Chemical kinetics and catalysis

Outline • Classification of chemical reactions • Definition of chemical kinetics • Rate of chemical reaction • The law of chemical raction rate • Collision theory of reactions, transition state

and activation energy • Factors which make an impact on chemical

reaction rate • Catalysis and catalysts, effects on transition

state of molecules of reactants. • Biocatalysts

Classification of reactions according to phases of reactants

• In homogenic reactions, initial and final reactants are of the same phase (e.g. gases, liquids or solid compounds)

• In heterogenic reactions, initial and final

reactants are of different phases (e.g. one is gaseous, another is liquid or solid)

NO2 (g) + CO (g) NO (g) + CO2 (g)

NH4NO3 (l) NO2 (g) + 2 H2O (g)

Chemical Kinetics • How can we estimate velocity (rate) of chemical

reaction? • A branch of chemistry known as kinetics does study

rates of chemical reactions and factors which can make an impact on the rate of reaction.

• Rate or velocity of a chemical reaction is expressed as a change in a reactant concentration over a change of time.

• Rate units are concentration over time, e.g., mmol/s; mol /h; etc.

timeinchangeionconcentratinchangeRate =

The dependence of reaction rate on concentrations is expressed mathematically by the rate law. The formula of the rate law depends on complexity of a chemical reaction.

Reaction rate • The rate of a reaction is dependent on the

concentration of initial reactants A+B→C A and B are initial reactants or substrates, C is a final reactant or a products • When reactant concentrations decrease, the reaction

rate also do decrease • Factors which can make an impact on a rate of

chemical reaction are: 1) reactant concentration

2) temperature 3) presence and concentration of a catalyst 4) surface area of solids, liquids or catalysts

Complexity of reactions and their classification by a number of reactants 1. A single reactant reaction is unimolecular reaction

A --> B + C (a decomposition) NH4NO3 (l) NO2 (g) + 2 H2O (g)

2. Two reactants reaction is bimolecular reaction A + B --> D + C (most common)

NO2 (g) + CO (g) NO (g) + CO2 (g)

The Rate Law of Unimolecular reactions

• Consider a single substrate reaction The rate, or velocity, v of this reaction is the amount of P formed or

the amount of A consumed per unit time. Thus: Rate law states that: Where k is rate constant. v is a function of [A] to the first power, or

the first order. k is called first order constant.

dtAdvor

dtPdv ][][

−==

PA →

][][ AkdtAdv =−=

First-Order Concentration vs. Time Graphs

The Rate Law of Bimolecular Reactions

• Consider a bimolecular reaction The rate, or velocity, v of this reaction is the amount of P or Q formed

or the amount of A or B consumed per unit time. Thus: Rate law states that: Where k is rate constant. v is a function of [A][B], or second order. k

is the second order rate constant.

dtBd

dtAdvor

dtQd

dtPdv ][][][][

−=−===

QPBA +→+

]][[][ BAkdtAdv =−=

Collision theory of reactions • In a reaction mixture, molecules do collide. • Not each collision results in production of final

reactants (products). • Final products can be formed when colliding

molecules have enough energy. • “Enough energy” means that before collision

molecules moved with big speed. • The minimum collision energy that reactants must

have in order to form products is called activation energy.

Collision theory

Diagram of chemical reaction path

Ground state is a base line state of molecules with low kinetic energy . Transition state is the state corresponding to the highest energy along the reaction coordinate. At this point colliding reactant molecules will always go on to form products.

Change in Activation Energy in exoergonic reactions

The Activation Energy (Ea) is the minimum collision energy that reactants must have in order to form products.

Change in Activation Energy in endergonic reaction

Other factors that affect the rate of reaction

• Temperature at which a reaction occurs. • Concentrations of reactants. • Catalysts.

Effect of temperature on reaction rates

• An increase in T generally increases reaction rate, because more molecules possess enough energy for entering into transition state.

• A 10 oC increase in T usually doubles rate • T affects the rate constant in the reaction rate

equation. • Effect of T on the reaction rate is characterized by

Arrhenius equation

Arrhenius Equation

• Temperature dependence of reaction rate

k = Ae -Ea/RT

• A = collision frequency factor (pZ) • Ea = activation energy

(J)

• R = gas constant (8.314 J/mol-K) • T = temperature (K)

Dependence of the reaction rate on concentration of

reactants • In homogenic systems, the reaction rate

is directly proportional to initial concentrations of reactants:

For reaction A+B→C+D, There fore we can rite the ratio:

K= [A] [B] x [C] [D] x

This is acting mass ratio, where K is a constant of equilibrium

Chemical Equilibrium-1

2 A + B C + D Overall Reaction Suppose the reaction mechanism is:

A + A A2

A2 + B C + D

k1

k2

Reaction Rates k1 [A]2

k2 [A2] [B]

Then the reverse reactions and rates would be:

A + A A2

A2 + B C + D k-2

k-1 [A2]

k-2 [C] [D]

k-1 Reaction Rates

Chemical Equilibrium-2 at equilibrium: forward rate = reverse rate

A2 + B C + D k2

k2 [A2] [B] = k-2 [C] [D]

A + A A2 k1

k1 [A]2 = k-1 [A2]

A + A A2 k-1

Forward Reverse

Similarly…

A2 + B C + D k2

Consider the reaction: A B

Rearrangement of acting mass ratio

vforward = k+1[A] vreverse = k-1[B]

[B]/[A] = Keq = k+1/k-1

• This equation demonstrates that the

equilibrium constant for a chemical reaction is not only equal to the equilibrium ratio of product and reactant concentrations, but is also equal to the ratio of the characteristic rate constants of the reaction.

k+1

k-1

Catalysis • Catalyst

– provides a lower energy path, but it does not alter the energy of the starting material and product

– rather it changes the energy of the transition state in the reaction

– has no effect on the thermodynamics of the overall reaction. – increases the fraction of molecules that have enough energy

to attain the transition state, thus making the reaction go faster in both directions

– does not change the position of the equilibrium (the amount of product versus reactant)

– changes kl and k-1 by the same factor and therefore the equilibrium constant, K, is unchanged, because K = kl/k-1.

Effect of catalyst on reaction energy

Enzymes

• Are biological catalysts. Proteins. • Increase reaction rates by lowering activation

energy. • Increase rates by 106-1012. • Allow reactions to occur under much milder

conditions (low temperature, atmospheric pressure, around neutral pH).

• Enzymes do not affect the thermodynamic properties of a reaction- they do not alter ∆G.

Sequence of events in enzyme catalysed reaction. Non-elementary

reactions Enzymes have an active site- a cleft into which

substrate molecules fit • 1. E + S → ES.

– Enzyme and substrate collide. Substrate binds to active site of enzyme. A transition state forms where the structure of the substrate is altered.

• 2. ES → EP. – Enzyme catalyses the conversion of substrate to

product. Both substrate and product remain in active site.

• 3. EP → E + P. – Product is released from active site.

Activation energy of enzyme catalysed reaction

The rate of a reaction is inversely proportional to ∆G‡. The smaller ∆G‡, the faster the rate of the reaction

Enzyme kinetics • The rate of unimolecular elementary reaction is proportional to the

concentration of the reactant. Thus rate is linearily dependent on [A].

• But if this reaction is catalyzed by an enzyme, the rate shows saturation behavior.

PA → ][][ AkdtAdv =−=

v

[A]

PA Enzyme →v

[A]

The Michaelis-Menten Equation

• This is the complete chemical formula for an enzyme-catalyzed (E) reaction of substrate, S and product, P;

• Michaelis-Menten equation describes the relationship between reaction rate and substrate concentration. It can explain the saturation behavior in catalyzed reactions as shown in the previous slide.

• Michaelis-Menten equation is derived based on the following three conditions: – State steady assumption ([ES] remains constant); – Initial velocity assumption (the reaction rate that is measured

during early reaction period); – Rate law (vforward = vreverse).

PEESSE ++k1

K-1

k2

K-2

The Michaelis-Menten Equation

• From rate constants of previous reaction, the Michaelis-Menten equation was derived.

• Vmax is the maximum velocity of the reaction - when all enzyme molecules are fully active. Km is the concentration of substrate at Vmax/2.

[S]K[S]VV

m

max0 +

×=

Lineweaver-Burk plot

• The values of Vmax and Km can be determined from a Lineweaver-Burk plot - linear transformation of Michaelis-Menten equation.

maxmax

m

0 V1

[S]VK

V1

+=