Enzym Kinetics

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TERM PAPER

CHE-101

“ENZYM KINETICS”

DOA:-26/8/10

DOR:-28/9/10

DOS: 6/11/10

SUBMITTED TO:-

SUBMITTED BY:-

Ms. GEETIKA ARORA Mr.Vivek Kumar

Department Of chemistry, Roll no :-

40



Reg.

No:-11000518

Secti

on:-E6001

ACKNOWLEDGMENTS

This is a humble effort to express our sincere gratitudetowards those who have guided and helped us to complete this project.

A project reported is major milestone during the study period of a student. We could have faced many problems but our teachers’ kind response to our needs and requirement, their patient approach and their positive criticism helped us in making

our project. Very warm thanks to our project-in-charge “MS.GEETIKA ARORA MAM” with her support and constantencouragement AND LPU LIBRARY it was not very easywithout whose support to finish our project .

With the motivation of our parent it was very easy to

finish our project successfully and satisfactorily in short span of

time.

NISHANT KUMAR GARG



CONTENTS

1. Introduction2. Rates, rate laws and rate constant3. Rate of reaction4. Rate laws and rate constants

•

simple rate laws• First order • Second order reaction

1. Importance of rate law2. Pseudo chemical reaction3. Kinetic experiments related to first order.4. Collision theory of reaction rate (arrhenius theory of reaction rate)



INTRODUCTION

Kinetics is the study of the rates of chemical processes in an effort to understandwhat it is that influence these rates and to develop theories which can be used to

predict them.

CHEMICAL KINECTICS is the area of chemistry concerned with the speeds,or rates,at which a chemical reaction occurs.Kinectics refers to the rates of the reaction,or chemical reaction rate,which is thechange in the concentration of the reactant or a product with time.



RATES, RATE LAWS AND RATE CONSTANTS

In this Section we will introduce the language and terms used to describethe rates of chemical reactions. At this stage we will not be concerned withthe theory of reactions or mechanisms, but just stand back and describe theoverall rates.

Rate of reactionThe rate is defined as change in concentration of the reactant and product withrespect to time.Generally,

Reactants=productsAssume,

A+B=C

Rate=-Δ[A]Δt

Rate=-Δ[B]Δt

Rate=Δ[C]Δt

We can talk about the rate of formation or loss of any species – reactant,intermediate or product. It is, however, important to specify which specieswe are talking about. The rate can be positive or negative: a positive ratemeans that the concentration is increasing with time e.g. a product; anegative rate means that the concentration is falling with time e.g. areactant.The rate may vary with time (and concentration), so it is usual to definethe rate over a very small time, . We think of the rate as the derivative of

concentration with respect to time

Rate=Δ[Concentration]Δt



Rate laws and rate constantsExperimentally it is found that rates depend on the concentrations of thespecies involved in the reaction equation (and sometimes on theconcentrations of species which do not appear at first sight to be involved!).The relation between the rate and these concentrations can often be

expressed mathematically in the form of an equation called a rate law.Some rate laws are very simple and some are very complicated. A rate lawmay be determined experimentally (Section 4) or may be the result of atheoretical prediction, or both.THE rates law expresses the relationship of the rate of a reaction to the rateconstant and the concentration of the reactants raised to some powers .

aA+Bb=Cc+Dd

rate=k[A]a[B] b

where k is constant, characteristic of a particular reaction, called the rateconstant or the rate coefficient. The powers a, b ... are also constants: a isthe order with respect to A, b is the order with respect to B.

Simple rate laws

First order

A first order rate law is one in which the rate is proportional to theconcentration raised to the power 1 (hence "first")A=PRODUCTS

Rate=Δ[A]Δt

Rate=k[A]

is called a first order rate constant . The rate equation, and the reactionit describes, is said to be first order in A or it is said that the order with

respect to A is one. As the units of r are concentration time–1 and the unitsof [A] are concentration, the units of RATE in first order reaction are found astime–1.



Second order reactionA=PRODUCTS

Rate=Δ[A]Δt

Rate=k[A]2 A second order reaction has the concentration raised to the power of 2is called a second order rate constant . The rate equation, and thereaction it describes, is said to be second order in A, or the order with



respect to A is two. The units of k 2nd are found to be conc.–1 time–1.

IMPORTANCE of rate law.1. If we know the rate law and the constants in it we can use this to predictthe rate for any set of conditions (concentrations). The rate law is thus avery succinct and practical way of expressing the rate. You might use this,

for example, in a model of the atmosphere or in predicting the rate of anenzyme catalysed reaction.2. The form of the rate law can tell us something about the mechanism of the reaction. This is a point which we will consider in more detail below.3. Knowing the rate law enables us to separate the concentrationdependence from the underlying, fundamental effect which is the size of therate constant.

PSEUDO CHEMICAL REACTIONConsider the general reactions...

A+B=PRODUCTSIn which order with respect to each reactants is 1 that the overall order of reaction

is 2.The rate law is

Rate=k[A][B]however one of the react is present in large excess.,e.g.,one of the reactant may besolvent ,its concentration will remain almost constant.



In that case,the rate of the reaction depend only on the concentration of the reaction present in smallar amount.Theus,the reaction becomes a first order reaction.

There are some reactions which appear to be second order but in factthese are first order reaction with respect to the different reactants i.e.

Now, if one of the reactant is present in high concentration (solvent) then there isvery little change in its concentration. In other words the concentration of thatreactant remains practically constant during the reaction. For example,If [A] = 0.01 M and that of solvent water [B] = 55.5 M, the concentration of Bchanges only from 55.5 to 55.49 M even after the completion of the reaction.Under such conditions, the rate of the given reaction will be according to first order reaction

The reaction therefore, behaves as a first order reaction not a secondorder reaction.

Some examples are1) Pseudo reaction can be explained by taking an example of hydrolysis

of ethyl acetate:The molecularity of the reaction is two because it involves two reacting species,ethyl acetate and water. But the concentration of ethyl acetate changes during the



reaction while the concentration of water remains constant since it is present insuch large excess.

CH3COOC2H5 + H2O= CH3COOH+C2H5OH

According to reaction equation the absolute changes [A] and [B] have the samemagnitude. Since the initial amount of A is smaller, the effect on the concentrationand the reaction rate is much greater for A as for B

You can illustrate this with some numerical values:

Let initial concentartions be [A]₀ = 1 and [B]₀=100At the instant where half of A has reacted away:[A] = 0.5 and [B]= 99.5So [B] has changed only by 0.5% while [A] changed by 50%.Compare reaction rate to intial rate

r = k·0.5·[A]₀·0.995·[B]₀ = 0.4975·k·[A]₀·[B]₀ = 0.4975·r ₀ You can see, that the drop in reaction rate is almost entirely determined by thechange of [A], because the relative change in concentration of A is much larger.

Therefore you can ingnore the change of concentration in [B]thorughout the reaction, if B is in large excess:

[B] ≈ [B]₀The rate equation simplifies to:r = k'·[A]

where k' = k·[B]₀So you can describe reaction kinetics by a pseudo 1st order rate law.

Kinetic Experiments RELATED TO FIRST ORDER.• Bromination of Reactive Aromatics• Fading of Triphenylmethane Dyes• Fading of Phenolphtalein in Alkaline SolutionThe bromination of acetanilide, 4-nitrophenol and diphenylether is based on a

second order reaction:

-Δ[Br]Δt =k.[Ar][Br]If the initial concentration of the aromatic reactant (Ar) is much larger than the

bromine concentration, the concentration of Ar will not change appreciably duringthe course of the reaction The concentration of the aromatic reactant in excess



remains (essentially) constant. Thus the rate’s dependence on bromine can beisolated and the rate law can be written

Δ[Br]Δt=k ’[Br] where k ’=k[Ar]……….(2)

Equation (2) represents the differential form of the rate law. Integration of thisequation and determination of the integration constant C produces thecorresponding integrated law.Substituting [Br] = c into equation (2) yields: -Δ[c]c=k ’.dt ………………..(3)Integrating equation (3) gives:

lnc = −k'⋅t +C ……………. (4)sThe constant of integration C can be evaluated using boundary conditions. At t =0 theconcentration of bromine is C0.Therefore: C = lnC0 …………….. (5)Accordingly is obtained:

lnc = lnc0− k'⋅ t …………………… (6)or

C=C0 e-k’.t ………………… ⋅ (7)The decrease in the bromine concentration can be followed by photometricmeasurement.

COLLISION THEORY OF REACTION RATE (ARRHENIUS

THEORY OF REACTION RATE)



A collision between high energy molecules overcomes the forcesof repulsion and brings the formation of an unstable moleculecluster, called the activated complex. The life span of anactivated complex is very small. Thus, the activated complexbreaks either into reactants again or new substances, i.e.,products. The activation energy (Ea) depends upon the nature of chemical bonds undergoing rupture and is independent of enthalpies of reactants and products. The energy changes duringexothermic and endothermic reactions versus the progress of thereaction

Enzym Kinetics

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