Chapter 6 Chemical Reaction Equilbrum

Chapter 6 Chemical Reaction Equilibrium

Dr. Rajan

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Ref: Chapter 13, Introduction to Chemical Engineering, Smith, Van Ness & Abbott, 7th Edition

T,P & Composition

• The rate of a chemical reaction and the maximum possible (or equilibrium) conversion of a chemical reaction are of primary concern and depend on the temperature, pressure and composition of the reactants.

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Rate

• Considering the reaction, oxidation of SO2 to SO3 as an example, a catalyst is required if a reasonable reaction rate is to be attained. With V2O5 catalyst, the rate becomes appreciable at about 573.15 K and continues to increase at higher temperatures.

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Rate Vs Equilibrium

• On the basis of rate alone, one would operate the reactor at the highest practical temperature. However, the equilibrium conversion to SO3 falls as temperature rises decreasing from about 90 % at 793.15 K to 50 % at about 953.15 K. These values represent maximum possible conversion regardless of catalyst or reaction rate.

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Equilibrium & Rate

• Hence both equilibrium and rate has to be considered in the process design .

• Equilibrium conversions can be obtained by thermodynamic calculations.

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Reaction coordinate

• The general chemical reaction can be written as:

where is the stoichiometric coefficient Ai stands for chemical formula are called as stoichiometric numbers It is Positive for products and Negative for reactants

.............. 44332211 AAAA

i

i

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Stoichiometric Numbers

For the reaction

Stoichiometric numbers are:

• Stoichiometric number of an inert species is zero.

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224 3HCOOHCH

3

1

1

1

2

2

4

H

CO

OH

CH

Stoichiometric Numbers

The changes in the numbers of moles of the species are in direct proportion to the stoichiometric numbers. If 0.5 mol of CH4 disappears by reaction, 0.5 mol of H2O must also disappear. Simultaneously 0.5 mol of CO and 1.5 mol of H2 are formed.

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Reaction Coordinate

• This new variable is called the reaction coordinate, characterizes the extent or degree to which a reaction has taken place.

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),....2,1(,.

....3

3

2

2

1

1

1

1

3

3

1

1

2

2

Niddnei

ddndndn

dndn

dndn

ii

Reaction Coordinate

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0

0

0

0

0

0

,

),....3,2,1(

0

n

n

n

ny

isispeciesoffractionmole

nn

nnn

Ninn

ddn

iii

i

i

i

i

i

i

i

iii

i

n

n

i

i

i

Relationship between Conversion and Extent of Reaction

The relation between conversion and the extent of reaction can be written as

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iionz

Equilibrium Criteria to Chemical Reactions

When a chemical reaction occurs at equilibrium, there is no change in the Gibbs free energy of the system , provided the change is taking place at constant temperature and pressure.

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.0)( , PT

tdG

Equilibrium Condition – Closed System

• Total Gibbs energy of a closed system at constant T and P must decrease during an irreversible process and that the condition for equilibrium is reached when total Gibbs energy attains its minimum value.

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The total Gibbs energy in relation to the reaction coordinate

When Gt is plotted against the reaction coordinate, the reaction coordinate has the minimum value at the minimum of the curve. At Equilibrium The total Gibbs energy is at minimum. Its differential is zero.

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Validity

Although the equilibrium expressions are developed for closed systems at constant T and P, they are not restricted in application to systems that are actually closed and reach equilibrium states along paths of constant T and P.

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THE STANDARD GIBBS-ENERGY CHANGE AND THE EQUILIBRIUM CONSTANT

The fundamental property relation for single-phase systems, provides an expression for the total differential of the Gibbs energy:

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Thus the quantity represents, in general, the rate of change of the total Gibbs energy of the system with the reaction coordinate at constant T and P.

Criterion of chemical-reaction equilibrium

Criterion of chemical-reaction equilibrium is therefore:

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Relationship between Standard Gibbs energy change and the equilibrium

constant:

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RT

GK

0

exp

KelvininetemperaturtheisT

tconsgasuniversalKkmol

JR

changeenergyGibbsdardstheisG

tconsmequilibriutheisK

tan.

8314

tan

tan

0

Equilibrium Constant & Standard Gibbs Energy Change

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Equilibrium Constant as Function of Temperature

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If the standard enthalpy of reaction is constant within a

particular temperature range,

1

0

1 T

1

T

1

R

ΔH

K

Kln

Effect of T on K

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• The effect of temperature on the equilibrium constant K is determined by the sign of .

• Thus when is positive, i.e., when the standard reaction is endothermic, an increase in T results in an increase in K.

Standard Heat of Reaction

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