IB Chemistry on Equilibrium Constant, Kc and Reaction Quotient, Qc

http://lawrencekok.blogspot.com

Prepared by

Lawrence Kok

Tutorial on Dynamic Equilibrium, Equilibrium

constant Kc and Reaction quotient Qc.

http://lawrencekok.blogspot.com/

Dynamic Equilibrium

Closed system

Reversible

Forward Rate, Kf

Reverse Rate, Kr

2NO2(g) N2O4(g)

combining dissociation

Conc vs time Rate vs time

Conc

Time

Conc NO2

Conc N2O4

2NO2(g) N2O4(g)

Forward rate

Backward rate

brown colourless

Dynamic Equilibrium

Closed system

Reversible

Forward Rate, Kf

Reverse Rate, Kr

2NO2(g) N2O4(g)

Chemical system

Forward rate rxnRate Combining

Backward rate rxnRate dissociation

Reversible rxn happening, same time with same rate

Rate of forward = Rate of backward

Conc of reactant and productremain UNCHANGED/CONSTANT not EQUAL

combining dissociation


Conc

Time

Conc NO2

Conc N2O4

With time• Conc NO2 decrease -Forward rate decrease

• Conc N2O4 increase - Backward rate increase

2NO2(g) N2O4(g)

Forward rate

Backward rate

Forward Rate = Backward Rate

Conc NO2 and N2O4 remain UNCHANGED/CONSTANT

brown colourless

How dynamic equilibrium is achieved in closed system?

Conc of NO2 decrease ↓over time

NO2

2NO2(g) N2O4(g)

Conc of N2O4 increase ↑ over time

N2O4

1 As reaction proceedsconcentration



Forward rate, Kf decrease ↓ over time

NO2

2NO2(g) N2O4(g)


N2O4

Reverse rate, Kr increase ↑ over time

NO2

N2O4

1

2

As reaction proceedsconcentration

As reaction proceedsrate



Forward rate, Kf decrease ↓ over time

Forward Rate = Reverse Rate

NO2

2NO2(g) N2O4(g)


N2O4

Reverse rate, Kr increase ↑ over time

NO2

N2O4

1

2

Conc of reactant/product remain constant

Rate

3

Time

Conc

NO2

N2O4

At dynamic equilibrium

As reaction proceedsconcentration

As reaction proceedsrate

Time

Click here to view simulation

https://www.youtube.com/watch?v=C5jDmG4nVV8



Conc vs Time

How dynamic equilibrium is achieved in a closed system?

40 0

Rate forward = ½ breakdown = ½ x 40 = 20

Rate reverse = ¼ form = ¼ x 0 = 0

20 20



15 25



13 27



13 27

At dynamic Equilibrium Rate forward = Rate reverseBreakdown (7) = Formation (7)

At dynamic Equilibrium Conc reactant 13 /Product 27 constant

Rate vs Time

4/1

2/1

..tan..

..tan..

1

1 reversetconsrate

forwardtconsrate

K

K

213

27

tan

treac

productK c

24/1

2/1

1

1 K

KK c

or

Dynamic Equilibrium

Reversible (closed system)

Forward Rate, K1 Reverse Rate, K-1

At Equilibrium

Forward rate = Backward rateConc reactants and products remain

CONSTANT/UNCHANGE


A + B

C + D

Conc

Time

Dynamic Equilibrium



Conc of product and reactantat equilibrium

At Equilibrium


CONSTANT/UNCHANGE

aA(aq) + bB(aq) cC(aq) + dD(aq)

coefficient

Solid/liq not included in Kc

Conc represented by [ ]

K1

K-1

Equilibrium Constant Kc


A + B

C + D

Conc

Time

Dynamic Equilibrium



Kc = ratio of molar conc of product (raised to power of their respective stoichiometry coefficient) to molar conc of reactant (raised to power of their respective stoichiometry coefficient)

Conc of product and reactantat equilibrium

At Equilibrium


CONSTANT/UNCHANGE



coefficient

Solid/liq not included in Kc

Conc represented by [ ]

K1

K-1

ba

dc

cBA

DCK

1

1

K

KKc


express in


A + B

C + D

Conc

Time

Click here notes on dynamic equilibrium

Excellent Notes

reversetconsrate

forwardtconsrate

K

K

..tan..

..tan..

1

1

http://www.pmstllc.com/Laney/Chem_30A_Documents_files/Lecture_21_notes.pdf



Magnitude of Kc

ba

dc

cBA

DCK

Extend of reaction

How far rxn shift to right or left?

Not how fast

ba

dc

cBA

DCK

cKcK

Position of equilibrium

92103 cK81103cK

2107.8 cK1

Large Kc

• Position equilibrium shift to right• More products > reactants

Magnitude of Kc

ba

dc

cBA

DCK

Extend of reaction


Not how fast

ba

dc

cBA

DCK

Small Kc

• Position equilibrium shift to left• More reactants > products

cKcK


2CO2(g) ↔ 2CO(g) + O2(g)

92103 cK

2H2(g) + O2(g) ↔ 2H2O(g)

81103cK

H2(g) + I2(g) ↔ 2HI(g)

2107.8 cK1

Kc

• Position equilibrium lies slightly right• Reactants and products equal amount

Large Kc

• Position equilibrium shift to right• More products > reactants

Magnitude of Kc

ba

dc

cBA

DCK

Extend of reaction


Not how fast

ba

dc

cBA

DCK

Small Kc

• Position equilibrium shift to left• More reactants > products

cKcK


2CO2(g) ↔ 2CO(g) + O2(g)

92103 cK

2H2(g) + O2(g) ↔ 2H2O(g)

81103cK

H2(g) + I2(g) ↔ 2HI(g)

2107.8 cK1

Kc

• Position equilibrium lies slightly right• Reactants and products equal amount

Reaction completion

Product favouredReactant favoured Reactant/Product equal

cK

Temp dependent

Extend of rxn

Not how fast


ba

dc

cBA

DCK


Conc of product and reactant at equilibrium

Equilibrium expression HOMOGENEOUS gaseous rxn

4NH3(g) + 5O2(g) ↔ 4NO(g) + 6H2O(g) N2(g) + 3H2(g) ↔ 2NH3(g)

NH4CI(s) ↔ NH3(g) + HCI(g)

2SO2(g) + O2(g) ↔ 2SO3(g)

52

4

3

6

2

4

ONH

OHNOKc

32

1

2

2

3

HN

NHKc

11

3 HCINHKc

04

11

3

CINH

HCINHKc

12

2

2

2

3

OSO

SOKc

Equilibrium expression HETEROGENOUS rxn

CaCO3(s) ↔ CaO(g) + CO2(g)

03

1

2

1

CaCO

COCaOK c

12

1COCaOK c

CH3COOH(l) + C2H5OH(l) ↔ CH3COOC2H5(l) + H2O(l)

152

1

3

1

2

1

523

OHHCCOOHCH

OHHCOOCCHK c

Equilibrium expression HOMOGENEOUS liquid rxn

Cu2+(aq) + 4NH3(aq) ↔ [Cu(NH3)4]

2+

43

12

2

43 )(

NHCu

NHCuK c

Reactant/product same phase

Reactant/product diff phase

aA bB

2aA 2bB

bB aA

aA bB

aA bB

a

b

cA

BK

aA bB

Equilibrium Constant Kc Equilibrium Constant Kc

b

a

cB

AK

'

c

cK

K1'

inverse

X2 coefficient

2'

cc KK

coefficient

2

1

a

b

c

A

BK

21

21

'

ccc KKK 21'

a

b

cA

BK

a

b

cA

BK

a

b

cA

BK

2

2'

2

1

aA bB bB cC

a

b

ciA

BK

b

c

ciiB

CK

+ 2 reactions+ aA cC

a

c

a

b

b

c

cA

C

A

B

B

CK

'

ciciic KKK '

Effect on Kc

Inverse Kc

Square Kc

Square root cK

Multiply both Kc

2

1

ciiK ciK

N2(g) + O2(g) ↔ 2NO(g)

2NO(g) + O2(g) ↔ 2NO2(g)

19103.2 ciK

6103ciiK

2NO2(g) ↔ N2(g) + 2O2(g)

13

619

107

103103.2

c

c

ciicic

K

K

KKKN2(g) + 2O2(g) ↔ 2NO2(g)

13107 cK

12'

13

'

1042.1

107

11

c

c

c

K

KK

HF(ag) ↔H+(aq) + F -(aq)

H2C2O4(ag) ↔ 2H+(aq) + C2O4

2 -(aq)

4108.6 ciK

6108.3 ciiK

2HF(ag) + C2O42- ↔ 2F -(aq) + H2C2O4(aq)

2HF(ag) ↔ 2H+(aq) + 2F -(aq)

2H+(ag) + C2O4

2- ↔H2C2O4(aq)

7242'106.4108.6 cic KK

5

6

''106.2

108.3

11

cii

cK

K

12.0106.2106.4 57

'''

c

ccc

K

KKK

Kc for diff rxnAdding 2 rxns

+

Inverse rxn

Adding 2 rxns

2HF(ag) + C2O42- ↔ 2F -(aq) + H2C2O4(aq)

+

HF(ag) ↔H+(aq) + F -(aq)

4108.6 ciK

x2 coefficient

H2C2O4(ag) ↔ 2H+(aq) + C2O4

2 -

Inverse rxn

6108.3 ciiK

2HF(ag) ↔ 2H+(aq) + 2F -(aq)

2H+(ag) + C2O4

2- ↔H2C2O4(aq)

Add 2 rxn

7'106.4 cK

5''106.2 cK+

Effect on Kc Effect on Kc

Inverse rxn Inverts expression

Doubling rxn coefficient Squares expression

Tripling rxn coefficient Cubes expression

Halving rxn coefficient Square root expression

Adding 2 reactions Multiplies 2 expression

cK

1

2

cK

3

cK

cK

ii

c

i

c KK

Square Kc

Invert Kc

Multiply Kc

1

2

3

N2(g) + 2O2(g) ↔ 2NO2(g)

H2 + I2 ↔ 2HI

50cK

12

1

2

2

IH

HIK c

2HI ↔ H2 + I2

2

1

2

1

2'

HI

IHK c

02.050

11'

c

cK

K

2SO2 + O2 ↔ 2SO3

12

2

2

2

3

OSO

SOKc

200cK

SO2 + O2 ↔ SO3

1.14200'

cc KK

2

1

4SO2 + 2O2 ↔ 4SO3

40000

200

,

22'

c

cc

K

KK

N2(g) + 3H2(g) ↔ 2NH3(g)

32

1

2

2

3

HN

NHKc

Kc is 170 at 500K Determine if rxn is at equilibrium when conc are at:[N2] =1.50, [H2] = 1.00, [NH3] = 8.00

00.150.1

00.8

3

2

1

2

2

3

c

c

Q

HN

NHQ

• Rxn not at equilibrium

• Shift to right, favour product

• Qc must increase, till equal to Kc

IB Questions

Determine Kc for inversing rxn

inverse

Determine Kc for halving rxn

2

1

1

2

2

2

2

3

OSO

SOK c

halving

Determine Kc for doubling rxn

2SO2 + O2 ↔ 2SO3

doubling

12

2

2

2

3

OSO

SOKc

200cK

2

1

2

2

2

2

3

OSO

SOK c

21

34

170cK7.42cQ

cc KQ

Kc and Qc

H2(g) + I2(g) ↔ 2HI(g)

12

1

2

2

IH

HIK c

At equilibrium Initial conc of H2 , I2 and HI

4.461012.01014.1

1052.21212

22

cK 4.46cK

Expt InitialConc H2

InitialConc I2

Initial Conc HI

1 2.40 x 10-2 1.38 x 10-2 0

Expt EquilibriumConc H2

EquilibriumConc I2

EquilibriumConc HI

1 1.14 x 10-2 0.12 x 10-2 2.52 x 10-2

At equilibrium conc

Kc and Qc

H2(g) + I2(g) ↔ 2HI(g)

12

1

2

2

IH

HIK c

At equilibrium Initial conc of H2 , I2 and HI

00.4cQ

12

1

2

2

IH

HIQc

4.461012.01014.1

1052.21212

22

cK 4.46cK

Expt InitialConc H2

InitialConc I2

Initial Conc HI

1 0.0500 0.0500 0.100

Initial conc of H2 , I2 and HI

Expt InitialConc H2

InitialConc I2

Initial Conc HI

1 2.40 x 10-2 1.38 x 10-2 0


EquilibriumConc I2

EquilibriumConc HI

1 1.14 x 10-2 0.12 x 10-2 2.52 x 10-2

At equilibrium conc

Not at equilibrium

H2(g) + I2(g) ↔ 2HI(g)

00.4050.0050.0

100.02

cQ

Kc and Qc

H2(g) + I2(g) ↔ 2HI(g)

cK

Constant at fixed Temp

12

1

2

2

IH

HIK c

At equilibrium

Independent of initial conc


00.4cQ

12

1

2

2

IH

HIQc

4.461012.01014.1

1052.21212

22

cK 4.46cK

Expt InitialConc H2

InitialConc I2

Initial Conc HI

1 0.0500 0.0500 0.100


Expt InitialConc H2

InitialConc I2

Initial Conc HI

1 2.40 x 10-2 1.38 x 10-2 0


EquilibriumConc I2

EquilibriumConc HI

1 1.14 x 10-2 0.12 x 10-2 2.52 x 10-2

At equilibrium conc

Not at equilibrium

H2(g) + I2(g) ↔ 2HI(g)

00.4050.0050.0

100.02

cQ

Predict the direction of rxn

Difference between

cQ

Conc of product/reactant

at equilibruim conc

Reaction quotient at particular time

Not at equilibrium conc

Varies NOT constant

Kc and Qc

H2(g) + I2(g) ↔ 2HI(g)

12

1

2

2

IH

HIK c

4.461012.01014.1

1052.21212

22

cK 4.46cK

At equilibrium conc

cc KQ cc KQ cc KQ

Reaction at equilibriumExpt Initial

Conc H2

InitialConc I2

Initial Conc HI

1 0.0500 0.0500 0.100


Expt InitialConc H2

InitialConc I2

Initial Conc HI

1 0.0250 0.0350 0.300


Kc and Qc

H2(g) + I2(g) ↔ 2HI(g)

12

1

2

2

IH

HIK c

4.461012.01014.1

1052.21212

22

cK 4.46cK

At equilibrium conc

cc KQ cc KQ cc KQ

Reaction at equilibrium

More product > reactant

Rxn shift left more reactant

→

cc KQ

cQ

Bring Qc down

More reactant > product

Rxn shift right → more product

Bring Qc up cQ

cc KQ

cQ

Expt InitialConc H2

InitialConc I2

Initial Conc HI

1 0.0500 0.0500 0.100


12

1

2

2

IH

HIQc

00.4050.0050.0

100.02

cQ

cQ

Expt InitialConc H2

InitialConc I2

Initial Conc HI

1 0.0250 0.0350 0.300


12

1

2

2

IH

HIQc

1030350.00250.0

300.02

cQ

Click here to view notes

http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch16/equilib.html



Kc from reaction stoichiometry

H2(g) + I2(g) ↔ 2HI(g)

4.46 sameK c

12

1

2

2

IH

HIK c

Kc = 46.4 ( 730K)At equilibrium 4 diff initial conc of H2 , I2 and HI

4.461012.01014.1

1052.21212

22

cKRxn 1

same

Rxn 2, 3, 4diff initial conc H2(g) + I2(g) ↔ 2HI(g)

12

1

2

2

IH

HIKc


H2(g) + I2(g) ↔ 2HI(g)

4.46 sameK c

12

1

2

2

IH

HIK c


4.461012.01014.1

1052.21212

22

cKRxn 1

same

Rxn 2, 3, 4diff initial conc

more products

H2(g) + I2(g) ↔ 2HI(g)

cQ

Rxn shift to right

Rxn shift to leftmore reactants

treac

productQc

tan

treac

productQc

tan

cQ

12

1

2

2

IH

HIKc


H2(g) + I2(g) ↔ 2HI(g)

4.46 sameK c

12

1

2

2

IH

HIK c


4.461012.01014.1

1052.21212

22

cKRxn 1

same

Qc = Kc - rxn at equilibrium, no side/shift occurQc < Kc– rxn shift right, favour product Qc > Kc – rxn shift left, favour reactant

Rxn 2, 3, 4diff initial conc

more products

H2(g) + I2(g) ↔ 2HI(g)

cQ

Rxn shift to right

Rxn shift to leftmore reactants

treac

productQc

tan

treac

productQc

tan

cQ

cc KQ cc KQ cc KQ

12

1

2

2

IH

HIKc

Kc and Qc

H2(g) + I2(g) ↔ 2HI(g)

12

1

2

2

IH

HIK c

00.4cQ

12

1

2

2

IH

HIQc

4.461012.01014.1

1052.21212

22

cK 4.46cK

Expt InitialConc H2

InitialConc I2

Initial Conc HI

1 0.0500 0.0500 0.100


At equilibrium conc

Not at equilibrium

H2(g) + I2(g) ↔ 2HI(g)

00.4050.0050.0

100.02

cQ

cc KQ cc KQ


More reactant > product

Rxn shift right → more product

Bring Qc up cQ

cQ

cc KQ

00.4cQ 4.46cK<

Kc and Qc

H2(g) + I2(g) ↔ 2HI(g)

12

1

2

2

IH

HIK c

103cQ

12

1

2

2

IH

HIQc

4.461012.01014.1

1052.21212

22

cK 4.46cK


At equilibrium conc

Not at equilibrium

H2(g) + I2(g) ↔ 2HI(g)

cc KQ cc KQ


More product > reactant

Rxn shift left more reactant

→

cc KQ

cQ

Bring Qc down cQ

Expt InitialConc H2

InitialConc I2

Initial Conc HI

1 0.0250 0.0350 0.300

1030350.00250.0

300.02

cQ

103cQ 4.46cK>

How dynamic equilibrium is shifted when H2 is added ?

N2(g) + 3H2(g) ↔ 2NH3(g) 07.4cK

At equilibrium Conc reactant/product no change

Equilibrium Conc H2 = 0.82MEquilibrium Conc N2 = 0.20MEquilibrium Conc NH3 = 0.67M

32

1

2

2

3

HN

NHKc

31

2

82.020.0

67.0cK

07.4cK


N2(g) + 3H2(g) ↔ 2NH3(g) 07.4cK

Equilibrium disturbedH2 added. More reactant


24.2cQ


32

1

2

2

3

HN

NHKc

31

2

82.020.0

67.0cK

New Conc H2 = 1.00MConc N2 = 0.20MConc NH3 = 0.67M

32

1

2

2

3

HN

NHQc

31

2

00.120.0

67.0cQ

07.4cK


N2(g) + 3H2(g) ↔ 2NH3(g) 07.4cK



At new equilibrium Conc reactant/product no change

24.2cQ


32

1

2

2

3

HN

NHKc

31

2

82.020.0

67.0cK


32

1

2

2

3

HN

NHQc

31

2

00.120.0

67.0cQ

07.4cK

New Equilibrium Conc H2 = 0.90MNew Equilibrium Conc N2 = 0.19MNew Equilibrium Conc NH3 = 0.75M

31

2

90.019.0

75.0cK

32

1

2

2

3

HN

NHKc

07.4cK


• Add H2 , Qc decrease• Position equilibrium shift to right• Rate forward and reverse increase• New equilibrium conc achieved when

Rate forward Kf = Rate reverse Kr

• More product NH3 ,but Kc unchanged

N2(g) + 3H2(g) ↔ 2NH3(g) 07.4cK




24.2cQ


32

1

2

2

3

HN

NHKc

31

2

82.020.0

67.0cK


32

1

2

2

3

HN

NHQc

31

2

00.120.0

67.0cQ

07.4cK

New Equilibrium Conc H2 = 0.90MNew Equilibrium Conc N2 = 0.19MNew Equilibrium Conc NH3 = 0.75M

31

2

90.019.0

75.0cK

32

1

2

2

3

HN

NHKc

07.4cK

Shift to the right - Increase product - New Conc achieve- Qc = Kc again

cc KQ






N2(g) + 3H2(g) ↔ 2NH3(g) 07.4cK

07.4 cc KQ

cc KQ


cc KQ






N2(g) + 3H2(g) ↔ 2NH3(g) 07.4cK

07.4 cc KQ


cc KQ

Equilibrium shift to right Rate forward Kf > Rate reverse Kr

cQ


cc KQ cc KQ






N2(g) + 3H2(g) ↔ 2NH3(g) 07.4cK

07.4 cc KQ


cc KQ

Equilibrium shift to right Rate forward Kf > Rate reverse Kr

cQ



Qc increase until Qc = Kc

cQ


cc KQ cc KQ cc KQ

Click here to view simulationClick here simulation using paper clips Click here simulation on reversible rxn

Click here on reversible rxn

Simulation on Dynamic equilibrium

Click here on equilibrium constant

http://www.ejmste.com/022006/d8.pdf



http://www3.fed.cuhk.edu.hk/chemistry/files/Simulation.pdf



https://www.youtube.com/watch?v=60Sylqei2DY


http://phet.colorado.edu/en/simulation/reversible-reactions




https://www.youtube.com/watch?v=cHAjhM3y3ds



Acknowledgements

Thanks to source of pictures and video used in this presentation

Thanks to Creative Commons for excellent contribution on licenseshttp://creativecommons.org/licenses/

Prepared by Lawrence Kok

Check out more video tutorials from my site and hope you enjoy this tutorialhttp://lawrencekok.blogspot.com

http://creativecommons.org/licenses/

http://lawrencekok.blogspot.com/

Education

IB Chemistry on Equilibrium Constant, Kc and Reaction Quotient, Qc