Chemical Reaction Equilibria Chapter 13-Part I

Definition of reaction coordinate A A + B B  C C + D D Stoichiometric coefficients: by convention are 0 for products As the rxn progresses, there is a change in the number of moles of each species, proportional to the stoichiometric numbers

Reaction coordinate (e) We defined: dn i = i d  Integrating between n i o and n i and between 0 and  : n i = n i o + i  Summing over all species: Mole fractions:

example 4NH 3 (g)+ 5O 2 (g)  4NO(g)+6H 2 O(g) Initially there are 2 mol NH 3 and 5 mol O 2 Find mole fractions of reacting species as functions of the reaction coordinate,  n NH3 = 2 -4 

Two or more simultaneous reactions One reaction coordinate  j for each reaction

example C 2 H 4 (g) + ½ O 2 (g)  ((CH 2 ) 2 )O(g) C 2 H 4 (g) + 3 O 2 (g)  2CO 2 (g) +2H 2 O(g) Initially there are 2 mol of C 2 H 4 (g) and 3 mol of O 2 (g). Find expressions for the mole fractions of the reacting species as functions of the reaction coordinates for the two reactions.

j iC2H4C2H4 O2O2 ((CH 2 ) 2 )OCO 2 H2OH2O j 1 2 n o = C 2 H 4 (g) + ½ O 2 (g)  ((CH 2 ) 2 )O(g) C 2 H 4 (g) + 3 O 2 (g)  2CO 2 (g) +2H 2 O(g) n o (C 2 H 4 ) =2; n o (O 2 )=3

Equilibrium criteria for chemical reactions We showed that the total Gibbs energy of a closed system at constant T and P must decrease during an irreversible process. At equilibrium: (dG) T,P =0 For a reacting system, G must be a minimum at equilibrium

Given G=G  minimize and get the value of  at equilibrium. Then you can calculate the equilibrium mole fractions y(  )

how to introduce  in the dG expression

Criterion of chemical equilibrium Now we need to express the chemical potentials as functions of fugacities Solve for  i and substitute in the equilibrium criterion

Definition of equilibrium constant K

Equilibrium constant K where K is a function of temperature

Example: Water-gas shift reaction H 2 (g)+CO 2 (g)  H 2 O(g)+CO(g) Data for  G 0 is given. For a temperature of 1000 K and for a feed of 1 mol H 2 and1 mol CO 2, Determine the equilibrium value of  = n o = y H2 = y CO2 = y H2O = y CO =

 G o data (J/mol) T(K)H2OH2OCOCO 2 1, , , ,790 1, , , ,960 1, , , ,020 1, , , ,080 1, , , ,130 1, , , ,160 dG/d  = 0   =0.453