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Chemical Reaction Equilibrium SVNA 13. If sufficient data exist, we can describe the equilibrium state of a reacting system. If the system is able to lower its Gibbs energy through a change in its composition, this reaction is favourable.

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Chemical reaction equilibrium svna 13
Chemical Reaction Equilibrium SVNA 13

  • If sufficient data exist, we can describe the equilibrium state of a reacting system.

    • If the system is able to lower its Gibbs energy through a change in its composition, this reaction is favourable.

    • However, whether or not a reaction will occur in a finite period of time is a question of reaction kinetics.

  • There are several industrially important reactions that are both rapid and “equilibrium limited”.

    • Synthesis gas reaction

    • production of methyl-t-butyl ether (MBTE)

  • In these processes, it is important to know the thermodynamic limit of the reaction extent under different operating conditions.


Reaction extent
Reaction Extent

  • Given a feed composition for a reactive system, we are most interested in the degree of conversion of reactants into products.

    • A convenient measure is the reaction extent, e.

  • Consider the following reaction:

  • In terms of stoichiometric coefficients:

  • where, nCH4 = -1, nH20 = -1, nCO = 1, nH2 = 3

  • For any change in composition due to this reaction,

  • 13.2

  • where de is called the differential extent of reaction.


Reaction extent1
Reaction Extent

  • Note that:

  • (i=1,2,…,N) 13.3

  • The extent of reaction is zero before the reaction starts.

  • We can integrate 13.3 from the start from the start of the reaction to find the number of moles of any species in terms of 

  • so that

  • 13.4

  • How does this help us?


Reaction extent and mole fractions
Reaction Extent and Mole Fractions

  • Relating the reaction extent to mole fractions is accomplished by calculating the total number of moles in the system at the given state.

  • Where,

  • Mole fractions for all species are derived from:

  • 13.5

  • What happens if there is an inert component in the reaction mixture?


Multiple reactions and the reaction extent
Multiple Reactions and the Reaction Extent

  • The reaction extent approach can be generalized to accommodate two or more simultaneous reactions.

  • For j reactions of N components:

  • (i=1,2,…,N)

  • and the number of moles of each component for given reaction extents is:

  • 13.6

  • and the total number of moles in the system becomes:

  • where we can write:


Chemical reaction equilibrium criteria
Chemical Reaction Equilibrium Criteria

  • To determine the state of a

  • reactive system at equilibrium,

  • we need to relate the reaction

  • extent to the total Gibbs

  • energy, GT.

  • We have seen that GT of a

  • closed system at T,P

  • reaches a minimum at

  • an equilibrium state:

  • Eq. 14.64 [14.68]


Reaction extent and gibbs energy
Reaction Extent and Gibbs Energy

  • Consider a single-phase system in which chemical reactions are possible.

    • Changes in Gibbs energy resulting from shifts in temperature, pressure and composition are described by the fundamental equation:

    • At constant temperature and pressure, this reduces to:

  • and the only means the system has to lower the Gibbs

  • energy is to alter the number of moles of individual

  • components.

    • Let’s relate the changes in moles to the reaction extent.


Criterion for chemical equilibrium
Criterion for Chemical Equilibrium

  • For a single chemical reaction, we can apply equation 13.3 which relates the reaction extent to the changes in the number of moles:

  • 13.3

  • Substituting for dni in the fundamental equation yields:

  • At equilibrium at constant T and P, we know that d(nG)/d, = 0. Therefore,

  • 13.8


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