Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of chemical reactions and the design of the reactors in which they take place. Lecture 4

Lecture 4 – Tuesday 1/18/2011 2

ReactorDifferentialAlgebraicIntegral CSTR PFR Batch X t PBR X W 3 Review Lecture 2

6 Only valid if there are no side streams Review Lecture 2

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Two steps to get Step 1: Rate Law Step 2: Stoichiometry Step 3: Combine to get Review Lecture 2

9 A reactor follows an elementary rate law if the reaction orders just happens to agree with the stoichiometric coefficients for the reaction as written. e.g. If the above reaction follows an elementary rate law 2nd order in A, 1st order in B, overall third order Review Lecture 3

E = Activation energy (cal/mol) R = Gas constant (cal/mol*K) T = Temperature (K) A = Frequency factor (same units as rate constant k) (units of A, and k, depend on overall reaction order) 10 T k Review Lecture 3

These topics build upon one another Mole BalanceRate LawsStoichiometry 11 Review Lecture 3

Step 1: Rate Law Step 2: Stoichiometry Step 3: Combine to get 12 Review Lecture 3

A is the limiting Reactant. 13

For every mole of A that react, b/a moles of B react. Therefore moles of B remaining: Let Θ B = N B0 /N A0 Then: 14

SpeciesSymbolInitialChangeRemaining BB N B0 =N A0 Θ B -b/aN A0 X N B =N A0 ( Θ B -b/aX) AAN A0 -N A0 XN A =N A0 (1-X) InertI N I0 =N A0 Θ I N I =N A0 Θ I F T0 N T =N T0 + δ N A0 X Where: and CC N C0 =N A0 Θ C +c/aN A0 X N C =N A0 ( Θ C +c/aX) DD N D0 =N A0 Θ D +d/aN A0 X N D =N A0 ( Θ D +d/aX) 15 δ = change in total number of mol per mol A reacted

Note:If the reaction occurs in the liquid phase or if a gas phase reaction occurs in a rigid (e.g. steel) batch reactor Then etc. 16

Suppose Batch: 17 Equimolar feed: Stoichiometric feed:

and we have ifthen Constant Volume Batch 18

Consider the following elementary reaction with K C =20 dm 3 /mol and C A0 =0.2 mol/dm 3. X e ’ for both a batch reactor and a flow reactor. Calculating the equilibrium conversion for gas phase reaction,X e 19

Step 1: Step 2: rate law, Calculate X e 20

SymbolInitialChangeRemaining B0½ N A0 XN A0 X/2 AN A0 -N A0 XN A0 (1-X) Totals:N T0 =N A0 N T =N A0 - N A0 equilibrium: -r A =0 21 Calculate X e

SpeciesInitialChangeRemaining AN A0 -N A0 XN A =N A0 (1-X) B0+N A0 X/2N B =N A0 X/2 N T0 =N A0 N T =N A0 -N A0 X/2 Solution: At equilibrium Stoichiometry Constant volume Batch Calculating the equilibrium conversion for gas phase reaction 22

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AAF A0 -F A0 XF A =F A0 (1-X) SpeciesSymbolReactor FeedChangeReactor Effluent BB F B0 =F A0 Θ B -b/aF A0 X F B =F A0 ( Θ B -b/aX) Where: 24

SpeciesSymbolReactor FeedChangeReactor Effluent Where: InertI F I0 = A0 Θ I F I =F A0 Θ I F T0 F T =F T0 + δ F A0 X CC F C0 =F A0 Θ C +c/aF A0 X F C =F A0 ( Θ C +c/aX) DD F D0 =F A0 Θ D +d/aF A0 X F D =F A0 ( Θ D +d/aX) and Concentration – Flow System 25

SpeciesSymbolReactor FeedChangeReactor Effluent AAF A0 -F A0 XF A =F A0 (1-X) BB F B0 =F A0 Θ B -b/aF A0 X F B =F A0 ( Θ B -b/aX) CC F C0 =F A0 Θ C +c/aF A0 X F C =F A0 ( Θ C +c/aX) DD F D0 =F A0 Θ D +d/aF A0 X F D =F A0 ( Θ D +d/aX) InertI F I0 =F A0 Θ I F I =F A0 Θ I F T0 F T =F T0 + δ F A0 X Where:and Concentration – Flow System 26

Concentration Flow System: Liquid Phase Flow System: Flow Liquid Phase etc. 27 We will consider C A and C B for gas phase reactions in the next lecture

Mole Balance Rate Laws Stoichiometry Isothermal Design Heat Effects 28

End of Lecture 4 29