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Physical-Chemistry II

Chapter-2-The rates of chemical reactions

الكيميائيةسرعات التفاعالت

Dr. El Hassane ANOUAR

Chemistry Department, College of Sciences and Humanities, Prince Sattam bin

Abdulaziz University, P.O. Box 83, Al-Kharij 11942, Saudi Arabia.

4/28/2017 College of Science and humanities, Al-kharj 1

Physical

Chemistry II

(Chem 3320)

Important :

These slides are prepared in reference to chapter 21 in Physical Chemistry, Ninth

Edition, Peter Atkins, and Julio De Paula


3. Examples of reaction mechanisms

3.1 Unimolecular reactions

First-order gas-phase reactions are widely called ‘unimolecular reactions’

because they also involve an elementary unimolecular step in which the reactant

molecule changes into the product.

Example: The isomerization of cyclopropane:

𝐜𝐲𝐜𝐥𝐨 − 𝐂𝟑𝐇𝟔 → 𝐂𝐇𝟑𝐂𝐇 = 𝐂𝐇𝟐 𝒗 = 𝐤𝐫 [𝐜𝐲𝐜𝐥𝐨 − 𝐂𝟑𝐇𝟔]

In a first-order rate laws, presumably a molecule acquires enough energy to react

as a result of its collisions with other molecules.

However, collisions are simple bimolecular events, so how can they result in a

first-order rate law?

The overall mechanism has bimolecular as well as unimolecular steps.


3.1.2 The Lindemann–Hinshelwood mechanism



In Lindemann–Hinshelwood mechanism, it is supposed

that a reactant molecule A becomes energetically excited

by collision with another A molecule in a bimolecular

step. 𝐀 + 𝐀 → 𝐀∗ + 𝐀 𝐯 =

𝐝 𝐀∗

𝐝𝐭= 𝐤𝐚 𝐀

𝟐

A* might lose its excess energy by collision

with another molecule

𝐀 + 𝐀∗ → 𝐀 + 𝑨

𝒗 =𝐝 𝐀∗

𝐝𝐭= −𝒌𝒂

′ 𝐀 𝐀∗

Alternatively, A* might shake itself apart and form

products P (i.e., it might undergo the unimolecular

decay

𝐀∗ → 𝐏

𝒗 =𝐝 𝐀∗

𝐝𝐭= −𝐤𝒃 𝐀

∗





𝐀 + 𝐀 → 𝐀∗ + 𝐀

𝐯 =𝐝 𝐀∗


𝟐

𝐀 + 𝐀∗ → 𝐀 + 𝑨

𝒗 =𝐝 𝐀∗


′ 𝐀 𝐀∗

𝐀∗ → 𝐏

𝒗 =𝐝 𝐀∗

𝐝𝐭= −𝐤𝐚 𝐀

∗

If the unimolecular step is slow enough to be the

rate-determining step

The overall reaction will have first-order kinetics,

as observed.

This conclusion can be demonstrated explicitly by

applying the steady-state approximation to the net

rate of formation of A*:

𝐝 𝐀∗


𝟐 − 𝒌𝒂′ 𝐀 𝐀∗ − 𝐤𝐛 𝐀

∗ ≈ 𝟎

𝐀∗ =𝐤𝐚 𝐀

𝟐

𝐤𝐛 + 𝐤𝐚′ 𝐀





𝐀 + 𝐀 → 𝐀∗ + 𝐀

𝐯 =𝐝 𝐀∗


𝟐

𝐀 + 𝐀∗ → 𝐀 + 𝑨

𝒗 =𝐝 𝐀∗


′ 𝐀 𝐀∗

𝐀∗ → 𝐏

𝒗 =𝐝 𝐀∗


∗

𝐝 𝐏

𝐝𝐭= 𝐤𝐛 𝐀

∗ =𝐤𝐚𝐤𝐛 𝐀

𝟐


So, the rate law for the formation of P is

At this stage the rate law is not first-order.

However, if the rate of deactivation by (A*,A) collisions

is much greater than the rate of unimolecular decay:

ka′ A A∗ ≫ kb A

∗ or ka′ A ≫ kb

Thus 𝐝 𝐏

𝐝𝐭= 𝐤𝐫 𝐀 ; 𝐤𝐫 =

𝐤𝐚𝐤𝐛𝐤𝐚′

Is a first-order rate law





𝐀 + 𝐀 → 𝐀∗ + 𝐀

𝐯 =𝐝 𝐀∗


𝟐

𝐀 + 𝐀∗ → 𝐀 + 𝑨

𝒗 =𝐝 𝐀∗


′ 𝐀 𝐀∗

𝐀∗ → 𝐏

𝒗 =𝐝 𝐀∗


∗

Lindemann–Hinshelwood mechanism can be

tested because it predicts that, as the

concentration (and therefore the partial

pressure) of A is reduced, the reaction should

switch to overall second-order kinetics. Thus,

when ka′ [A] << kb, the rate law

𝐝 𝐏

𝐝𝐭= 𝐤𝐛 𝐀

∗ =𝐤𝐚𝐤𝐛 𝐀

𝟐

𝐤𝐛 + 𝐤𝐚′ 𝐀≈ 𝐤𝐚 𝐀

𝟐


The physical reason for the change of order is that at

low pressures the rate-determining step is the

bimolecular formation of A*




𝐀 + 𝐀 → 𝐀∗ + 𝐀

𝐯 =𝐝 𝐀∗


𝟐

𝐀 + 𝐀∗ → 𝐀 + 𝑨

𝒗 =𝐝 𝐀∗


′ 𝐀 𝐀∗

𝐀∗ → 𝐏

𝒗 =𝐝 𝐀∗


∗

𝐝 𝐏

𝐝𝐭= 𝐤𝐫 𝐀 𝐤𝐫 =

𝐤𝐚𝐤𝐛 𝐀


The effective rate constant, kr, can be rearranged to

𝟏

𝐤𝐫= 𝐤𝐚′

𝐤𝐚𝐤𝐛+ 𝟏

𝐤𝐚 𝐀

a test of the theory is to plot 1/kr against 1/[A], and to

expect a straight line


3.1.2 The activation energy of a composite reaction



Although the rate of each step of a complex

mechanism might increase with temperature and

show Arrhenius behaviour. Is that true of a

composite reaction? 𝐀 + 𝐀 → 𝐀∗ + 𝐀

𝐯 =𝐝 𝐀∗


𝟐

𝐀 + 𝐀∗ → 𝐀 + 𝑨

𝒗 =𝐝 𝐀∗


′ 𝐀 𝐀∗

𝐀∗ → 𝐏

𝒗 =𝐝 𝐀∗


∗

Consider the high-pressure limit of the Lindemann–

Hinshelwood mechanism as expressed in eqn:

𝐤𝐫 = 𝐤𝐚𝐤𝐛𝐤𝐚′

If each of the rate constants has an Arrhenius like

temperature dependence, we can write





𝐀 + 𝐀 → 𝐀∗ + 𝐀

𝐯 =𝐝 𝐀∗


𝟐

𝐀 + 𝐀∗ → 𝐀 + 𝑨

𝒗 =𝐝 𝐀∗


′ 𝐀 𝐀∗

𝐀∗ → 𝐏

𝒗 =𝐝 𝐀∗


∗

If each of the rate constants has an Arrhenius like

temperature dependence, we can write

𝐤𝐫 = 𝐤𝐚𝐤𝐛𝐤𝐚′ =

𝐀𝐚𝐞−𝐄𝐚(𝐚)/𝐑𝐓 𝐀𝐛𝐞

−𝐄𝐛(𝐛)/𝐑𝐓

𝐀𝐚′ 𝐞−𝐄𝐚

′(𝐚)/𝐑𝐓

=𝐀𝐚𝐀𝐛𝐀𝐚′ 𝐞−{𝐄𝐚 𝐚 +𝐄𝐛 𝐛 −𝐄𝐚

′ 𝐚 }/𝐑𝐓

The composite rate constant kr has an Arrhenius-like

form with activation energy

𝐄𝐚 = 𝐄𝐚 𝐚 + 𝐄𝐛 𝐛 − 𝐄𝐚′ 𝐚





The composite rate constant kr has an Arrhenius-like form with activation energy

𝐄𝐚 = 𝐄𝐚 𝐚 + 𝐄𝐛 𝐛 − 𝐄𝐚′ 𝐚

Provided Ea a + Eb b > Ea′ a

=> Ea is positive and the rate increases with T.

However, it is conceivable that Ea a +

Eb b < Ea′ a => Ea is negative and the

rate will decrease as T is raised.



3.2 Polymerization kinetics

There are two major classes of polymerization processes

stepwise polymerization:

Any two monomers present in the reaction mixture can link together at any time and

growth of the polymer is not confined to chains that are already forming.

As a result, monomers are consumed early in the reaction and, as we

shall see, the average molar mass of the product grows with time.


Chain polymerization:

An activated monomer, M, attacks another monomer, links to it, then that unit attacks

another monomer, and so on. The monomer is used up as it becomes linked to the

growing chains.



High polymers are formed rapidly and only the yield, not the average molar mass, of

the polymer is increased by allowing long reaction times.




3.2.1 Stepwise polymerization

Stepwise polymerization commonly proceeds by a condensation reaction, in which

a small molecule (typically H2O) is eliminated in each step.

Stepwise polymerization is the mechanism of production of polyamides, as in the

formation of nylon-66:

H2N(CH2)6NH2 + HOOC(CH2)4COOH → H2N(CH2)6NHCO(CH2)4COOH + H2O →

H–[NH(CH2)6NHCO(CH2)4CO]n–OH

Because the condensation reaction can occur between molecules containing any

number of monomer units, chains of many different lengths can grow in the

reaction mixture.





H2N(CH2)6NH2 + HOOC(CH2)4COOH → H2N(CH2)6NHCO(CH2)4COOH + H2O →

H–[NH(CH2)6NHCO(CH2)4CO]n–OH

Because the condensation reaction can occur between molecules containing any number of

monomer units, chains of many different lengths can grow in the reaction mixture.

In the absence of a catalyst, we can expect the condensation to be overall second order in

the concentration of the –OH and –COOH (or A) groups, and write

𝐝 𝐀

𝐝𝐭= −𝐤𝐫 𝐎𝐇 𝐀

because there is one –OH group for each –COOH group, this equation is the same as

𝐝 𝐀

𝐝𝐭= −𝐤𝐫 𝐀

𝟐





Assume the rate constant for the condensation is independent of the chain length,

then kr remains constant throughout the reaction. Thus, the solution of the above

rate law is

𝐝 𝐀

𝐝𝐭= −𝐤𝐫 𝐀

𝟐

𝐀 =𝐀 𝟎

𝟏 + 𝐤𝒓𝒕 𝐀 𝟎

The fraction, p, of –COOH groups that have condensed at time t is

𝐩 =𝐀 𝟎 − 𝐀

𝐀 𝟎=𝐤𝒓𝒕 𝐀 𝟎𝟏 + 𝐤𝒓𝒕 𝐀 𝟎

The degree of polymerization defined as the average number of monomer

residues per polymer molecule. This quantity is the ratio of the initial concentration

of A, [A]0, to the concentration of end groups, [A], at the time of interest, because

there is one A group per polymer molecule.


The average number of monomers per polymer

molecule, ⟨N⟩, is




𝐍 =𝐀 𝟎𝐀=𝟏

𝟏 − 𝐩

𝐩 =𝐤𝒓𝒕 𝐀 𝟎𝟏 + 𝐤𝒓𝒕 𝐀 𝟎

we express p in terms of the rate constant kr

𝐍 = 𝟏 + 𝐤𝒓𝒕 𝐀 𝟎

The average length grows linearly with

time. Therefore, the longer a stepwise

polymerization proceeds, the higher the

average molar mass of the product.




3.2.2 Chain polymerization

In a chain reaction, a reaction intermediate produced in one step generates an

intermediate in a subsequent step, then that intermediate generates another

intermediate, and so on.

The intermediates in a chain reaction are called chain carriers.

In a radical chain reaction the chain carriers are radicals (species with unpaired

electrons).

Chain polymerization occurs by addition of monomers to a growing polymer,

often by a radical chain process. It results in the rapid growth of an individual

polymer chain for each activated monomer.


The central feature of the kinetic analysis is that the rate of polymerization is

proportional to the square root of the initiator concentration:




𝒗 = 𝒌𝒓 𝑰𝟏/𝟐 𝑴

The kinetic chain length, ν, is the ratio of the number of monomer units consumed

per activated centre produced in the initiation step:

𝝂 =𝐧𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐦𝐨𝐧𝐨𝐦𝐞𝐫 𝐮𝐧𝐢𝐭𝐬 𝐜𝐨𝐧𝐬𝐮𝐦𝐞𝐝

𝐧𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐚𝐜𝐭𝐢𝐯𝐚𝐭𝐞𝐝 𝐜𝐞𝐧𝐭𝐫𝐞𝐬 𝐩𝐫𝐨𝐝𝐮𝐜𝐞𝐝

The kinetic chain length can be expressed in terms of the rate expression

𝝂 =𝐫𝐚𝐭𝐞 𝐨𝐟 𝐩𝐫𝐨𝐩𝐚𝐠𝐚𝐭𝐢𝐨𝐧 𝐨𝐟 𝐜𝐡𝐚𝐢𝐧𝐬

𝐫𝐚𝐭𝐞 𝐨𝐟 𝐩𝐫𝐨𝐝𝐮𝐜𝐭𝐢𝐨𝐧 𝐨𝐟 𝐫𝐚𝐝𝐢𝐜𝐚𝐥𝐬


By making the steady-state approximation, we set the rate of production of radicals

equal to the termination rate




𝜈 =𝑘𝑝 M• 𝑀

2𝑘𝑡.M 2 =𝑘𝑝 𝑀

2𝑘𝑡. M•

When we substitute the steady-state expression, for the radical concentration, we

obtain

𝝂 = 𝒌𝒓 𝑴 𝐈−𝟏/𝟐 𝒌𝒓 =

𝟏

𝟐𝒌𝒑(𝒇𝒌𝒊𝒌𝒕)

−𝟏/𝟐





Consider a polymer produced by a chain mechanism with mutual termination. In

this case, the average number of monomers in a polymer molecule, ⟨N⟩, produced

by the reaction is the sum of the numbers in the two combining polymer chains.

The average number of units in each chain is 𝜈. Therefore,

𝐍 = 𝟐𝝂 = 𝟐𝒌𝒓 𝑴𝐈 −𝟏/𝟐

the slower the initiation of the chain (the smaller the initiator

concentration and the smaller the initiation rate constant), the

greater the kinetic chain length, and therefore the higher the

average molar mass of the polymer.



3.3 Phytochemistry

Many chemical reactions can be initiated (or started)

by the absorption of electromagnetic radiation.

In photochemical processes the radiant energy of the

Sun is absorbed (captured) by at least one

component of a reaction mixture.

Heating of the atmosphere during the daytime

by absorption of ultraviolet radiation.

The absorption of visible radiation during

photosynthesis.

Without photochemical processes, the Earth would

be simply a warm, sterile, rock.



3.3 Phytochemistry

Examples of photochemical processes



3.3 Phytochemistry

In a primary process, products are formed directly from the excited state of a

reactant.

Products of a secondary process originate from intermediates that are formed

directly from the excited state of a reactant.

Primary photophysical processes that can deactivate the excited state compete

with the formation of photochemical products.

Therefore, it is important to consider the timescales of excited state formation

and decay before describing the mechanisms of photochemical reactions.



3.3 Phytochemistry

Examples of photophysical processes


Electronic transitions caused by absorption of ultraviolet and visible radiation

occur within 10−16–10−15 s.

Fluorescence is slower than absorption, with typical lifetimes of 10−12–10−6 s.


3.3 Phytochemistry

We expect, then, that the upper limit for the rate constant of a first-

order photochemical reaction is about 1016 s−1.

The excited singlet state can initiate very fast photochemical reactions

in the femtosecond (10−15 s) to picosecond (10−12 s) timescale.

The initial events of vision

Photosynthesis

…



3.3 Phytochemistry

Typical intersystem crossing (ISC) and phosphorescence times for large organic

molecules are 10−12–10−4 s and 10−6–10−1 s, respectively.

Excited triplet states are photochemically important.

Because phosphorescence decay is several orders of magnitude slower than

most typical reactions, species in excited triplet states can undergo a very large

number of collisions with other reactants before deactivation.



3.3 Phytochemistry

3.3.1 The primary quantum yield

We shall see that the rates of deactivation of the excited state by radiative, non-

radiative, and chemical processes determine the yield of product in a

photochemical reaction.

The primary quantum yield, ∅

∅ =𝐧𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐞𝐯𝐞𝐧𝐭𝐬

𝐧𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐩𝐡𝐨𝐭𝐨𝐧𝐬 𝐚𝐛𝐬𝐨𝐫𝐛𝐞𝐝 When we divide both the

numerator and denominator

of ∅ by the time interval

over which the events

occurred ∅ =𝐫𝐚𝐭𝐞 𝐨𝐟 𝐩𝐫𝐨𝐜𝐞𝐬𝐬

𝐢𝐧𝐭𝐞𝐧𝐬𝐢𝐭𝐲 𝐨𝐟 𝐥𝐢𝐠𝐡𝐭 𝐚𝐛𝐬𝐨𝐫𝐛𝐞𝐝 =𝒗

𝐈𝐚𝐛𝐬



3.3 Phytochemistry


A molecule in an excited state must either:

Decay to the ground state

or

Form a photochemical product

The total number of molecules deactivated by radiative processes, non-radiative

processes, and photochemical reactions must be equal to the number of excited

species produced by absorption of light.

Therefore

We conclude that the sum of primary quantum yields ∅𝒊 for all photophysical

and photochemical events i must be equal to 1, regardless of the number of

reactions involving the excited state.

∅𝒊𝒊

= 𝒗𝒊 𝐈𝐚𝐛𝐬𝒊

= 𝟏


For an excited singlet state that decays to the ground state only via the

photophysical processes


3.3 Phytochemistry


∅𝐟 + ∅𝐈𝐂 + ∅𝐩 = 𝟏

Note: Intersystem crossing from the singlet to the triplet state is taken into account

with the measurement of ∅𝐩).

quantum yields of fluorescence

Quantum yields of internal conversion

Quantum yields of phosphorescence

The quantum yield of photon emission by fluorescence and phosphorescence is

∅𝐞𝐦𝐢𝐬𝐬𝐢𝐨𝐧 = ∅𝐟 + +∅𝐩 ∅𝐞𝐦𝐢𝐬𝐬𝐢𝐨𝐧 is less than 1


If the excited singlet state also participates in a primary photochemical reaction

with quantum yield ∅𝒓, we write:


3.3 Phytochemistry


∅𝐟 + ∅𝐈𝐂 + ∅𝐩 + ∅𝐫 = 𝟏

We can now strengthen the link between reaction rates and primary quantum yield

∅ =𝒗

𝒗𝒊𝒊

𝑣𝑖𝑖

= Iabs and ∅ =𝒗

𝐈𝐚𝐛𝐬

The primary quantum yield may be determined

directly from the experimental rates of all

photophysical and photochemical processes that

deactivate the excited state.

Therefore



3.3 Phytochemistry

3.3.2 Mechanism of decay of excited singlet states

Consider the formation and decay of an excited singlet state in the absence of a

chemical reaction:

Absorption: S + hνi → S∗ 𝑣𝑎𝑏𝑠 = Iabs

Fluorescence: S∗ → S + +hνf 𝑣𝑓 = kf S∗

Internal conversion: S∗ → S 𝑣𝐼𝐶 = kIC S∗

Intersystem crossing: S∗ → T∗ 𝑣𝐼𝑆𝐶 = kISC S∗

Absorbing species Excisted singlet state

Excisted triplet state

Energy of incident photons

Energy of fluorescent photons

𝐑𝐚𝐭𝐞 𝐨𝐟 𝐟𝐨𝐫𝐦𝐚𝐭𝐢𝐨𝐧 𝐨𝐟 𝑺∗ = Iabs

𝐑𝐚𝐭𝐞 𝐨𝐟 𝐝𝐞𝐜𝐚𝐲 𝐨𝐟 𝑺∗ = − kf S∗ − kIC S

∗ − kISC S∗ = −(kf + kISC + kIC) S

∗


It follows that the excited state decays

by a first-order process so, when the

light is turned off, the concentration of

S* varies with time t as:


3.3 Phytochemistry


S + hνi → S∗ 𝑣𝑎𝑏𝑠 = Iabs

S∗ → S + +hνf 𝑣𝑓 = kf S∗

S∗ → S 𝑣𝐼𝐶 = kIC S∗

S∗ → T∗ 𝑣𝐼𝑆𝐶 = kISC S∗

𝐑𝐚𝐭𝐞 𝐨𝐟 𝐟𝐨𝐫𝐦𝐚𝐭𝐢𝐨𝐧 𝐨𝐟 𝑺∗

= Iabs

𝐑𝐚𝐭𝐞 𝐨𝐟 𝐝𝐞𝐜𝐚𝐲 𝐨𝐟 𝑺∗

= −(kf + kISC + kIC) S∗

𝐒∗ 𝐭 = 𝐒∗𝟎𝐞−𝐭/𝛕𝟎

The observed lifetime, τ0, of

the first excited singlet state 𝛕𝟎 =

𝟏

𝐤𝐟 + 𝐤𝐈𝐒𝐂 + 𝐤𝐈𝐂

The quantum yield of fluorescence (Justify) is

𝛟𝐟 = 𝐤𝐟




3.3 Phytochemistry

3.3.2 Mechanism of decay of excited singlet states 𝛕𝟎 = 𝟏


The observed fluorescence lifetime, 𝛕𝟎 can be measured by using a pulsed laser

technique.

First, the sample is excited with a short light pulse from a laser using a

wavelength at which S absorbs strongly.

Then, the exponential decay of the fluorescence intensity after the pulse is

monitored. it follows that

𝛕𝟎 = 𝟏

𝐤𝐟 + 𝐤𝐈𝐒𝐂 + 𝐤𝐈𝐂=

𝐤𝐟𝐤𝐟 + 𝐤𝐈𝐒𝐂 + 𝐤𝐈𝐂

×𝟏

𝐤𝐟=𝛟𝐟𝐤𝐟



3.3 Phytochemistry


Example:

In water, the fluorescence quantum yield and observed fluorescence lifetime of

tryptophan are ϕf = 0.20 and τ0 = 2.6 ns, respectively.

It follows that the fluorescence rate constant kf is

τ0 = ϕfkf =

0.20

2.6 × 10−9s = 7.7 × 107 s−1



3.3 Phytochemistry

3.3.3 Quenching

Quenching is the shortening of the lifetime of the excited state by the presence of

another species, called quencher, Q.

Quenching

Desired process, e.g electron transfer

Undesired side reaction that can decrease ϕ

of a desired photochemical reaction.

Quenching effects may be studied by monitoring the emission from the excited

state that is involved in the photochemical reaction.

The addition of a quencher, Q, opens an additional channel for deactivation of S*:

may be either a

𝐐𝐮𝐞𝐧𝐜𝐡𝐢𝐧𝐠: 𝐒∗ + 𝐐 → 𝐒 + 𝐐 𝐯𝐐 = 𝐤𝐐 𝐐 𝐒∗



3.3 Phytochemistry

3.3.3 Quenching 𝐐𝐮𝐞𝐧𝐜𝐡𝐢𝐧𝐠: 𝐒∗ + 𝐐 → 𝐒 + 𝐐 𝒗𝑸 = 𝐤𝐐 𝐐 𝐒

∗

The Stern–Volmer equation relates the fluorescence quantum yields ϕf,0 and ϕf

measured in the absence and presence, respectively, of a quencher Q at a molar

concentration [Q]

𝛟𝐟,𝟎𝛟𝐟= 𝟏 + 𝛕𝟎𝐤𝐐 𝐐

Stern–Volmer plot

ϕf,0/ϕf against [Q]

Note: The method may also be applied to

the quenching of phosphorescence.



3.3 Phytochemistry

3.3.3 Quenching

Because the fluorescence intensity and lifetime are both

proportional to the fluorescence quantum yield.

If,0/If against [Q]

τ0 /τ against [Q] Straight line

Slope = 𝛕𝟎𝐤𝐐

Intercept = 1

Same slope and intercept

Stern–Volmer equation

𝛟𝐟,𝟎𝛟𝐟= 𝟏 + 𝛕𝟎𝐤𝐐 𝐐



3.3 Phytochemistry

3.3.3 Quenching

Example: Determining the quenching rate constant

2,2′-bipyridine (1, bpy) forms a complex with the Ru2+ ion.

Ruthenium (II) tris-(2,2′-bipyridyl), Ru(bpy)3 2+ (2), has a strong

metal-to-ligand charge transfer (MLCT) transition at 450 nm.

The quenching of the *Ru(bpy)3 2+ excited state by Fe(OH2)6

3+ in

acidic solution was monitored by measuring emission lifetimes at

600 nm. Determine the quenching rate constant for this reaction

from the following data:

[Fe(OH2)6 3+]/(10−4 mol dm−3) 0 1.6 4.7 7 9.4

τ /(10−7 s) 6 4.05 3.37 2.96 2.17

Solution (word file p. 62)



3.3 Phytochemistry

3.3.3 Quenching

Three common mechanisms for bimolecular quenching of an excited singlet (or

triplet) state are proposed:

Collisional deactivation: S* + Q→S + Q

Resonance energy transfer: S* + Q→ S + Q*

Electron transfer: S* + Q→ S+ + Q− or S− + Q+

Note: The quenching rate constant itself does not give much insight into the

mechanism of quenching.

There are some criteria that govern the relative efficiencies of collisional

quenching, energy transfer, and electron transfer.



3.3 Phytochemistry

3.3.3 Quenching

There are some criteria that govern the relative efficiencies of collisional

quenching, energy transfer, and electron transfer.

Collisional deactivation: S* + Q→S + Q

Resonance energy transfer: S* + Q→ S + Q*

Electron transfer: S* + Q→ S+ + Q− or S− + Q+

Collisional quenching is particularly efficient when Q is a heavy species (e.g.,

iodide ion), which receives energy from S* and then decays primarily by internal

conversion to the ground state.


According to the Marcus theory of electron transfer, the rates of electron transfer

(from ground or excited states) depend on:

The distance between the donor and acceptor, with electron transfer

becoming more efficient as the distance between donor and acceptor

decreases.

The reaction Gibbs energy, ΔrG, with electron transfer becoming more

efficient as the reaction becomes more exergonic (e.g., efficient

photooxidation of S requires that the reduction potential of S* be lower than

the reduction potential of Q).


3.3 Phytochemistry

3.3.3 Quenching



3.3 Phytochemistry

3.3.3 Quenching

The reorganization energy, the energy cost incurred by molecular

rearrangements of donor, acceptor, and medium during electron transfer.

The electron transfer rate is predicted to increase as this reorganization

energy is matched closely by the reaction Gibbs energy.

According to the Marcus theory of electron transfer, the rates of electron transfer

(from ground or excited states) depend on:

Electron transfer can also be studied by time-resolved spectroscopy. The

oxidized and reduced products often have electronic absorption spectra distinct

from those of their neutral parent compounds. Therefore, the rapid appearance of

such known features in the absorption spectrum after excitation by a laser pulse

may be taken as indication of quenching by electron transfer. In the following

section we explore energy transfer in detail.



3.3 Phytochemistry

3.3.3 Quenching

Electron transfer can also be studied by time-resolved spectroscopy.

The oxidized and reduced products often have electronic absorption spectra

distinct from those of their neutral parent compounds. Therefore, the rapid

appearance of such known features in the absorption spectrum after excitation by

a laser pulse may be taken as indication of quenching by electron transfer.



3.3 Phytochemistry

3.3.4 Resonance energy transfer

We visualize the process S* + Q → S + Q* as follows:

The oscillating electric field of the incoming electromagnetic radiation

induces an oscillating electric dipole moment in S.

Energy is absorbed by S if the frequency of the incident radiation, ν, is such

that ν = ΔES/h, where ΔES is the energy separation between the ground and

excited electronic states of S and h is Planck’s constant.

=> This is the ‘resonance condition’ for absorption of radiation.

The oscillating dipole on S now can affect electrons bound to a nearby Q molecule

by inducing an oscillating dipole moment in the latter. If the frequency of

oscillation of the electric dipole moment in S is such that ν =ΔEQ/h then Q will

absorb energy from S. The efficiency, ηT, of resonance energy transfer is defined

as



3.3 Phytochemistry


If the frequency of oscillation of the electric dipole moment in S is such that

ν =ΔEQ/h

then Q will absorb energy from S.

𝜼𝑻 = 𝟏 −𝝓𝒇

𝝓𝒇,𝟎

According to the Förster theory of resonance energy transfer, energy transfer is

efficient when:

The energy donor and acceptor are separated by a short distance (of the order

of nanometres).

Photons emitted by the excited state of the donor can be absorbed directly by

the acceptor.

The efficiency, ηT, of resonance energy transfer is defined as



3.3 Phytochemistry


For donor–acceptor systems that are held rigidly either by

covalent bonds or by a protein ‘scaffold’, ηT increases with

decreasing distance, R.

𝛈𝐓 =𝐑𝟎𝟔

𝐑𝟎𝟔 + 𝐑𝟔

Is a parameter (with units of distance) that

is characteristic of each donor–acceptor

pair



3.3 Phytochemistry


The emission and absorption spectra of

molecules span a range of wavelengths, so

the second requirement of the Förster

theory is met when the emission spectrum

of the donor molecule overlaps significantly

with the absorption spectrum of the

acceptor.

In the overlap region, photons emitted by

the donor have the proper energy to be

absorbed by the acceptor.



3.3 Phytochemistry


In many cases, the energy transfer is the predominant mechanism of quenching if

the excited state of the acceptor fluoresces or phosphoresces at a characteristic

wavelength.

In a pulsed laser experiment, the rise in fluorescence intensity from Q* with a

characteristic time that is the same as that for the decay of the fluorescence of S* is

often taken as indication of energy transfer from S to Q.


𝐑𝟎𝟔 + 𝐑𝟔

forms the basis of fluorescence resonance energy transfer

(FRET), in which the dependence of the energy transfer

efficiency, ηT, on the distance, R, between energy donor and

acceptor can be used to measure distances in biological

systems.



3.3 Phytochemistry


In a typical FRET experiment, a site on a biopolymer or membrane is labelled

covalently with an energy donor and another site is labelled covalently with an

energy acceptor.

In certain cases, the donor or acceptor may be natural constituents of the system,

such as amino acid groups, co-factors, or enzyme substrates.

The distance between the labels is then calculated from the known value of R0 and

the equation:

Several tests have shown that the FRET technique is useful for measuring

distances ranging from 1 to 9 nm.


𝐑𝟎𝟔 + 𝐑𝟔



3.3 Phytochemistry


Brief illustration

Consider a study of the protein rhodopsin. When an amino

acid on the surface of rhodopsin was labelled covalently

with the energy donor 1.5-I AEDANS, the fluorescence

quantum yield of the label decreased from 0.75 to 0.68 due

to quenching by the visual pigment 11-cis-retinal.

ηT = 1 − (0.68/0.75) = 0.093

From the known value of R0 = 5.4 nm for the 1.5-I

AEDANS/11-cis-retinal pair => R = 7.9 nm

Therefore, we take 7.9 nm to be the distance between the

surface of the protein and 11-cis-retinal.



3.3 Phytochemistry


If donor and acceptor molecules diffuse in solution or in the gas phase, Förster

theory predicts that the efficiency of quenching by energy transfer increases as the

average distance travelled between collisions of donor and acceptor decreases.

That is, the quenching efficiency increases with concentration of quencher, as

predicted by the Stern–Volmer equation.

Thank you for your presence and intention

& Many thanks to P. Atkins, J. D Paula for

their nice book “ Physical chemistry”

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