05 Chem Equilibrium

7/31/2019 05 Chem Equilibrium

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Chapter 5 Chemical equilibrium


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5.1 The general equilibrium expression

For any chemical reaction, the general reaction

equation can be written as

B

B

0 B Recall the criterion of Gibbs function, at constant T, p

and W=0

m

spontaneity

0 equilibriumrG

mrA G Define: is called the chemical affinity


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if an infinitesimal amount of reaction takes place at constant T

andp, the change in the Gibbs function is given by

B B

B

dG dn

B B

B

dG d

,

B B r m

BT p

GG

is the change of Gibbs function per mole of reaction.r mG


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At constant temperature and pressure,

0r mG

0r mG

0r mG


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We now consider a reaction of ideal gasesA B C Da b c d ln BB B

pRT

p $

$

ln Br m B B B B B

B B B

pG RT

p

$ $

r m B B

B

G $ $ lnB

Br m r m

B

pG G RT

p

$ $

B

Bp

B

pJ

p

$ lnr m r m pG G RT J $

The quantity Jp is called the pressure quotient.


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5.2 Chemical reactions of ideal gases

5.2.1 Standard equilibrium constant

When a chemical reaction attains equilibrium at constanttemperature and pressure

eqln 0r m r m pG G RT J $

We call the standard equilibrium constant and

denote it by K. It is only a function ofT.

eq

pJ

eq

B

B(ideal gases)

B

p

K p

$

$


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2 2 3N (g) + 3H (g) = 2NH (g)

2

3

1 32 2

(NH )

(N ) (H )

eq

eq eq

p

pK

p p

p p

$

$

$ $

31 2 2 32 2N (g)+ H (g)=NH (g)

312 2

3

2

2 2

(NH )

(N ) (H )

eq

eq eq

p

pK

p pp p

$

$

$ $

2

1 2

( )K K$ $ ,1 ,22r m r mG G $ $

r mln /K G RT $ $


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r m, then 0, 0pJ K G A $

r m

, then 0, 0p

J K G A $

r m, then 0, 0pJ K G A $

the forward reaction is

spontaneous

the reverse reaction is

spontaneous.

the reaction is at

equilibrium.

$


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5.2.2 Reactions involving pure condensed phases

and gases

If the pressure of a system does not differ very muchfromp, the chemical potentials of pure condensed

phases approximate the standard state chemical

potentials, i.e.

B(condensed) B(condensed) $

B(condensed) B(condensed) $

The activity of a pure liquid or solid is

1 (pure condensed phases near )B

a p $

Therefore, the condensed substances can be omitted

from the expression of equilibrium constant .B(g)eq

B(g)

B(g)

pK

p

$ $


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For example, for the reaction,12

C(s) + O2(g) = CO(g)

eq

1/2eq

2

(CO,g) /

(O ,g) /

p pK

p p

$

$

$


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5.2.3 Relationship between equilibrium constants of

related reactions

When the equilibrium constant for a particular reaction isnot available, it can be found by combining the

constants for an appropriate set of reactions. For

example

2 2 r m,1 1(1) C(s) + O (g) = CO (g) lnG RT K $ $

12 2 r m,2 22

(2) CO(g) + O (g) = CO (g) lnG RT K $ $

2 r m,3 3(3) CO (g) + C(s) = 2CO(g) lnG RT K $ $

Because (3)=(1)-2(2), we have

r m,3 r m,1 r m,22G G G $ $ $ 2

3 1 2/ ( )K K K$ $ $

5 2 4 M t f ilib i


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5.2.4 Measurement of equilibrium

constants

Physical methodChemical method

5.2.5 Calculation of chemical equilibrium composition

Example: The standard Gibbs function of reaction for

the decomposition

is 11808kJ mol-1 at 2300K. What is the degree of

dissociation of H2O at 2300K and 100kPa?

1

2 2 22

H O(g) H (g)+ O (g)


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Solution The equilibrium constant is 33

r m

118.08 10exp( / ) exp 2.08 10

8.3145 2300K G RT

$ $


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5.2.6 Equilibrium constants in other form

For example

eq

BB

( )B

pK p

1

2 2 22H O(g) H (g)+ O (g)

2 2

2

1/2

H O 1/2

H O

Pap

p pK

p

/ ( ) BpK K p $ $


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B B B B

BB BB y

p py p pK y K

p pp p

B

B B B BBB

B B Bc

nRT

p c RT cc c RT c RT VK Kc p c pp p p

B

B BB

B

B

BBB n

B B

n

p np p pK n K

p n p np p

5 3 T t d d f th


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5.3 Temperature dependence of the

equilibrium constant

2( / )

p

G T HT T

r m r m

2( / )d G T H

dT T

$ $

r m lnG RT K $ $

r m

2

ln Hd K

dT RT

$$

This is called the vant Hoff equation.


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If is temperature independent, carrying out theintegrationr mH

$

If an indefinite integral is taken, the result is

2 2

1 1

r m

2d ln d

K T

K T

HK T

RT

$

$

$

$

2 r m

1 2 1

1 1ln ( )

K H

K R T T

$ $

$

ln K


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A plot of versus 1/Tshould yield a straight line

with slope and intercept C.

r mln HK CRT

$

ln K

ln K

r mH

R

$


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5.4 Effects on the equilibrium

5.4.1 Le Chatelier's principle

equilibrium systems tend to compensate for the effects

of perturbing influences.

If the concentration of a reactant is increased, the

equilibrium position shifts to use up the added reactants.

If the pressure on an equilibrium system is increased,

then the equilibrium position shifts to reduce the pressure.

If the volume of a gaseous equilibrium system is reduced

then the equilibrium position shifts to increase the volume.If the temperature of an endothermic equilibrium system

is increased, the equilibrium position shifts to use up the heat

by producing more products.


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5.4.2 The effect of pressure on the equilibrium

BB B B

B

B

B BB

B B B

B BB

B

B BB

B

B

B

since ( ) ( ) ( )

if 0, then

if 0, then

if 0, no effect

p y p p

K yp p p

p y

p y

$

$ $ $

For example

CaCO3(s) = CaO(s) + CO2(g) pgo backward

N2(g) + 3H2(g) = 2NH3(g) pgo forward

5 4 3 Th ff t f i t t th


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5.4.3 The effect of inert components on the

equilibrium

B

B

B 0 BB

B

B 0 BB

B

if 0, then

if 0, then

n n

n n

BB

B 0 B

( )n p

n n pK

$

$

Suppose nB is componentn0 is inert componentB B

B

B0 B

B

/( )

p pn

n n

$

Therefore, for reactions of , the addition of inert gases, such aswater vapor or nitrogen, will make the reaction produce more products.

B

B

0

5 4 4 Th ff t f t ti ti th


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5.4.4 The effect of concentration ratio on the

equilibrium

For gas reactionA B Y Za b y z

suppose there is no product in the beginning, and let

the mole ratio of reactants B to A be

B

A

nr

n

When, that is, the molar ratio of two reactants is

equal to the ratio of their stoichiometric coefficients, thecontent of products Y and Z have the maximum values of

mole fraction.

br

a


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5.5 Reactions involving real gases

B B ln Bf

RTp

$ $Real gas

B

eq

Br m ln ( ) ln

fG RT RT K

p

$ $$

B B B

eq eqeqB BB

B B B

( ) ( )f p

Kp p

$ $ $

B B Bf p

KK

5 6 Ch i l ilib i i li id i t


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5.6 Chemical equilibriums in liquid mixture

and solution

B B BlnRT a $

5.6.1 Chemical equilibriums in a liquid mixtureunder ordinary pressure

Beq

r m B

Bln ( ) lnG RT a RT K

$ $

Beq

B

B

( )K a $ B B Ba f x

For ideal liquid mixtures

B

B B

B

1 , 1f f B

eq

B

B

( )K x $


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5.6.2 Chemical equilibriums in a solution under

ordinary pressure

A A AlnRT a $

A Beq eq

r m A BBln( ) ( ) lnG RT a a RT K

$ $

A Beq eq

A B

B

( ) ( )K a a $

solute

For ideal dilute solutions

B

eq

B

B

( )b

Kb

$ $

solvent

B B BlnRT a $

equilibrium

A A Aa f x

B B B/a b b$

eq

B

B

bif is mall


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JACOBUS HENRICUS VANT HOFF

JACOBUS HENRICUS VANT HOFF (1852-1911)Dutch physical chemist, received the first Nobel

Prize in chemistry in 1901 for the discovery of the laws

of chemical dynamics and of osmotic pressure. VantHoff was one of the early developers of the laws of

chemical kinetics, developing methods for

determining the order of a reaction; he deduced the

relation between temperature and the equilibrium

constant of a chemical reaction.


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JACOBUS HENRICUS VANT HOFF

In 1874, vant Hoff (and also J.A. Le Bel, independently)

proposed what must be considered one of the most

important ideas in the history of chemistry, namely the

tetrahedral carbon bond. Vant Hoff carried Pasteurs

ideas on asymmetry to the molecular level , and

asymmetry required bonds tetrahedrally distributed

about a central carbon atom. Structural organic

chemistry was born.


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VANT HOFF (1852-1911) Dutch physical chemist


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Home work

5.1 (calculation of equilibrium constant)5.3 (equilibrium and components)

5.10 (calculation of enthalpy, vant Hoff equation)

5.13 (thermodynamics)

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05 Chem Equilibrium