Chap 14 14.1 Reaction Coordinate 14.2 - 14.3 Equilibrium - - PowerPoint PPT Presentation

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Chap 14 14.1 Reaction Coordinate 14.2 - 14.3 Equilibrium Compositions 14.4-5, 14.7 Effect of T,P on Equilibrium 14.6 Energy Balances for Reacting Systems 14.8 Multiple Reactions

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14.1 Reaction Coordinate CH4 + H2O = CO + 3 H2 νi

• 1 - 1 1 3

Note: Elliott and Lira νi is stoichiometric number - USE THIS Felder and Rousseau νi is stoichiometric coefficient βi is stoichiometric number Reaction Coordinate dξ = dni /νi

dn dn

1 1 2 2

ν ν =

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At reaction equilibria, Gibbs energy minimized: ni

f

ni

i

viξ + =

4

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Standard State - denoted with superscript o T of system Specified Po, usually 1 bar or 1 atm Composition State of aggregation 14.2 Equilibrium Constraint

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Standard State Gibbs Energy of Rxn at T.

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14.3 Equilibrium Constant for Gas Phase Reaction

8

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Modification of Example 14.3 CO + 2H2 --> CH3OH n · CO2 1 = n · H2 3 = 500 K 10 bar

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Relation of Kinetic Constants to Ka for elementary reaction.

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14.4 Temperature effects on . van’t Hoff Eqn (14.25) (14.26) GT

• and Ka

∆ ∂ ∂ ( / ) D D G RT T H RT

T

• T
• = -

2

∆ ∆ ∆ G RT H RT dT G RT

T

• T
• T

T R

• R

R

= − +

z

2

∆ ∆ ∆ H H C dT

T

• R
• P

T T

R

= +z

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Standard Heat of Reaction (14.27) HR

• ∆

viHR i

,

• ∑

≡ vi HfR i

,

• ∆

∑

νi HfR i

,

• ∆

products

∑

νi HfR i

,

• ∆

reac ts tan

∑

– = =

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Eqn 14.26 becomes

∆ ∆ ∆ ∆ ∆ ∆ ∆ ∆ ∆ ∆ H H a T T b T T c T T d T T J aT b T c T d T

T

• R
• R

R R R

= + − + − + − + − = + + + + ( ) ( ) ( ) ( ) 2 3 4 2 3 4

2 2 3 3 4 4 2 3 4

∆ ∆ ∆ ∆ ∆ G RT J RT a R T bT R cT R dT R I

• =

− − − − + ln 2 6 12

2 3

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Example 14.5 C2H4 + H2O = C2H5OH Kcalc.xls

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Shortcut van’t Hoff (14.31) Example 14.6 (repeat Ex14.5 by shortcut method) C2H4 + H2O = C2H5OH

ln K K G RT G RT H R T T

a aR T

• R
• R

R

• R

F H G I K J =

− = − −

F H G I K J

∆ ∆ ∆ 1 1

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ξ at equilibrium Temperature exothermic reaction endothermic reaction Qualitative behavior of equilibrium conversion for exothermic and endothermic reactions.

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15.6 Energy Balances for Reacting Systems Method 1 n · i

in components

∑

CP i

, TR Tin

∫

dT n · i

• ut

components

∑

CP i

, TR Tout

∫

dT – Q · W ·

S

ξ · HR

• ∆

– + + =

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Method 2 where and Hinn · in Houtn · out – Q · W ·

S

+ + = Hinn · in n · i

in components

∑

H ∆

fR i ,

• CP

TR Tin

∫

dT +     = Houtn · out n · i

• ut

components

∑

H ∆

fR i ,

• CP

TR Tout

∫

dT +     =

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Adiabatic Reactors Example 14.7 1/2 N2 + 3/2 H2 → NH3 Feed 25°C, 100 bar, stoichiometric feed. Find outlet T, ξ for reaction (provided we get it started). n · i

in components

∑

CP i

, TR Tin

∫

dT n · i

• ut

components

∑

CP i

, TR Tout

∫

dT – ξ · HR

• ∆

– =

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Graphical Energy Balance n · i

in components

∑

CP i

, TR Tin

∫

dT n · i

• ut

components

∑

CP i

, TR Tout

∫

dT – ξ · HR

• ∆

– = Tout Tin ξ · HR

• ∆

m · CPm

• –

≈

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ξ at equilibrium Temperature exothermic reaction slope m · CPm HR

• ∆

–

• Tin

Tout ξ

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14.7 Pressure Effects (Doesn’t change Ka) 14.8 Multiple Reactions Example 14.8 solved by Excel

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Summary Relation of ξ to Ka. Relation of Ka to ∆GT

• .

Calculation of ∆GT

• from ∆G298
• and ∆H298
• .

Calculation of ∆G298

• from ∆Gf,298
• for species.

Calculation of ∆H298

• from ∆Hf,298
• for species.

Determination of equilibria for multiple reactions.