H o m o g e n e o u s a n d h e t e r o g e n e o u s r e a c t i o n s 1

System — arbitrarily defined part of the universe

Phase — a part of system which is uniform in chemical composition and physical state

Homogeneous system — a system that consists of a single phase

Heterogeneous system — a system that consists of two or more phases

H o m o g e n e o u s a n d h e t e r o g e n e o u s r e a c t i o n s 2

R a t e o f c h e m i c a l r e a c t i o n 3

v = Δn/(V • Δt) Δc = Δn / V v = Δc/Δt

Homogeneous reactions

Rate of homogeneous reaction — the amount of a substance consumed (or produced) in the course of the reaction in one unit of volume per unit of time; or the change of the amount concentration of a substance per unit of time

R a t e o f c h e m i c a l r e a c t i o n 4

Example 1. The amounts of a substance formed per second in the flasks above are 1 and 2 mol, respectively. Compare ν1 and ν2.

V1 = 1 L V2 = 2L

R a t e o f c h e m i c a l r e a c t i o n 5

Example 2. In the first flask, 1.8 g H2O was formed in 1 second. In the second flask 8.1 g HBr was formed in 2 seconds. Compare ν1 and ν2.

V1 = 1 L V2 = 2L

R a t e o f c h e m i c a l r e a c t i o n 6

v = Δn / (S • Δt)

Heterogeneous reactions

Rate of heterogeneous reaction — the amount of substance consumed (or produced) in the course of the reaction on one unit of the phase surface per unit of time

R a t e o f c h e m i c a l r e a c t i o n 7

Example 3. Hydrochloric acid was divided equally between two beakers. One piece of iron was placed into the first beaker; two exactly the same pieces of iron were placed into the second beaker. Compare: a) initial v1 and v2; b) c1(HCl) and c2(HCl) several minutes later; c) v1 and v2 at that moment.

R a t e o f c h e m i c a l r e a c t i o n 8

A v e r a g e a n d i n s t a n t a n e o u s r a t e 9

A → B

A v e r a g e a n d i n s t a n t a n e o u s r a t e 10

νavr = (c2–c1)/Δt = Δca/Δt

νinst = Δc/Δt = (c'2–c1)/Δt =

Δci/Δt = tg α

If t→0 then c'2→c2,

Δci→Δca, and νavr→νinst

S t o i c h i o m e t r y a n d t h e r e a c t i o n r a t e 11

Example: 2 NO2 → N2O4

c1, mol/L 0.5 0.0 t1 = 0 s

Δc, mol/L –0.2 +0.1 Δt = 1 s

c2, mol/L 0.3 0.1 t2 = 1 s

Reaction rate should be always positive, so:

ν(NO2) = –Δc(NO2)/Δt = 0.2/1 = 0.2

ν(N2O4) = Δc(N2O4)/Δt = 0.1/1 = 0.1

S t o i c h i o m e t r y a n d t h e r e a c t i o n r a t e 12

aA + bB → cC + dD

νavr = –(1/a) · νA = –(1/b) · νB = (1/c) · νC = (1/d) · νD

S t o i c h i o m e t r y a n d t h e r e a c t i o n r a t e 13

"General" rate of reaction — the rate defined as above, i. e. νavr or νinst (without index).

Rate of disappearance (consumption) — usually measured for reactants (in a forward process). For example, νA is the rate of the decrease in concentration of reactant A.

Rate of appearance (formation*) — usually measured for products (in a forward reaction). For example, νD is the rate of the increase in concentration of the product D.

M e c h a n i s m s o f c h e m i c a l r e a c t i o n s 14

The reaction energy landscape:

A → B A → [X] → B

E

A

B

transition state E

A

B

transition state 1

Xtransition state 2

mediateinter-

M e c h a n i s m s o f c h e m i c a l r e a c t i o n s 15

Transition state — an assembly of atoms through which the reaction must pass on going from reactants to products in either direction.

Reaction intermediate — molecular entity that is formed from the reactants and reacts further to give the reaction products.

Elementary (simple) reaction proceeds in one step (no intermediates are detected).

Composite (complex) reaction involves more than one elementary reactions.

M e c h a n i s m s o f c h e m i c a l r e a c t i o n s 16

Common types of composite reactions:

Consecutive (stepwise) A B C

Parallel B A C

Consecutive-parallel BACD

Cyclic ABD

CX Y

F a c t o r s a f f e c t i n g t h e r e a c t i o n r a t e 17

a) Nature and structure of reactants — the most obvious but least understood factor.

b) Type of reaction — homogeneous or hetero-geneous.

c) Concentration — the Rate Law (usually applies for homogeneous reactions).

d) Temperature — all elementary and most (but not all) other reaction rates increase with temperature (van't Hoff's rule).

e) Presence of catalysts — catalysis and inhibition, enzymatic catalysis.

T h e R a t e L a w 18

aA + bB → cC + dD

v

= k

• cx(A) • cy(B) v

= k

• cm(C) • cn(D)

In most cases x, y, m, n have small integer values (0, 1, or 2)

For elementary reactions x = a, y = b, m = c, n = d

T h e r e a c t i o n o r d e r a n d m o l e c u l a r i t y 19

The rate coefficient, or rate constant (for an elementary reaction) is concentration independent.

A reaction order in a reactant (x for A, y for B, etc.) can be determined by experiment only.

The overall reaction order — the sum of reaction orders in all reactants (x + y).

The reaction molecularity — the number of reactant molecules involved in the elementary reaction.

T h e r e a c t i o n o r d e r a n d m o l e c u l a r i t y 20

Unimolecular reactions (usually decomposition): 

O3 → O2 + O

N2O4 → 2NO2

Bimolecular reactions (most common): 

2NO2 → N2O4

NO + O3 → NO2 + O2

Termolecular reactions (extremely rare): 

2NO + O2 → N2O4

T h e r e a c t i o n o r d e r a n d m o l e c u l a r i t y 21

Rate controlling step (rcs) — an elementary reaction in a composite reaction sequence the rate constant for which exerts the strongest effect on the overall reaction rate

In most cases the overall rate is equal to the rate of rcs

T h e r e a c t i o n o r d e r a n d m o l e c u l a r i t y 22

Zeroth-order reactions (rare) — the reaction rate is concentration independent: ν = k. Typical for physical processes (evaporation, sublimation, etc.).

First-order reactions (common) — the reaction rate is proportional to a reactant concentration: ν = kcA.

Second-order reactions (most common) — the reaction rate is either first-order in each of two reactants (mixed second-order reaction, ν = kcAcB) or proportional to a square concentration of one of the reactants (simple second-order reaction, ν = kc2

A).

Third-order reactions (very rare) — only a few cases of mixed third-order reactions (ν = kc2

AcB) are known.

K i n e t i c s o f e l e m e n t a r y r e a c t i o n s 23

Zeroth order First order Second order

A → B A → B A → Bν = k ν = k cA ν = k c2

A

c = c0 – kt c = c0e–kt c =

c0/(1 + c0kt)

c

vZero orderFirst orderSecond order

K i n e t i c s o f e l e m e n t a r y r e a c t i o n s 24

Half-life, or half-conversion (t1/2) of a reactant is the time taken for the reactant concentration to decrease two times.

Zeroth order First order Second order

t1/2 = c0/(2k) t1/2 = ln 2/k t1/2 = 1/(c0k)

t

cZero order

First order

Second order

D r u g e l i m i n a t i o n a n d r a d i o a c t i v e d e c a y 25

Most drugs are eliminated by the liver and kidney. Usually it is a first-order process.

Elimination rate constant (Kel) — the fraction of drug eliminated per unit of time.

D r u g e l i m i n a t i o n a n d r a d i o a c t i v e d e c a y 26

Typical t1/2 for drugs are 1.5–36 h (Kel 0.5–0.02 h–1)

50

25

12.56.25

100

4 8 12 16 20 24

c, %

t, h

Drug elimination(Kel = 0.17 h–1)

D r u g e l i m i n a t i o n a n d r a d i o a c t i v e d e c a y 27

Radioactive decay — usually a first-order process.

Example. Isotope 131I is commonly used for the diagnostics of thyroid dysfunction. Calculate the time required to decrease the 131I activity 100 times if the isotope half-life is 8 days.

S t e a d y - s t a t e c o n c e n t r a t i o n 28

Steady-state concentration (ssc) — a period in therapy when the amount of drug administered during a dosing interval exactly replaces the amount of drug eliminated. Usually achieved in six half lives of the drug:

0

0.005

0.01

0.015

0.02

0.025

0 10 20 30 40 50 60 70 80 t, h

c, mmol/L

Drug concentration in plasma Severe side effects level Therapeutic level

S t e a d y - s t a t e c o n c e n t r a t i o n 29

With a higher initial dose, the ssc may be achieved faster (ideally, after the second administration):

0

0.005

0.01

0.015

0.02

0.025

0 10 20 30 40 50 60 70 80 t, h

c, mmol/L

Drug concentration in plasma Severe side effects level Therapeutic level

R e a c t i o n r a t e a n d t e m p e r a t u r e 30

Van't Hoff's rule: the rise in temperature by 10 degrees increases the reaction rate constant 2–4 times:

R e a c t i o n r a t e a n d t e m p e r a t u r e 31

However, van't Hoff's rule does not work for some reactions:

v

T

v

T

v

T20 30 40

Most Few composite Enzymatic reactions reactions  reactions

R e a c t i o n r a t e a n d t e m p e r a t u r e 32

Example. Reaction rate of a reaction with normal temperature dependence is 0.02 mol/(L • s) at 20 °C and 0.18 mol/(L • s) at 40 °C. Calculate the temperature coefficient and the reaction rate at 50 °C.

A c t i v a t i o n e n e r g y 33

A + B ⇄ C + D

Activation energy (Ea) — an empirical parameter

that characterizes the exponential temperature depen-dence of the reaction rate coefficient.

E

A + B

C + D

Ea

A + B

E

C + D

Ea

A c t i v a t i o n e n e r g y 34

Arrhenius equation:

A c t i v a t i o n e n e r g y 35

Increase in temperature increases average energy of particles in the reaction mixture. As a result, the number of particles with any given energy also increases:

Reaction rates are temperature dependent because effective collisions require certain kinetic energy.

T1 T2<n

E

C a t a l y s i s 36

Catalyst — a substance that increases the rate of a reaction but does not affect the overall ΔG0

reaction.

Inhibitor — a substance that decreases the rate of a chemical reaction (sometimes called "negative catalyst").

Catalyst is both a reactant and a product of the reaction, i. e. it does not change in the overall reaction process.

C a t a l y s i s 37

A + B ⇄ C + D

Without catalyst: With catalyst (X):

A + B AB (slowest, E

a) A + X AX (fast)

AX + B AXB (slow, E

a) AB CD (fast) AXB CXD (fast) CXD CX + D (fast) CD C + D (fast) CX C + X (fast)

C a t a l y s i s 38

E

A + B

C + DAXB

EaEa Ea

Ea

A + B ⇄ C + D

C a t a l y s i s 39

Homogeneous catalysis — both the catalyst and the reactants are in the same phase (usually in a solution).

Heterogeneous catalysis — the reaction occurs at or near the surface between phases

T y p i c a l m e c h a n i s m s o f c a t a l y s i s 40

Heterogeneous catalysis (selective or non-selective)

a) Bond formation:

b) Bond cleavage:

X X X X

A B

X X X XA B

A B

X X X X

A B

X X X X X X X XA B

X X X X

A B

T y p i c a l m e c h a n i s m s o f c a t a l y s i s 41

Enzymatic catalysis (highly selective, or specific):

Enzyme — a macromolecule, mostly of protein nature, that functions as a (bio)catalyst.

Substrate — a substance that undergoes a reaction catalyzed by enzyme.

M i c h a e l i s – M e n t e n k i n e t i c s 42

Catalytic saturation — a substrate (S) is present in a large excess over the concentration of enzyme (E).

Typical enzyme-catalyzed reaction ("opposing" process):

E + S [ES] E + Pk1

k1 k2

Michaelis–Menten equation:

M i c h a e l i s – M e n t e n k i n e t i c s 43

Km is equal to the substrate concentration when ν = νmax/2.

Km is not a constant! It depends on the substrate, pH, temperature and concentration of the enzyme.Typical Km values are from 10–5 to 10–1 mol/L.

The lower the Km, the faster the reaction.

v

vmax

Km cS

Firstorder

reaction

Zeroorderreaction

vmax2