Catalysis - Chemical Kinetics Chemistry Notes | EduRev

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Chemistry : Catalysis - Chemical Kinetics Chemistry Notes | EduRev

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CATALYSIS

A catalyst is a substance that participates in chemical reaction by increasing the rate of reaction, yet the catalyst itself remains intact after the reaction is complete.
The mechanism describing a catalytic process is as follows:

Catalysis - Chemical Kinetics Chemistry Notes | EduRev

Where S represents the reactant; C is catalyst and P is the product. The reactant or substrate-catalyst complex is represented by SC and is an intermediate.
The rate expression for product formation is

 Catalysis - Chemical Kinetics Chemistry Notes | EduRev             …(1)

Because SC is an intermediate than apply S.S.A. on the formation of SC.

Catalysis - Chemical Kinetics Chemistry Notes | EduRev
Catalysis - Chemical Kinetics Chemistry Notes | EduRev                               …(2)
Catalysis - Chemical Kinetics Chemistry Notes | EduRev= composite constant 

then   Catalysis - Chemical Kinetics Chemistry Notes | EduRev                           …(3)

The relationship between initial concentration and the concentration of all species present after the reaction is:
          [S]0 = [S] + [SC] + [P]
          [C]0 = [C] + [SC]
then   [S] = [S]– [SC] – [P]               …(4)
&        [C] = [C]0 – [SC]                             …(5)
Substituting these values in equation (2), we get

 Catalysis - Chemical Kinetics Chemistry Notes | EduRev

Km[SC] = ([S]0 – [SC] – [P]) ([C]0 – [SC])

Catalysis - Chemical Kinetics Chemistry Notes | EduRev 

then rate of the reaction becomes

 Catalysis - Chemical Kinetics Chemistry Notes | EduRev

Case I.             

[C]0 <<  [S]0

i.e. much more substrate is present in comparison to catalyst. Then

 Catalysis - Chemical Kinetics Chemistry Notes | EduRev

if                           km < [S]0

Then Catalysis - Chemical Kinetics Chemistry Notes | EduRev

i.e. zero order reaction with respect to substrate.

&  Catalysis - Chemical Kinetics Chemistry Notes | EduRev

Catalysis - Chemical Kinetics Chemistry Notes | EduRev

 when concentration of substrate [S]0 >> km then reaction rate

R0 = k2[C]0 = Rmax

i.e. the rate of reaction will reach a limiting value where the rate becomes zero order in substrate concentration.
 

Case II.

[C]0 >>  [S]0

 Catalysis - Chemical Kinetics Chemistry Notes | EduRev

i.e. the reaction rate is first order in [S]0, but can be first or zero order in [C]0 depending on the size of [C]relative to km.

Michaelis-Menten Enzyme Kinetics.

Enzyme are protein molecules that serve as catalysts in a chemical reaction.

 Catalysis - Chemical Kinetics Chemistry Notes | EduRev
                                                                            Catalysis - Chemical Kinetics Chemistry Notes | EduRev

The kinetic mechanism of enzyme catalyst can be described using the Michaelis-Menten mechanism.

 Catalysis - Chemical Kinetics Chemistry Notes | EduRev

The kinetic mechanism of enzyme catalyst can be described using the Michaelis-Menten mechanism.

 Catalysis - Chemical Kinetics Chemistry Notes | EduRev

But in this mechanism substrate concentration is greater than that of enzyme i.e.

[S]0 >> [E0]
then rate of formation of product in enzyme catalyst is

 Catalysis - Chemical Kinetics Chemistry Notes | EduRev                …(1)

The co mposite constant km is referred to as the Michaelis constant in enzyme kinet ics and the equation is referred to as the Michaelis-Menten rate law.
When [S]0 >> km, the Michaelis constant can be neglected, resulting new expressio n for the rate.
R0 = k2[E]= Rmax 

The reciprocal equation of equation (1) is the Lineweaver-Burk equation i.e.

 Catalysis - Chemical Kinetics Chemistry Notes | EduRev

Catalysis - Chemical Kinetics Chemistry Notes | EduRev             …(2)

This equation is known as Lineweaver-Burk equation.
The plot of reciprocal of rate is known as Linewearver-Burk plot. k2 is known as turn over numberof the enzyme. “The turn over number is the maximum number of substrate molecules per uit time that can be converted into product.”

 Catalysis - Chemical Kinetics Chemistry Notes | EduRev

This is Linewearver-Burk plot.
We know that    

 Catalysis - Chemical Kinetics Chemistry Notes | EduRev

Case I. ` [S]>> km

 Catalysis - Chemical Kinetics Chemistry Notes | EduRev

i.e. rate is maximum due to all enzyme are present

R = Rmax = k2[E]0

This is zero order w.r.t. substrate.

 Case II.      If                    [S]= km

Catalysis - Chemical Kinetics Chemistry Notes | EduRev

Case III.       If                    [S] << km

Catalysis - Chemical Kinetics Chemistry Notes | EduRev

This is first order w.r.t. substrate.

 Catalysis - Chemical Kinetics Chemistry Notes | EduRev

This is graph between initial rate and concentration of substrate.
 

G.S. Eadie Plot 

We know that,

 Catalysis - Chemical Kinetics Chemistry Notes | EduRev

Multiplying with R,

 Catalysis - Chemical Kinetics Chemistry Notes | EduRev

Multiplying with Catalysis - Chemical Kinetics Chemistry Notes | EduRev

 Catalysis - Chemical Kinetics Chemistry Notes | EduRev

 or

 Catalysis - Chemical Kinetics Chemistry Notes | EduRev

Catalysis - Chemical Kinetics Chemistry Notes | EduRev 

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