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Interpretation of Batch Reactor Data A rate equation characterizes the rate of reaction, and its form may either be suggested by theoretical considerations or simply be the result of an empirical curve-fitting procedure.The determination of the rate equation is usually a two-step procedure; first the concentration dependency is found at fixed temperature and then the temperature dependence of the rate constants is found, yielding the complete rate equation. Equipment by which empirical information is obtained can be divided into two types,Batch ReactorFlow ReactorBatch ReactorThe batch reactor is simply a container to hold the contents while they react. All that has to be determined is the extent of reaction at various times, and this can be followed in a number of ways, for example: 1. By following the concentration of a given component. By following the change in some physical property of the fluid, such as the electrical conductivity or refractive index. By following the change in total pressure of a constant-volume system. By following the change in volume of a constant-pressure system.This reactor is a relatively simple device adaptable to small-scale laboratory set-ups, and it needs but little auxiliary equipment or instrumentation. Thus, it is used whenever possible for obtaining homogeneous kinetic data. There are two procedures for analyzing kinetic data, Integral and the Differential methods.Interpretation of Batch Reactor Data CONSTANT-VOLUME BATCH REACTORConstant-volume batch reactor we are really referring to the volume of reaction mixture, and not the volume of reactor.Constant-density reaction systemIn a constant-volume system the measure of reaction rate of component i becomes

ConversionIntegral Method of Analysis of DataThe integral method of analysis always puts a particular rate equation to the test by integrating and comparing the predicted C versus t curve with the experimental C versus t data. If the fit is unsatisfactory, another rate equation is guessed and tested.Irreversible Uni-molecular Type First-Order ReactionsConsider the reaction

Irreversible Bimolecular-Type Second-Order Reactions

The integrated expression depends on the stoichiometry as well as the kinetics

When a stoichiometric reactant ratio is used the integrated form is

Irreversible tri-molecular type Third-Order Reactions

Empirical Rate Equations of nth Order

The order n cannot be found explicitly from above Eq. so a trial-and-error solution must be made. Just select a value for n and calculate k. The value of n which minimizes the variation in k is the desired value of n.One curious feature of this rate form is that reactions with order n > 1 can never go to completion in finite time. On the other hand, for orders n < 1 this rate form predicts that the reactant concentration will fall to zero and then become negative at some finite time.

Since the real concentration cannot fall below zero we should not carry out the integration beyond this time for n < 1Zero-Order ReactionsA reaction is of zero order when the rate of reaction is independent of the concentration of materials.

conversion is proportional to timeAs a rule,Reactions are of zero order only in certain concentration ranges (the higher concentrations). If the concentration is lowered far enough, we usually find that the reaction becomes concentration-dependent, in which case the order rises from zero. Zero-order reactions are those whose rates are determined by some factor other than the concentration of the reacting materials, e.g.,The intensity of radiation within the vat for photochemical reactions,.The surface available in certain solid catalyzed gas reactions.Zero-Order ReactionsOverall Order of Irreversible Reactions from the Half-Life t1/2

Half-Life t1/2The half-life method requires making a series of runs, each at a different initial concentration, and shows that The fractional conversion in a given time rises with increased concentration for orders greater than one.Drops with increased concentration for orders less than one.Conversion is independent of initial concentration for reactions of first order.

Fractional Life Method tFThe half-life method can be extended to any fractional life method in which the concentration of reactant drops to any fractional value F = CA/CAo in time tF.

Irreversible Reactions in ParallelConsider the simplest case, A decomposing by two competing paths, both elementary reactions

Irreversible Reactions in Parallel

Irreversible Reactions in Parallel

ExerciseConsider the reaction aA Products. [A]0 = 5.0 M and k = 1.0 x 102 (assume the units are appropriate for each case). Calculate [A] after 30.0 seconds have passed, assuming the reaction is:

Zero order First order Second order4.7 M3.7 M2.0 M33a) 4.7 M

[A] = (1.0102)(30.0) + 5.0

b) 3.7 M

ln[A] = (1.0102)(30.0) + ln(5.0)

c) 2.0 M

(1 / [A]) = (1.0102)(30.0) + (1 / 5.0)

Homogeneous CatalystsThese are catalysts that have the same phase as the reactants. Example:

The formation of SO3 from SO2 and O2 is an exothermic reaction, but the activation energy is very high. The reaction is very slow at low temperature. Increasing the temperature increases the reaction rate, but lowers the yield. Adding nitric oxide, which leads to the formation of transition-state complexes that have lower activation energy, makes the reaction go faster at a moderate temperature.

Homogeneous Catalyzed Reactions

First order rates can be characterized by a "half-life": By definition, the half-life, t1/2, is the time at which [A] = [A]o /2.Substituting this condition in the integrated rate law, we find

Thus the time it takes the reaction to proceed 50% is independent of the initial amount of material! 1Kg or 1mg will react 50% in the same time

-d[A]/dt = k [A]2 Second order processesA------> ProductsThe rate constant depends on the units of concentration, and the probability of reaction per unit time is not a constant throughout the reaction, but depends on the amount of [A] present at any time -d[A]/[A] 1/dt = k [A]

Equation (6) can be directly integrated from [A]o to [A] and t=0 to t to give

The half-life may be derived in the same way as for first order k has units conc-1time-1(not so useful; depends on [A]o)

The half life, t1/2, of a substance is defined as the time it takes for the concentration of the substance to fall to half of its initial value.Another way of determining the reaction order is to investigate the behavior of the half life as the reaction proceeds. Specifically, we can measure a series of successive half lives. t = 0 is used as the start time from which to measure the first half life, t1/2 (1).Then t1/2 (1) is used as the start time from which to measure the second half life, t1/2 (2), and so on.

DEDUCING MECHANISMS FROM RATE DATA

COMPLEX REACTIONS (combinations of elementary steps)Reversible unimolecularParallel unimolecularConsecutive unimolecularConsecutive reversible unimolecular

Reversible unimolecular

1. A connection between kinetics and thermodynamicsThe rate lawNet rate = forward rate - reverse rated[A]/dt = 0At equilibriumk1[A]eqm = k-1[B]eqm

RATE EQUATIONIn an experiment between A and B the initial rate of reaction was found for various starting concentrations of A and B. Calculate...

the individual orders for A and B the overall order of reaction the rate equation the value of the rate constant (k) the units of the rate constant0.5121.5160.528123[A][B]Initial rate (r)r initial rate of reaction mol dm-3 s-1[ ] concentrationmol dm-3