.
Row product concentrations should all
change in the opposite direction and havethe opposite sign.
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9.5 Equilibrium calculations9.5 Equilibrium calculations
Calculating equilibrium concentrations
from initial concentrations
Involves the use of initial concentrationsand Kcto calculate equilibrium
concentrations
Require a little applied algebra
Concentration tables can be very helpful
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9.5 Equilibrium calculations9.5 Equilibrium calculations
The water-gas shift reaction:
CO(g) + H2O(g) CO2(g) + H2(g)
has Kc= 4.06 at 500 C.
If 0.100 mol of CO and 0.100 mol of H2O(g)
are placed in a 1.00-litre reaction vessel at
this temperature, what are the concentrationsof the reactants and products when the
system reaches equilibrium?
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9.5 Equilibrium calculations9.5 Equilibrium calculations
? A? A? A? A
06.4OHCO
HCO
2
22 !!cK
CO(g) + H2O(g) CO2(g) + H2(g)
Initial concentration (mol L-1) 0.100 0.100 0.0 0.0
Change in concentration (mol L-1) -x -x +x +x
Equilibrium concentration (mol L-1) 0.100-x 0.100-x x x
06.4100.0100.0
!
!xx
xxKc
06.4
100.0 2
2
! x
x
01.206.4
100.0!!
xx
xx
xx
01.2201.0
100.001.2
!
!
201.001.2 ! xx201.001.3 !x0668.0!x
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9.5 Equilibrium calculations9.5 Equilibrium calculations
? A? A? A? A
c
c
Q
Q
2 2
2
2
2
CO H
CO H O
0.0668
4.10.033
!
! !
? A M033.00668.0100.0100.0CO !!! x? A x2H O 0.100 0.100 0.0668 0.033M! ! !? A M0668.0CO2 !! x
? A x2H 0.0668M! !
Rounding Kc to 2 significant figures gives 4.1, so the
calculated concentrations are correct.
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