Part 4. Formal Kinetics of Complex Reactions · Complex Reaction Catalysis and Chemical Engineering / L2 What means ‘complex ’ ? Reactions of ‘Simple Types’ – rate can be

Catalysis as Phenomenon Catalysis and Chemical Engineering / L2

Part 4. Formal Kinetics of

Complex Reactions

Complex Reaction Catalysis and Chemical Engineering / L2

What means ‘complex’ ?

Reactions of ‘Simple Types’ – rate can be described by

the Law of Mass Action in itsbasic form

In the framework of the Formal Kinetics

Complex reaction – combination of several reactions of ‘simple types’:

1. parallel

2. consecutive A → В → Р

3. reversible (two-side)

Further Complication – combination of more than two ‘simple’ reactionsin general – x(1) + y(2) + z(3)

Complex Reaction Catalysis and Chemical Engineering / L2

What means ‘complex’ ?

2 H2 + O2 → 2 H2O

Complex Reaction Catalysis and Chemical Engineering / L2

What means ‘complex’ ?

CH4 + O2 → <products>

Complex Reaction Catalysis and Chemical Engineering / L2

What means ‘complex’ ?

Chemical Kinetics – the doctrine of the Chemical Processes,

their mechanisms and developmentin time and space

Mechanism of reaction:

for complex (multi-step) reaction –

the sequence of chemical steps and intermediate products(intermediates) that leads from the initial reactant(s) to the finalproduct(s);

for elementary reactions –

trajectories of motions of atomic nuclei, variations of electrondensity and energetic state of the system during its transition from reactant(s) to product(s)

Reverse Kinetic Problem (Task) –

to determine the type of kinetic model (to chose among

possible types of description, kinetic equations, etc.) and/orits parameters based on the existing data on the system

behaviour (experimental data)

– as a rule, incorrectly determined task; has no rigorous andunambiguous solution exclusively based on the kinetic data;

Direct Kinetic Problem (Task) –

to predict (simulate) the system behaviour based on the

existing kinetic model (reaction scheme, kinetic equations) and

its parameters

– requires repeated solution of Direct Kinetic Problem and selectionof ‘optimal’ description of experimental data

Complex Reaction Catalysis and Chemical Engineering / L2

Complex Reaction Catalysis and Chemical Engineering / L2

What means ‘complex’ ?

Reactions of ‘Simple Types’ – rate can be described by

the Law of Mass Action in itsbasic form

Laws and Principles Catalysis and Chemical Engineering / L2

Scientific Laws – models of Objects and Phenomena that reflect:

(i) the current level of their comprehension;

(ii) stable (repeatable, reproducible) relation(ship)sbetween them ⇒

based on practice (observations, experiment, etc.)

Principles – also based on practice ‘tools of knowledge’,

but sublimed to the level of ‘common sense’, i.e.

higher degree of generalization than laws.

Any scientific discipline (including Chemical Kinetics) operates

both laws and principles

Complex Reaction Catalysis and Chemical Engineering / L2

What means ‘complex’ ?

Reactions of ‘Simple Types’ – rate can be described by

the Law of Mass Action in itsbasic form

Complex reactions –

Independence Principle (W.F. Ostwald):

the Law of Mass Action can be used for each ‘simple’ reaction

occurring in the system as if it is the only reaction in given

conditions

Complex Reaction Catalysis and Chemical Engineering / L2

What means ‘complex’ ?

Reactions of ‘Simple Types’ – rate can be described by

the Law of Mass Action in itsbasic form

-d[A]/dt = k1[A] + k2[A] = k’[A]

-d[A]/dt = k1[A];

d[B]/dt = k1[A] – k2[B]

-d[A]/dt = k1[A] – k2[B]

+ mass-balance equations, i.e. [A] + [B] + [D] + [P] = [A]0

Complex Reaction Catalysis and Chemical Engineering / L2

if n1 = n2 = 1:

X = 1- e-(k1+k2)t; Yj = X kj/(Σki); Sj = kj/(Σki)

n1 A → P1

n2 A → P2

if n1 = n2: S1 = S2 @ any X

if n1 < n2: S1/S2 ↑ @ X ↑

‘Simple Complexity’ – some features of

parallel reactions:

Complex Reaction Catalysis and Chemical Engineering / L2

if n1 = n-1 = 1:

-d(1-X)/dt = k1(1-X) – k-1X; Y = 1 – X

and

‘Simple Complexity’ – some features of

reversible (two-side) reactions:

< 1

t → ∞ ⇒

k1C(A) = k-1C(P) ⇒ X → X∞ =

EQUILIBRIUM: rates of all reciprocally reverse processes

(i.e., chemical reactions) are equal

Complex Reaction Catalysis and Chemical Engineering / L2

REVERSIBILITY and EQUILIBRIUM

(L. Botzman, J.C. Maxwell, R. Wegscheider, R.C. Tolman,

A. Einstein, G.N. Lewis, L. Onzager, …)

Complex Reaction Catalysis and Chemical Engineering / L2

Microscopic Reversibility Principle (for Chemistry):

any ‘simple’ (elementary) chemical reaction can proceed in

both reciprocally reverse directions

REVERSIBILITY and EQUILIBRIUM

(L. Botzman, J.C. Maxwell, R. Wegscheider, R.C. Tolman,

A. Einstein, G.N. Lewis, L. Onzager, …)

Detailed Equilibrium (or Balance) Principle:

if the state of global equilibrium is reached in some system, any

partial equilibria are also achievedor

at equilibrium each elementary process should be balanced

by its reverse process

Complex Reaction Catalysis and Chemical Engineering / L2

Microscopic Reversibility Principle (for Chemistry):

any ‘simple’ (elementary) chemical reaction can proceed in

both reciprocally reverse directions

‘thermodynamic consistency’ in microkinetic analysis –

ensures that complex system reaches global equilibrium

at t → ∞

Complex Reaction Catalysis and Chemical Engineering / L2

Detailed Equilibrium (or Balance) Principle:

if the state of global equilibrium is reached in some system, any

partial equilibria are also achieved

Example: Selection of catalysts

СO + H2O СO2 + H2

СH4 + H2O СO + 3H2

! ! ! !

СH4 + CO2 2СO + 2H2

‘basic’ reactions:

‘target’ reaction:

Complex Reaction Catalysis and Chemical Engineering / L2

Detailed Equilibrium (or Balance) Principle:

if the state of global equilibrium is reached in some system, any

partial equilibria are also achieved

Example: Selection of catalysts

СH4 + H2O СO + 3H2

С2H6 + 2H2O 2СO + 5H2

! ! ! !

С2H6 + H2 2СH4

‘basic’ reactions:

‘target’ reaction:

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