Plug flow Steady-state flow. Mixed flow

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IDEAL REACTOR TYPES Batch Plug flow Steady-state flow Mixed flow

Ideal Batch Reactor It has neither inflow nor outflow of reactants or products when the reaction is being carried out. Uniform composition everywhere in the reactor (perfectly mixed) No variation in the rate of reaction throughout h t the reactor volume

Batch Reactor All reactants are supplied to the reactor at the outset. The reactor is sealed and the reaction is performed. No addition of reactants or removal of products during the reaction. Vessel is kept perfectly mixed. This means that there will be uniform concentrations. Composition changes with time. The temperature will also be uniform throughout the reactor - however, it may change with time. Generally used for small scale processes. Low capital cost. But high labour costs. Multipurpose, therefore allowing variable product specification.

Typical Laboratory Typical Laboratory Glass Batch Reactor

Typical Commercial Batch Reactor

Ideal Mixed Flow Reactor Normally run at steady state. Uniformly mixed, same composition everywhere within the reactor and at the exit. Generally modelled d as having no spatial variations in concentration, temperature, or reaction rate throughout the vessel CONTINUOUS STIRRED TANK REACTOR (CSTR) BACKMIX REACTOR

Backmixed, Well mixed or CSTR F A0 (C A0 ) Usually U employed for liquid phase reactions. F A (C A ) C A C A Use for gas phase usually in laboratory C A for kinetic studies. Assumption: Perfect mixing occurs.

Characteristics Perfect mixing: the properties of the reaction mixture are uniform in all parts of the vessel and identical to the properties of the reaction mixture in the exit stream (i.e. C A, outlet =C A, tank ) The inlet stream instantaneously mixes with the bulk of the reactor volume. ACSTR reactor is assumed dto reach steady state. t Therefore reaction rate is the same at every point, and time independent. What reactor volume, V r, do we take? V r refers to the volume of reactor contents. Gas phase: V r = reactor volume = volume contents Liquid phase: V r = volume contents

Cutaway view of a CSTR/ Batch Reactor

Ideal Plug Flow Reactor Normally operated at steady state t Fluid passes through the reactor with no mixing of earlier and later entering fluid No radial variation in concentration Referred to as a plug-flow reactor The reactants are continuously consumed as they flow down the length of the reactor. PLUG FLOW REACTOR (PFR), TUBULAR REACTOR

All fluid element have same residence time. Used for either gas phase or liquid phase reactions. The plug flow assumptions tend to hold when there is good radial mixing i (achieved at high h flow rates Re >10 4 ) and when axial mixing may be neglected (when the length divided by the diameter of the reactor > 50 (approx.))

Selection of Reactors Batch Small scale Production of expensive products (e.g. pharmacy) High labor costs per batch Difficult for large-scale production CSTR : most homogeneous liquid-phase flow reactors When intense agitation is required Relatively easy to maintain good temperature control The conversion of reactant per volume of reactor is the smallest of the flow reactors - very large reactors are necessary to obtain high conversions PFR : most homogeneous gas-phase flow reactors Usually produces the highest conversion per reactor volume of any of the flow reactors Difficult to control temperature within the reactor Hot spots can occur

Suppose a single-phase reaction The Rate Equation The most useful measure of reaction rate for reactant A is then: In addition, the rates of reaction of all materials are related by:

Experience shows that the rate of reaction is influenced by the composition and the energy of the material. By energy we mean the temperature (random kinetic energy of the molecules), the light intensity within the system (this may affect the bond energy between atoms), the magnetic field intensity, etc. Ordinarily we only need to consider the temperature, so let us focus on this factor. Thus, we can write

Rate constant, k It is strongly dependent on temperature. In gas-phase reactions It depends on catalysts and may be a function of total pressure. In liquid idsystem It can be a function of total pressure. It may depend d on ionic i strength th and choice of solvent. Here, we consider the temperature t only.

Rate of reaction and temperature Empirical Observations. It was the Swedish chemist Svante Arrhenius who first suggested that the temperature dependence of the specific reaction rate constant, k, could be correlated by an equation of the type: k reaction rate constant Ae E RT Arrhenius Equation Where : A= preexponential factor or frequency factor (1/time) E= Activation energy, J/mol or cal/mol R= Gas constant, 8.314 J/mol K (or 1.987 cal/mol K) T= Absolute temperature, K

Arrhenius equation has been verified empirically to give the temperature behaviour of most reaction rate constants (within experimental accuracy) over fairy large experimental ranges. Activation energy determined experimentally by carrying out the reaction at several temperatures. After taking the natural logarithm of the Arrhenius equation : lnk ln A E 1 R T ln k -E/R 1/T

Example 3-1(Fogler) Calculate the activation energy for the firstorder decomposition reaction of benzene diazonium chloride to give chlorobenzene and nitrogen: ln k A 1/T Arrhenius Equation k (T) ( ) A Ae E/RT E 1 ln k A ln A R T

ln k 37.12 A 14017 T kj E (14017K)R (14017K) 8.314 116.5 mol K kj mol A 1.32 10 s 16 1 16 14017K k A (T) 1.3210 exp T Arrhenius Equation

Homogeneous Heterogeneous Elementary Non-elementary Single Multiple Classification of Reactions Chemical Bio-chemical Reversible Irreversible Exothermic Endothermic Constant density Variable density Catalytic Non-catalytic

When a single stoichiometric equation and single rate equation are chosen to represent the progress of the reaction, we have a single reaction. When more than one stoichiometric equation is chosen to represent the observed changes, then more than one kinetic expression is needed d to follow the changing composition of all the reaction components, and we have multiple reactions. Multiple reactions may be classified as: series reactions: parallel reactions, which are of two types:

and more complicated schemes, an example of which is Here, reaction proceeds in parallel with respect to B, but in series p p p with respect to A, R, and S.

Order of reaction One of the most general forms: a b d r kc AC B...C D where k = velocity constant or specific rate constant. If C A, C B,. = 1; then r=k a, b = reaction order with respect to C A, C B. a + b +... +d = overall order (this treatment is only applicable to simple reactions). Reaction order Power to which concentration is raised to make rate proportional p to it. It can only be determined experimentally.

Elementary reaction Elementary reaction is one that evolves a single step. Thestoichiometric coefficients in an elementary reaction are identical to the powers in the rate law: OCH OH CH3O OH 3 O k O C O C CH OH r 3 An elementary reaction has an elementary rate law. Some reaction follows an elementary rate law is not an elementary reaction. 2NO O 2NO 2 2 H I 2HI 2 2 r k NO r k NO C C 2 NO H2 H2 H2 I2 C C O 2

Molecularity This is the number of atoms, ions, or molecules involved (colliding) in a reaction. Examples: (i) Bimolecular reaction, since two species are involved in the reaction step. H I 2HI, p 2 2 (ii) 238 234 4 92U 90Th 2He Unimolecular urianium-238 thorium helium

Representation of an Elementary Reaction In expressing a rate we may use any measure equivalent to concentration (for example, partial pressure), in which case: Whatever measure we use leaves the order unchanged; however, it will affect the rate constant k. For brevity, elementary reactions are often represented by an equation showing both the molecularity and the rate constant. For example, k 2A 1 2R represents a biomolecular irreversible reaction with second-order order rate constant k 1, implying that the rate of reaction is

Representation of an Elementary Reaction It would not be proper p to write mentioned equation as: A k 1 for this would imply that the rate expression is: R Thus, we must be careful to distinguish between the one particular equation that represents the elementary reaction and the many possible representations of the stoichiometry.

Representation of an Elementary Reaction

Representation of a Nonelementary Reaction A nonelementary reaction is one whose stoichiometry does not A nonelementary reaction is one whose stoichiometry does not match its kinetics.

Kinetic Models for Nonelementary Reactions If the kinetics of the reaction: Indicates that the reaction is nonelementary, we may postulate a series of elementary steps to explain the kinetics, such as

Kinetic Models for Nonelementary Reactions Free radicals Ions and polar substances Types of intermediates Molecules Transition complexes

Nonchain Reactions Chain Reactions

Examples of mechanisms of various kinds

Free radicals chain reaction mechanism k 1 H Br 2HBr 2 2 k 2 r f k k 1 2 1C H CBr C 2 2 C 2 HBr Br 2 This is not a bimolecular reaction.

Because the reaction occurs as follows: Br2 2Br Br HBr H H H 2 Br 2 HBr H H2 2Br B HBr Br r 2 Br Initiation Propagation Termination Each step has a molecularity, which must be an integer. Thus, order and molecularity l are not necessarily identical for a given reaction.

Molecular intermediates nonchain mechanism The general class of enzyme catalyzed fermentation reactions: with experimental rate is viewed to proceed with intermediate (A. enzyme)* as follows:

Transition complex nonchain mechanism The spontaneous decomposition of azomethane

we hypothesize the existence of either of two types of intermediates. Type 1. An unseen and unmeasured intermediate X usually present at very small concentration This is called the steady-state approximation.

Type 2. a homogeneous catalyst of initial concentration Co is present in two forms, free catalyst C combined in an appreciable extent to form intermediate X

Example 2.1 SEARCH FOR THE REACTION MECHANISM The irreversible reaction A+B=AB has been studied kinetically, and the rate of formation of product has been found to be well correlated by the following rate equation: r kc independent of C 2 AB A B What reaction mechanism is suggested by this rate expression if the chemistry of the reaction suggests that the intermediate consists of an association of reactant molecules and that a chain reaction does not occur?

If this were an elementary reaction, the rate would be given by r kc C k[a][b] AB A B Model 1 1 2A A k * k 2 which h really involves four elementary reactions 2 k * 3 A2 B AAB k4 k 1 * 2A A 2 * A2 k 2 2A k A B 3 AAB * 2 k 4 A ABA * B 2

1 2 * rab k 3 [A 2 ][B] k 4 [A][AB] 2 * * r k A * 1[A] k 2[A 2] k 3[A 2][B] k 4[A][AB] 2 r 0 A * 2 [A ] * 2 1 2 k[a] 1 k[a][ab] 4 2 k k [B] 2 3 r AB 1 2 k 1k 3[A] [B] k2k 4[A][AB] 2 k k [B] [ ] 2 3

r AB 1 k k [A] 2 [B] 1 3 k k [A][AB] 2 4 2 k k [B] 2 3 if k 2, is very small, this expression reduces to r AB 1 kk[a][b] 2 1 3 kk[a][ab] 2 4 2 k k [B] 2 3 r 1 k [A] 2 AB 1 if k 2, is very small, this expression reduces to 2 r AB 2 (k1k3 2k 2)[A] [B] 1 (k k )[B] 3 2

Model 2 k 1 * BB B 2 k * 3 AB2 AAB k4

Example 2.2 SEARCH FOR A MECHANISM FOR THE ENZYMESUBSTRATE REACTION Here, a reactant, called the substrate, is converted to product by the action of an enzyme, a high molecular weight (MW > 10000) protein-like substance. An enzyme is highly specific, catalyzing one particular reaction, or one group of reactions. Thus, A Enzyme Many of these reactions exhibit the following behavior: 1. A rate proportional to the concentration of enzyme introduced into the mixture [E 0 ]. R 2. At low reactant concentration the rate is proportional to the reactant tconcentration, ti [A]. 3. At high reactant concentration the rate levels off and becomes independent d of reactant t concentration. ti Propose a mechanism to account for this behavior.

Michaelis and Menten (1913) were the first to solve this puzzle. They guessed that the reaction proceeded as follows: with the two assumptions 1 A E X 2 3 XRE [E 0 ]=[E]+[X] [X] d[x] dt d[x] 0 dt d[r] k[x] 3 dt k [A][E] k [X] k [X] 0 1 2 3

[X] k[a][e 1 0] (k k ) k [A] 2 3 1 d[r] dt k[x] 3 d[r] k1k 3[A][E 0] k 3[A][E 0] dt (k k ) k [A] (k k ) k [A] 2 3 1 2 3 1 d[r] k[a][e] 3 0 dt [M] [A] d[a] dt d[r] dt [E 0] [A] when [A] [M] isindependent of [A]when [A] [M]

TEMPERATURE-DEPENDENT TERM OF A RATE EQUATION Temperature Dependency from Arrhenius' Law r f (temperature) f (composition) i 1 2 k f (composition) 2 k k e 0 E RT where k 0 is called the frequency or pre-exponential p factor and E is called the activation energy of the reaction ln r 2 k2 E 1 1 ln r k RT T 1 1 1 2 provided that E stays constant.

TEMPERATURE-DEPENDENT TERM OF A RATE EQUATION Comparison of Theories with Arrhenius' Law m E RT k k0t e 0 m 1 summarizes the predictions of the simpler versions of the collision and transition state theories for the temperature dependency of the rate constant. For more complicated versions m can be as great as 3 or 4. Now, because the exponential term is so much more temperaturesensitive than the pre-exponential term, the variation of the latter with temperature is effectively masked, thus k 0 k e E RT

Reactions Any Fromgiven Arrhenius' the Arrhenius reaction with high lawis law, aactivation much plot theofvalue more ln kenergies vs of temperature-sensitive 1/T the gives frequency are avery straight factor temperature- line, k, adoes with low large sensitive; temperature not affect slopethe reactions for than temperature large ae with high andsensitivity. low temperature. small activation slope for small energies E. are relatively temperature-insensitive.

Example 2.3 SEARCH FOR THE ACTIVATION ENERGY OF A PASTEURIZATION PROCESS Milk is pasteurized if it is heated to 63 C for 30 min, but if it is heated to 74 C it only needs 15 s for the same result. Find the activation energy of this sterilization process. assuming an Arrhenius temperature dependency ln r 2 t1 E 1 1 ln r t RT T 1 2 1 2 ln t 1 30 E 1 1 ln E=422000 J/mol 0.25 t 8.314 336 347 2