Kinetic study Flow methods relaxation methods Electrochemical methods NMR Spectrophotometric Pulse Radiolysis

1. Dr.Vikas A.Thakur,
Department of Chemistry
Rayat Shikshan Sanstha’s
K.B.P.College,Vashi(Autonomous)
TECHNIQUES FOR DETERMINATION
OF RATE OF REACTION

2. INTRODUCTION
➢ Generally, Kinetic study proceeds after reactant, Products and
Stoichiometry of the reaction have been satisfactorily characterized.
➢ In this part, techniques often used in Inorganic studies have discussed.
➢ Emphasizes made on their time range and general area of applicability.
➢ Any Experimental Kinetic method monitor somehow change of
concentration with time.
➢ Many studies are done under Pseudo-first order conditions.
➢ Then one must monitor the deficient reactant or product(s) because
other species undergo small changes in concentration.
➢ The Kinetic methods of choice often will be dictated by time scale of
the reaction.
➢ Detection methods will be determined by Spectroscopic properties of
species to be monitored.
2

3. INTRODUCTION
❑ Efficient use of materials can be a significant factor in the choice of
method because Kinetic study generally involves a number of runs at
different concentration and temperature.
❑ Detection methods for species should be as Specific as possible.
❑ Ideally, it should measure both reactant disappearance and Product
formation.
❑ Methods must not have any interference from other reactants and
should be applicable under a wide range of concentration conditions so
that the rate law can fully explored.
❑ There is often a practical trade off between Specificity, Sensitivity and
reaction time.
❑ E,g. NMR is quite specific but it is rather slow. It has relatively low
sensitivity unless system allows time for signal accumulation.
3

4. INTRODUCTION
 Spectrophotometry in the UV and visible range often
has good sensitivity and speed but the specificity may
be poor due to broad absorption bands and
intermediates have Chromophoric(causing colour)
properties similar to reactant and/or products.
 Vibrational Spectrophotometry can be better if IR
bands are sharp like in case of metal carbonyls.
 But solvents must be chosen which provide
appropriate Spectral window.
 Conductivity change can be very fast but it is rather
unspecific.
4

5. 1. Flow Methods
 In these methods, the reagent solutions are brought together
by flowing them through a mixer.
 From the mixer reaction solution emerges to be analysed.
 The flow may be simply driven by gravity or by
mechanical pressure applied to syringes containing
reagents.
 The minimum time scale depends on various factors such
as reagent flow rate, efficiency of mixer and response time
of analyser.
 This general process has adapted in various ways to
minimize the amounts of reagents used, to optimize
detection sensitivity and shorten accessible reaction time.
5

6. 1(a). QUENCHED FLOW METHODS
❖ This method involves driving
the reagent solutions through a
Mixer and then have some
means of stopping(Quenching)
the reaction as solution emerges
from the Mixer.
❖ Reaction time can be controlled
by changing the length of
tubing between Mixer and
quencher.
❖ Calibration with a reaction at
known rate is necessary.
❖ The main trick is to find an
effective quenching methods.
6

7. 1(a). QUENCHED FLOW METHODS
 This will depend on chemical reactions, addition of acid, base or
precipitating agent and rapid cooling.
 The short time limit is ~ 20ms.But this depends on effectiveness
of quenching method.
➢ Advantages :
▪ Apparatus is simple and analysis of quenched solution can be
done without time constraints.
▪ The method is used especially for Isotope Exchange reaction
where subsequent analysis of isotopic content is a slow process.
➢ Disadvantages /Limitations:
▪ Sometimes analysis of many samples become tedious.
▪ Consumption of substantial amounts of reactants for each kinetic
run.
7

8. 1(b). STOPPED FLOW METHODS
o Method is most popular and
effective for reactions with half
times in the range ~ 10ms to ~ 60S.
o Several commercial instruments are
available.
o In a Typical instruments, the
reagent solutions are contained in
two drive syringes whose plungers
can be advanced by activating an
air pressure or electrical drive
system.
o This moves solution through a
Mixer into an Observation cell and
then to Stopping Syringe.
o A Mechanical stop on stopping
syringe or drive stops the flow and
triggers the observation and data
recording system.
8

9. 1(b). STOPPED FLOW METHODS
 The standard system mixes equal volumes (~ 0.2 to 0.5 mL) of each
reagent solution and uses single-wavelength, single-beam UV visible
Spectrophotometry as a detection methods.
 A Number of variations have been described using other detection
methods(Conductometry,Flurometry, NMR,ESR,EXAFS) and
multiwavelength at high pressure at subzero temp. and for multiple
mixing.
 It is apply first for two reagents, then for third after some time interval.
 The method is quite adaptable and widely applicable.
 The time range limitations are determined on the short end by the dead
time of system(the time for mixing of reagents and transfer to
observation cell) and on long end by diffusion of reagents into
observation cell.
 The experimental first order rate constant, Kexp can be corrected for
mixing time effect, Kmix to obtain the true Pseudo-first order rate
constant Ktrue.
9

10. 1(b). STOPPED FLOW METHODS
 It is obtained from following relationship suggested by Dickson and
Margerum.
➢ (Ktrue)-1 = (Kexp)-1 – (Kmix)-1
 The rearrangement of this expression we get
➢ Ktrue = Kexp(1 – Kexp/Kmix)-1 (1)
➢ Equation (1) is always shows that true rate constant is always larger
than experimental value.
• But the correction is insignificant if Kexp/Kmix << 1.
• To determine Kmix, measurements can be done on a well-characterized
system under Pseudo first order conditions with Ktrue = K1[R].
• Where K 1 is Known and R is the excess reagent whose concentration
can be varied to change Ktrue.
• The variation of Kexp with [R] is used to determine K.Mix.
❑ Margerum and co-workers have reported values of K.Mix for Durrum
and High-Tech Instruments of 1.7 x 103 and 2.9 x 103 S-1 respect.
10

11. 1(b). STOPPED FLOW METHODS
 The deadline is due primarily to
physical separation of the mixer,
observation cell and on flood
velocity.
 Typical deadline are in the 1 to 5
ms range. It can be determined by
extrapolation at the true time zero
as shown by dashed lines in fig.
 The actual time t is related to
experimentally recorded time, texp
and deadtime,td by
 t = texp + td (2)
 For Spectrophotometric
detection,fig.3 illustrates
relationship between these lines
and Ao
Pred ,the predicted
absorbance at true zero time and
Ao
obsd,the initial absorbance at the
11

12. 1(b). STOPPED FLOW METHODS
➢ The reaction has pseudo-first order rate constant
➢ Kexp = K1 [R] .So that dependence of the absorbance change is given by
❑ (A  - A) = (A  - Ao
Pred ) exp(-Kexp t ) (3)
 Where
 A -- is final absorbance and A--- is the absorbance at any time t.
 Both sides of equation(3) can be multiplied by exp.(Kexpt td )
 texp = t-td, we obtain.
 (A - A)exp(Kexp td) = (A - Ao
Pred ) exp(-Kexp
t d )
 = (A - Ao
Pred ) exp(-Kexp/texp) (4)
 Substituting limiting condition that A = Ao
obs when texp = 0 into equation 4 and
rearranging be given as
 (A – Ao
obs) = (A - Ao
Pred ) exp(-Kexp td) (5)
 Equation(5) can be used to determine td from measurable quantities Kexp, Ao
obs
, Ao
Pred
 Substitution of equation (2) and (5) into equation(3) gives
12

13. 1(b). STOPPED FLOW METHODS
❑ (A – A) = (A – AO
obs) exp(-Kexp
. texp) (6)
➢ Equation(6) shows that Kexp is independent of td and is determined
from dependence of (A - A) on texp.
 The situation is more complex for studies under second-order
conditions because reagent conc. at true zero time must be known.
❖ Limitations :
 The deadtime could be adjusted to give Ao
pred if true zero time value is
known.
❑ Meagner and Corabacher have suggested an empirical way of dealing
mixing problem.
➢ Reagent solution of similar composition in order to avoid spurious
effects due to inhomogeneous mixing.
➢ It is always advisable to do blank observations to ensure that no
apparent reaction is observed in absence of each reactant.
13

14. 1(b). STOPPED FLOW METHODS
❑ Applications:
➢ Numerous applications are in collection and analysis of experimental
rate constants are entirely straightforward.
➢ 1.Hydrolysis of Cobalt(III) carbonate chelates in acidic medium has
been model for carbonic anhydrase catalysed dehydration of CO2.
➢ The mechanism is shown in Scheme 1.
➢ For some systems the protonated species has been detected and Ka is
determined.
➢ The two steps in the reaction are chelate ring opening K1 and
decarboxylation K2 of monodentate bicarbonate complex.
➢ 2.Reaction with aqueous Iron(III) with various ligands often yield
highly coloured complex.
❑ The Classic example is deep red thiocyanate complex Fe(OH2)5(NCS)2+
➢ This system is ideal for study because of large absorbance change and
ready availability of reagents.
14

15. 1(b). STOPPED FLOW METHODS
❑Recent arguments suggested that substitution
mechanism is associative for Fe(OH2)6
3+ and
dissociative for Fe(OH2)5(OH)2+ .
 A number of pressure dependence studies have done in
expectation that ΔV* values help to violate reactivity
arguments.
 Fe(OH2)6
3+ + SCN- →K1 → Fe(OH2)5(NCS)2+ +
H2O
 Fe(OH2)5(OH)2+ + SCN- →K2 → Fe(OH2)4
(OH)(NCS)+ +
H2O (7)
15

16. 1(c). CONTINUOUS FLOW METHODS
➢ Theoretically, Continuous flow preceded Stopped flow as a method for
studying moderately fast reactions.
➢ The reactant solutions are made to flow continuously through the Mixer
and observation Chambers and time dependence of the reaction can be
obtained by changing the flow rate or moving the observation point to
various distances from the Mixer.
➢ The apparatus can be quite simple but large amounts of reagents are
consumed.
➢ In a pulse continuous flow method, a continuous flow is established for
a short time can reduce reagent consumption to ~5ml.
➢ The fast jet mixtures have lowered accessible reaction half-time to the
10S range.
➢ The concentration of reagent monitored can be lowered if integration
observation is used in which flowing solution is viewed down the
length of observation cell.
16

17. 1(d). PULSE ACCELERATED FLOW
METHODS
 In this method pulsed continuous flow has adapted in
which flow rate through the mixer and observation
chamber is varied during the course of one run.
❑Most recent application of this method is of Margerum
and his Co-workers.
❖Advantage:
 Method can be used for half-times down to ~ 10 S
compared to ~ 10 mS from Stopped flow.
❖Limitations:
 Because of complexity of analysis the method is
limited to first order reaction conditions.
17

18. 2. RELAXATION METHODS
➢ In these methods, a system at equilibrium is subjected to a perturbation and
kinetics of system relaxing to new equilibrium condition is followed.
➢ The perturbation(deviation) normally is a change in temperature, Pressure
or concentration of one of the reagents .
➢ The methods are known as temperature jump, Pressure jump and
concentration jumps respectively.
❑ Advantages :
➢ Perterbation especially of temp. and pressure can be applied very quickly
and reaction with half-times in the micro second range can be observed.
❑ Eigen and co-workers done Pioneering work greatly extends time scale for
solution kinetic studies.
❑ Limitations:
➢ Major limitation is that equilibrium position of the reaction must involve
significant concentration of both reactant and products.
➢ Hence relaxation methods are not applicable to essentially irreversible
reactions.
18

19. 2. RELAXATION METHODS
❑ Applications :
 These methods are especially useful for Lowry-Bronsted acid-
base reactions in which the equilibrium position can be adjusted
simply by changing the pH of solution.
 Method is useful for ligand substitution reactions that involve
Proton production or consumption.
❑ A Noteworthy feature of this method is the changes in
concentration caused by the perturbation should not be too large
so that Mathematical Analysis can be simplified.
 This poses some limitations for the detection method.
 This method must be fast but also sensitive enough to detect
these small concentration changes.
 But it is possible to repeat the perturbation and improve signal to
noise ratio through signal averaging.
19

20. 2. RELAXATION METHODS
 The standard Mathematical analysis can be illustrated for following system.
 A + B Kf→ C (8)
Kr
 After the perturbation, the system comes to new equilibrium with final
concentration [Ae], [Be] and [Ce] and these may be related to concentration at
any time through the concentration change variable Δ, so that
 [A] = [Ae] + Δ
 [B] = [Be] + Δ
 [C] = [Ce] - Δ
 Simple Differentiation shows that
 d Δ/dt = d[A]/dt = d[B]/dt = -d[C]/dt
 We can write the usual differential equation for system
 d Δ/dt = d[A]/dt =-Kf[A] [B] + Kr[C]
 = -Kf ( [ Ae] + Δ) ( [ Be] + Δ) +Kr([Ce]- Δ) (9)
20

21. 2. RELAXATION METHODS
 Expansion and collection of terms given is
 d Δ/dt = -Kf [ Ae] + [Be] Δ – Kr Δ)–Kf[Ae][Be]+Kr[Ce]- Kf(Δ) 2
(10)
 At equilibrium Kf = [Ae] [Be] = Kr[Ce], and these terms are cancelled.
 Next, the assumption is made that Δ is very small, so that the term in Δ2
can be neglected and Equation (10) can be simplified to
 d Δ/dt = -{Kf [ Ae] + [ Be] + Kr} Δ =Δ/  (11)
❑ Where t is called as relaxation time.
 If Expts. are done with varying positions of the eqm then Plot of -1
versus [Ae] + [Be] should have slope of Kf and an intercept of Kr.
 This is different from normal Pseudo-first order system.
 Experimental rate constant is kf + kr.
21

22. 2(a). TEMPERATURE JUMP
 For a system at eqm, if the temperature is changed by ΔT, then eqm
concentration will change due to thermodynamic relationship between
eqm constant and Enthalpy change
❑ (ln K/ T)P = -ΔH0
rxn/ RT2
 In early applications and commercial instruments, the temperature was
quickly changed, typically by ~ 50C by an electrical discharge.
 Sample was contained between two electrodes and subjected to a
voltage of ~ 10 to 100 KV across the electrodes to produce the
discharge.
 This requires that solution is electrically conducting and somewhat
invasive on sample.
 It is observed that ion Polarization at charged electrodes can cause
spurious but reproducible signals.
22

23. 2(a). TEMPERATURE JUMP
❑ Hague and Martin usedT-Jump to
study complexation of aqueous
Manganese(II) by 2,2’ bipyridine
shown in below
 Mn(OH2)6
2+ + bpy Kf
K→
Mn(OH2)4(bpy)2+ + 2 H2O (12)
 The work was extended by Doss
andVan Eldik to determine
Pressure dependence.
 From both studies, Kf = 2 x 10 5
M-1 s-1 and the pressure
dependence gave Δf* = -3 cm3M-1
 This negative value is as evidence
for an Ia mechanism for
substitution of Mn(OH2)6
2+
23

24. 2(b). PRESSURE JUMP
 The method requires a finite volume change for the reaction,
ΔV0 rxn so that eqm constant will change with Pressure due to
relationship.
 (ln K/ P)T = -ΔV0
rxn/ RT
➢ The experiment is done by putting the sample under high
Pressure and suddenly reduced the pressure by piercing a
diaphragm.
➢ High Pressure equipments and observation cells are required.
❖ But perturbation seems less invasive on the sample thanT-jump by
electrical discharge.
❑ Recently,A P-Jump system with conductivity has been detected.
24

25. 2(b).CONCENTRATION JUMP
 The system is perturbed by adding a small amount of one of
the species in the eqm reaction.
 Generally, apparatus is much simpler thanT-Jump or P-Jump
methods.
 But the perturbation cannot be done as quickly so that short
time limit is in the millisecond range.
25

26. 3. ELECTROCHEMICAL METHODS
 Various Electrochemical methods such as Cyclic Voltametry, Polarography,
Chronoamperometry and Chronopotentiometry can be used to measure
homogeneous reaction rates.
 In general, electrochemical observations can give information about
homogeneous reaction rates when an electrode reaction is coupled to
homogeneous chemical reaction.
 The rate of latter becomes limiting rate for the process at the electrode.
 Sometimes the chemical rate constant can be extracted fairly directly from
observation. Or
 It may require curve matching of experimental and simulated curves computed
with various rate constants.
 Size and composition of the electrode and diffusion coefficient of reagents
affects the kinetics of electrode reaction.
 Hence these factors will influence observations and effective time range.
 The field has a well developed nomenclature and symbolism.
26

27. 3. ELECTROCHEMICAL METHODS
 One electron electrode reaction is designated by E and a chemical
reaction by C.
 There are extensions of systems like E+E for two electron electrode
reaction, E- and E- for reduction and oxidation,C1 and C2 for first and
second order reactions and C1’ for Pseudo first order reactions.
 The most widely used technique describe is CyclicVoltammetry due to
availability of appropriate instrumentation and number of increasing
applications with recent software to simulate cyclic voltammograms.
 Such simulations are generally essential for determination of meaningful
kinetic parameters.
 An ideal cyclic voltammogram, CV, and some terminology of this
technique is shown in fig.
 The experiment is carried out by changing the voltage, E,of working
electrode at some constant sweep rate, v and measuring current, i.
27

28. 3. ELECTROCHEMICAL METHODS
 Then the sweeep rate and reagent
concentrations are changed and changes in
cathodic and anodic peak potential,Epc and
Epa and peak current ip are analyzed.
 Quantitative analysis requires knowledge of
rate(s) of heterogeneous electrode
reaction(s),reagent diffusion coefficients and
transfer coefficient.
 If electrode reaction is reversible ,most of
these parameters can be determined from
CV Experiments.
 The formal reduction potential E0’,differs
from standard reduction potential E0.
 Because latter is obtained by extrapolation
to infinite dilution while former refers to
actual experimental conditions of ionic
strength and temp.
28

29. 3. ELECTROCHEMICAL METHODS
 Potentials are often reported relative to some standard electrode such as
ferrocene/ferrocinium ion,saturated calomel,SCE or Ag/AgCl.
 This must be taken into account in comparing results from different sources.
 One restriction of these methods is that the medium must contain an inert
electrolyte to maintain electrical conductivity.
 Typically,0.1M tetraalkyl ammonium salts of PF6
-,CF3SO3
- or ClO4
- are used.
 Problems arises due to adsorption of reagents on electrode and uncertainties in
chemical characterization of the product of electrode reaction.
 The experiment can give number of electrons, n,involved and the reduction
potential and then nature of electrochemically generated reagent is inferred by
chemical reasoning and analogy.
 It is possible to couple the system to some Spectroscopic technique such as EPR or
IR Spectroscopy for further characterization.
29

30. 3. ELECTROCHEMICAL METHODS
 The substitution inertness of Cr(III) and
lability of Cr(II) have studied by Hecht,
Schultz and Speiser to observe some ring
opening and ring-closing reactions of
ammino-carboxylate ligands.
 The experiments used a stationary Hg drop
electrode in 1.0M Na2SO4 at pH 8.5 at
ambient temp.
 Their observations are explained in Scheme
2 where aliphatic substituent R gives trans-
N,N geometry shown.
 For such a system, initial CV reduction of
Cr(III) complex shows a broad cathodic
wave whose position shifts from about -1.4
to -1.6V as sweep rate is increased.
 This is a typical irrversible reduction with
sluggish electrode kinetics and is assigned to
Kshl Process.
30

31. 4.NUCLEAR MAGNETIC RESONANCE METHOD
 There is a wide variety of applications of NMR to problems in inorganic
kinetics.
 The time scale depends on type of system and can vary from hours to
microseconds .
 One great advantage of NMR is that temp. can be changed over a wide range
from about -2000C to +1500C without significant instrument modification.
 Another advantage is molecular specificity of NMR signal which often permits
an assignment of the composition and structure of stable intermediates and
products.
 The specificity is augmented by ability to detect a wide range of NMR active
nuclei;1H,13C, 19F and 31P are standard for most modern NMR instruments and
many metals have NMR active isotopes that can observed with appropriate
modifications.
❑ Unique feature of NMR is ability to measure rates of reactions in which there is
no net chemical change such as solvent exchange and ligand fluxionality.
31

32. 4.NUCLEAR MAGNETIC RESONANCE METHOD
❑ Limitation:
 Major limitation of NMR is sensitivity and concentrations must be typically
about 0.01M unless signal averaging is possible.
 However, the small sample size of 0.5 to 2 ml allows for modest materials
consumption.
 Discussion of theory and quantitative analysis in this area often use lifetime  of
a nucleus in a particular site as a kinetic interest.
❑ By conventional definition, Lifetime is concentration of nuclei in the site
divided by their rate of disappearance from the site.
 To establish relationship between rate constant and the lifetime, it is necessary
to define  clearly due to ambiguities of number and populations of sites.
 E,g.Exchange of nuclei between a hydrated metal ion
 M(OH2)n
Z+ and bulk solvent water can be represented by a reaction with whole
water molecule exchange or a just proton exchange.
32

33. 4.NUCLEAR MAGNETIC RESONANCE METHOD
 M(OH2)n z+ + H2O →M(OH2)n-1(OH2)z++ H2O (13)
 M(OH2)n z+ + H2O →M(OH2)n-1(OH2)(z-1)++H H2O + (14)
 In first case there are two lifetimes, m for the water ligands and s for
the bulk solvent.
 Ambiguity is in whether whole water molecule exchange with n
coordinated sites as in reaction(13) or proton exchange with 2n such
sites as in reaction(14).
 If 17O NMR is used, then only whole molecule exchange will be
observed and definitions are straightforward and given by
  m = n[M2+]/Rate s =[H2O ]/Rate Rate =k[M2+] x [H2O ]y (15)
 If 1H NMR is used, population in each site is multiplied by 2 because
there are two hydrogen per water molecule and the lifetimes are defined
by
  ’m =2x n[M2+]/Rate ’s =2x[H2O ]/Rate Rate =k’[M2+] x [H2O ]y
(16)
33

34. 4.NUCLEAR MAGNETIC RESONANCE METHOD
 If one believes that exchange involves a water molecule, then k in eqn(15) is the
rate constant for exchange of one water ligand.
 But k’ in eqn(16) is for exchange of one H and since there are two H atoms per
17O, then k = k’/2.
 But,if if H exchange occurs only by reaction (13) then k’is the rate constant as
defined in eqn. (16).
 Therefore 17O NMR will give k for water molecule exchange
 But the k’ from 1H NMR has an ambiguious assignment.
 For other solvents such as acetonitrile, DMF and DMSO where independent
exchange of methyl protons is very unlikely the site population factor in
eqn(16) is often omitted and  definition refer to whole solvent molecule
exchange.
 NMR methods are separated into four categories in the order of decreasing
time scale of their applicability.
 However latter is quite dependent on system. Different methods might be used
in different temperature ranges.
34

35. 4(a) SIGNAL MONITORING
 This method refers to simple monitoring of changes with time of concentration
of reactants and products.
 These are determined from integrated intensities of appropriate peaks in the
NMR spectrum. The short time scale is few minutes required for temp.
equilibrium and instrument help.
 Long time is limited only by sample stability.
 For pulsed Fourier transform instruments, it is important to remember the
repetition rate or relaxation delay must be 8 to 10 times longer than nuclear
relaxation time(s),T1 to obtain correct relative intensities.
 TheT1 values for 1H and 13C nuclei can be in the 1- to 10-s range.
 A special example of this type of application is measurement of exchange
reactions using appropriate isotope.
 E,g. Exchange between free CO and CO ligands in metal carbonyls can be
measured using 13C- enriched CO.
 Exchange between H2O and Oxo anions or water ligands can be measured in
suitably inert system using 17O enrichment.
35

36. 4(b) MAGNETIZATION TRANSFER
➢ This method is simple to qualitatively envisage and interpret.
 A selective pulse (or DANTE series of pulses) is used to produce spin inversion
or saturation at one site.
 After a variable waiting period, tm, a 900 pulse is used to generate normal
spectrum of system.
 As exchange proceeds, the inverted nuclei appear in other sites and the
intensities of the sites involved in the exchange will decrease.
 As tm is increased to stage where tm>T1, the natural nuclear relaxation process
tend to restore the intensity.
 Intensity of sites involved in the exchange will increase due toT1 process.
 The accessible range of exchange lifetimes,t, for this method is determined on
the short end by tm and on the long end byT1.
 For typical spectrometers tm can be as short as ~ 0.01S andT1 for protons is
often ~1s.so that first order rate constant of ~ 100 to 1 s-1 can be determined.
36

37. 4(b) MAGNETIZATION TRANSFER
37
 AsT1 is usually has a lower activation energy(-5 to 10 Kjmol-1)
than , it is often possible to adjust the temperature to meet the
requirement of this method that Ti  .
 Inversion of a multiplet due to spin-spin coupling can be achieved
with a single pulse ,broad enough to cover the multiplet for small
coupling constants or by pulses of different frequencies in the
DANTE sequence for large coupling constants.
 It has been found that spin-spin coupling does not adversely affect
rate constant determination by this method.
 Because of competition between exchange and t1 relaxation
processes, it is advantageous for quantitative analysis to measure
theT1 values independently under slow exchange conditions.

38. 4(c) TWO-DIMENSIONAL EXCHANGE SPECTROSCOPY
 It is called 2D EXSY method.
 In the experiment, a 900 pulse is applied to rotate the magnetization from +z to
the –x axis.
 After a time t1, which is called evolution or labelling time, a second 900 pulse
rotates the magnetization from the xy plane into xz plane.
 A field gradient or homospoil pulse is applied to dephase the magnetization
along x axis.
 After a further time tm, called as mixing time, a third 900 pulse rotates the
magnetization to the y axis and Free Induction Decay, FID is collected during
time t2.
 The magnetization evolves in the xy plane during the two time periods t1 and t2.
 For a single site, the angular rate of precession is , and maxima will occur
when Cos( t1) and Cos(t2) equal 1.
 Then a three dimensional plot of intensity versus t1 and t2 will show a
maximum when this condition is satisfied for t1 and t2.
38

39. 4(c) TWO-DIMENSIONAL EXCHANGE SPECTROSCOPY
39
 The peak is often represented by intensity contours and is really a cone.
 For a multisite system, nuclei in different environments have different
precessional rates, 1,but will give a maxima when Cos(1t1) and Cos(2t2)
equal 1.
 It gives a peak along the diagonal of the t1-t2 plane when t1=t2.
 When system is undergoing chemical exchange, magnetization can transfer
between the sites during mixing time.
 This produces off-diagonal cross peaks in the final three dimensional plot of
spectra.
 These cross peaks give a map of the sites that are undergoing exchange.
 The evaluation of rate constants from the information is based on the intensities
or more properly the volumes of the cross peaks.
❑ This analysis is not trivial, especially for multi state system and requires special
care in the collection and processing the data to ensure that volumes of the
peaks are properly evaluated.

40. 4(c) TWO-DIMENSIONAL EXCHANGE SPECTROSCOPY
40
➢ There are several other sources of cross peaks in 2D EXSY experiment.
➢ Dipolar coupling with nearby nuclei produces cross peaks as observed in
standard NOESY experiment.
➢ These can be identified because exchange usually has a larger
temperature dependence than dipolar coupling.
➢ Scalar coupling interferes with 2D EXSY by producing J cross peaks that
can be eliminated by phase cycling.
 Choice of mixing time is crucial for this method because it is quite time
consuming to do studies by varying tm,t1 and t2.
 Perrin and Dwyer have suggested optimum mixing time given by for
two-site(AB) system
 tm(opt) = 1/T1
-1 + kAB + kBA
 Thus, for a multi-site system with different exchange rates, there will
not be a single optimum value.

41. 4(c) TWO-DIMENSIONAL EXCHANGE SPECTROSCOPY
41
 2D EXSY method can be applied to
rearrangement of tris(dithiolene)
complexes of the general type
M(S2C2R1R2)3,where M isW or
Mo,R1 is Phenyl or substituted
phenyl and R2 is H or Phenyl.
 The structures in solution are
believed to be trigonal prismatic.
 Asymmetric substitution gives
possibility of cis and trans isomers.
 The authors assignment are shown
by left-hand structures.
 Low-temperature 1H NMR
spectrum has three peaks in the
R2=H region that were assigned to
H1,H2 and H3as shown in left.

42. 4(c) TWO-DIMENSIONAL EXCHANGE SPECTROSCOPY
42
 The peaks have approximately
1:2:1 intensity ratio, respec. Due to
~3:1 eqm mixture of trans : cis
isomer.
 Result of 2D EXSY experiment on
W(S22H(p-CH3Oph))3 are
represented in fig.
 In addition to diagonal peaks, cross
peaks are observed in all the
protons.
 This indicates all the sites are
undergoing exchange with each
other.
 Cross peaks for the H1-H3 protons
are weakest and give less certain
rate constants for this interchange.

43. 4(d) BANDSHAPE ANALYSIS
➢ This method was the first one used to show the applicability of NMR to
dynamic process.
➢ For a system with two sites, in slow exchange or low temp. limit,one can
observe normal spectrum with two peaks.
➢ If the temperature is raised and exchange starts to occur, the two peaks begin to
broader and come together.The peak will coalesce at some temp. Called as
coalesce temp.
➢ This depends on exchange rate and chemical shift separation between the peaks
in the absence of exchange.
➢ On further increase in temp. the signal changes to a single sharp resonance in
the fast exchange limit.
➢ For systems with several sites and hence several peaks in the slow exchange
limit, it is possible to observe the broadening and coalescence of exchanging
sites.
➢ Quantitative analysis normally involves calculating the spectrum for various
exchange models and rate constants .
43

44. 4(d) BANDSHAPE ANALYSIS
44
 Then choosing model that best fits the observed spectra and gives rate
constants having normal temp. dependence.
 Computer programme are available to generate the calculated spectra.
 The time scale for this method depends on chemical shift
difference.,ΔV0 between exchanging sites.
 At the coalescence temp., the rate constant is given by
 K =  ΔV0 /2 = 2.22 x ΔV0 (17 )
 Below coalescence temp, in the slow-exchange region, two peaks are
observed that are broadened over their natural full linewidth at half-
height by  v and k= 2  v in this region.
 Above coalescence temp, in the fast-exchange region, only one peak is
observed with a linewidth of v and k= 4pi v02/v. in this region.
 For a typical values for 1H NMR of v = 5Hz and v0= 100Hz,K can be
in range from ~30 to -3x104 s-1.

45. 4(d) BANDSHAPE ANALYSIS
45
 Since ΔV0 depends directly on magnetic field strength,the range can be
extended to larger k by working at higher fields.
 For other nuclei like 13C,19F and 31P and for paramagnetic systems, ΔV0 can be
much larger and upper limit can be greatly extended by ~102 by bandshape
analysis.
➢ Limitations:
➢ One needs chemical shift and line width for non-exchanging systems.
➢ When possible this is done by cooling the sample to well below slow exchange
limit, but temperature dependence of the shifts and line width is rarely
determined and are treated as constants in the analysis.
➢ Exchange pathways are not always clearly delineated by bandshape analysis,
especially in multisite systems.
➢ A model is chosen and fitted to the data but initial choice is somewhat
subjective and some pathways may be missed.
➢ A problem can be arises in the data collection on pulsed Fourier transform
instruments.

46. 4(d) BANDSHAPE ANALYSIS
46
 Applications :
 A typical application of bandshape analysis to inorganic mechanism
problem is the recent study of Raymond and co-workers on
fluxionality of tris-catecholate complex of Ga(III), where ligands
are 2,3-dihydroxy-N,N’-substituted-terephthalamides.
 Under slow-exchange conditions the 1H NMR at 300 MHz of the
isopropyl derivatives shows two methyl resonances due to
chirality.
 In D2O, as temperature is raised these two peaks merge and
coalesce at -570C.Further increase in temp. produces the expected
sharpening to one methyl signal.
 Similar studies were reported on asymmetrical amide ligand with
a benzyl group on one nitrogen and tertiary butyl on the other.

47. 4(e) RELAXATION RATE MEASUREMENTS
 This type is a specialised extention of bandshape analysis in which temp.
dependence of transverse nuclear relaxation time,T2,is used to measure
rate of exchange.
 T2 can be determined from width of NMR peak or more accurately by
special pulse sequences.
 The method is generally applied to simple systems with well-separated
peaks in the NMR spectrum.
 It is specially useful for measurements of solvent exchange rates from
paramagnetic metal ions.
 Swift and Connick first published the basic equations that are solution of
bloch equations modified for chemical exchange by Mcconnel.
 Analogous eqns have been given for T1,for three-site problems and for
rotating frame relaxation time in such systems.
47

48. 4(e) RELAXATION RATE MEASUREMENTS
48
 An ideal temperature dependence of
the relaxation rates is shown in fig.
 The parameter plotted isTip-1 is the
difference between the relaxation rates
in the presence of exchanging species
and the rate for the pure solvent
divided by metal ion concentration.
 In the high-temp.limit at the left of fig.
exchange is fast and relaxation is
controlled by the nuclear relaxation
rate in the inner coordination sphere of
the metal ion.T2m
-1.
 As temp.lowered,exchange becomes
slower and relaxation is controlled by
dephasing of nuclear precession
frequency due to difference in chemical
shift between bulk and coordinated
nucleus Δm.

49. 4(e) RELAXATION RATE MEASUREMENTS
49
 The slower is the exchange, more effective is dephasing so that measured
relaxation rate increases with decreasing temp. In the region called as non-
Arrhenius region.
 At still lower temp.exchange becomes slow enough so that dephasing is
controlled by exchange lifetime, m, and the relaxation rate decreases with
decreasing temp.inArrhenius region.
 Finally, at low temp.,inner sphere solvent exchange is so slow that only
relaxation due to outer-sphere interactions.,T20
-1 is observed.
 The latter effect occurs actually at all temps.
 At the maximum betweenArrhenius non-Arrhenius regions, m-1= Δm.
 As Δm in the range of 103 to 105 s-1 for paramagnetic systems, gives some
indication of range of applicability.
 In practice, a particular system often show only two or three of these specific
regions.

50. 4(e) RELAXATION RATE MEASUREMENTS
50
 The problem is to fit this temp. dependence to known
functions primarily to determine ΔH* and ΔS* for exchange
process.
 This also requires some knowledge or estimates of activation
energies Em and E0 forT2m andT20 respect.
 Measurement of T-1 can be helpful in this regard as T1 is not
affected by dephasing and exchange is apparent only in
Arrhenius region as shown in fig.
 Main difficulty is separating various factors that affect temp.
dependence of T2
-1 when limiting region are not well
defined.

51. 5.ELECTRON PARAMAGNETIC RESONANCE METHOD
➢ This is a powerful technique for the detection and monitoring of species
with unpaired electrons.
➢ This type of spectroscopy is designated by EPR,ESR,EMR(electron
Magnetic Resonance)
➢ EPR is quite sensitive with detection limits in the range of 10-6 M in
favourable cases. It is quite informative as to structure because of electron-
nuclear hyperfine coupling to metal and ligand nuclei.
➢ Disadvantages :
➢ Mainly many species with unpaired electrons do not give a leads to broad or
undetectable signals.
➢ Signals are more detactable in the crystalline or frozen glassy state.
➢ For the first row transition metals in their common oxidation state,solution
EPR is useful for complexes of V(IV),Mn(II) and Cu(II) while Cr(III) and
Fe)III) often give broad spectra in solution.
51

52. 5.ELECTRON PARAMAGNETIC RESONANCE METHOD
52
 Most organic radicals give EPR signals that are quite useful for detection and
identification of such species as reaction Intermediates.
 Most EPR spectra run at X-band frequency of 9.4GHz in the microwave region
of the electromagnetic spectrum.
 Magnetic field of ~ 0.3 T is changed into give resonance condition for signal
detection.
 Sample tube should be quartz to avoid impurity signals found in pyrex.
 The concentrations of paramagnetic species should be <10-3 M to minimize
signal broadening due to intermolecular relaxation interactions.
 EPR spectra are usually displayed as plots of the derivative of signal intensity
verses magnetic field.
 Double integeration of such data is necessary to get proper integrated signal
intensities.
 With proper calibration, the signal intensity gives direct measure of
concentration of EPR active species.

53. 5.ELECTRON PARAMAGNETIC RESONANCE METHOD
53
 Pulse EPR method is more widely available.
 A 900 pulse is typically in the range of 10 to 30ns and FID after
such a pulse can be used to measure the electron spin relaxation
time.
 It can also be used to monitor the decay of radicals produced by
some fast method like flash photolysis or pulse radiolysis.
 Most applications use EPR as a detection method for reactants and
products.
 Various flow methods can be coupled with EPR to monitor time
dependence of EPR active species.
 It is possible to use EPR line broadening to measure exchange
rates in time scale of ~ 10 -7 s.

54. 6.PULSE RADIOLYSIS METHOD
 It is possible to quickly generate reactive species and solvated electrons by
passing a high-energy pulse of electrons through solution.
 The pulse is typically 5 to 100 ns long with energies in the range of 2 to 20
MeV, depending on source apparatus.
 High energy electrons initially are present in hot spots and thermalized species
are present after ~ 10 -7 s.
 In water, the species and number produced per 100 ev of energy absorbed,in
brackets, are : eaq
-(2.65), *H(0.65), *OH(2.65), H2O2(0.72), H2(0.45)
 In most applications, the initial radiolysis products are scavanged by additives to
remove undesired species or to produce a new reactive species.
 E,G. Water saturated with N2O(~0.022 M under 1 atm of N2O) converts eaq-
to *OH in ~50ns by following reaction.
 Eaq- + N2O + H2O ------- *OH + N2 + OH-
54

55. 6.PULSE RADIOLYSIS METHOD
55
 Most studies in this area use spectrophotometric detection
and time scale can be from microseconds to seconds.
 The products are produced at low concentration, it is often
possible to do multiple radiation pulses on the same sample.
 The main problem is the lack of molecular specificity of the
spectrophotometric method so that the nature of reaction
and products are often inferred by analogy and by
concentration dependence of the reaction rate.

56. 7.FLASH PHOTOLYSIS METHOD
 This technique is somewhat analogous to pulse radiolysis in that the
system is subjected to a short high-energy pulse.
 Then subsequent events are monitored.
 In Flash photolysis the pulse is usually by a laser beam of photons.
 The immediate product is some photo excited state of absorbing
reactant(s).
 Then subsequent events are monitored on the nanosecond or longer
time scale most commonly by Fourier Transform IR or UV-visible
spectrophotometry.
 Flash photolysis is much cleaner than pulse radiolysis there is not the
multiplicity of initial reactants or need to add reagents to remove
undesired reactants.
 In both the methods there is a problem of identifying the reactive
intermediates from often limited spectroscopic signatures they provide.
56

57. 7.FLASH PHOTOLYSIS METHOD
57
 Many studies of the activation of C-H bonds by coordinatively
unsaturated species can be generated by flash photolysis.
 Recent study by Harris and co-workers have observed flash
photolysis of Rh(Tp*)(CO)2 in pentane with a 295nm laser
pulp(Tp* = hydridotris(3,5-dimethylpyrazolyl)borate).
 They observed reformation of Rh(Tp*)(CO)2 at 2054cm-1 with
 = 70 ps and cooling of a vibrationally excited intermediate with
 = 23 ps,to give a vibrational ground state absorbing at 1972cm-1
.
❑ The final product Rh(Tp*)(CO)(R)H, appears on a longer time
scale of ~ 500ns.
❖ Flash photolysis also provides access to electronic excited states
whose photochemistry, energy transfer and electron transfer
properties can be observed after the flash.

58. 8.Potentiometric Method
58
 When a ligand is substituted by another ligand,
then it indicates that a new complex is formed.
 The rate of such reaction can be measured by
using Potentiometer.
 It measures the current that the electron carries
during the substitution reaction.

59. 9. Spectrophotometric Method
59
 The rate of reaction can be determined by using a Spectrophotometer.
 It is based on Beer-Lambert law/
 A = ԑ Cl
 Where,
 A = Absorbance
 C = Conc. of analyte
 l = path length
 Consider a reaction of
 CuSO4 + EDTA ----[ Cu EDTA] Complex
 The free Cu2+ ions are complexed by hexadentate EDTA ligands.
 A number of solutions are prepared wherein the value of EDTA added is
measured for 0,1,2,3,4,5,6,and 7cm3.
 The absorbance for each of the solution of Cu2+ EDTA are recorded.
 From this the rate of reaction can be determined.

60. Beer-lambert law
60
 For given material, the sample path length and concentration
of the sample are directly proportional to the absobance of
the light.
 Q.Explain the following techniques for the
determination of rate of reaction in complexes.

61. REFERENCES
61

62. References
62
 1. D.Tzur and E. Kirowa-Eisner, Anal.Chim.Acta, 355,
85(1997).
 2. D.A. Skoog, Principles of Instrumental Analysis.
 3. D.A. Skoog and D. M.West, Principles of Instrumental
Analysis.
 4. D.A. Skoog and J. J. Leary, Instrumental Analysis.
 5. D. C. Harris, Quantitative Chemical Analysis.
 6. G. D. Christian, Analytical Chemistry.

63. THANK
YOU
63