Substitution Reaction Kinetics
2.4 Determining the Rates of Ligand Substitution Reactions .1 Reversible Second-Order Reactions .1 Reversible Second-Order Reactions
2.4.3 Instrumental Techniques Used in Chemical Kinetics
Kinetic investigations are normally performed by monitoring the dependence of a physical variable such as pressure, pH, conductivity, absorbance and density30 which is proportional to the concentration of the products or the reactants as a function of time.
The data is then analyzed by fitting to an appropriate model to determine the rate constant.9b A number of different techniques such as nuclear magnetic resonance (NMR), UV/visible spectrophotometry and pulsed methods are used to study the rate of reactions.23 However, the choice of technique used to follow the kinetics depends on the nature and rapidity of the reaction.31 Regardless of the technique employed, the physical property measured must be proportional to concentration as a function of time after mixing. The reactants must be mixed in the shortest time possible within the time scale of the reaction. The physical conditions such as temperature and pressure must be controlled accurately.
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A chemical reaction is generally considered as fast if 50% of the reaction completes in 10 seconds or less.31 Kinetic studies of very fast reactions such as reactions involving proton transfer, enzymes and non-covalent complex formation,23 that lie outside the time frame of the normal laboratory operations are studied using specialised techniques and instruments. Normally, for fast reactions, the time varies from 1 minute to 10-14 seconds.24 One approach of analysing fast reactions is to bring their rates into the conventional time range by changing the conditions such as temperature, concentration or the solvent which is reliable only if the half-life is greater than 1 hour.32 The two main methods often used to study fast reactions include flow methods and pulse methods.23
Sufficiently slow reactions are often studied using conventional methods such as UV/visible spectrophotometry which involve first mixing of the reagents and then determining the decrease in the concentration of the reactant(s) or the increase in the concentration of the product(s) with respect to time. Thus, the time taken to mix the reagents and take the necessary measurements should be short enough so that it does not interfere with the actual rate of the reaction. Despite the number of methods available,23 only the techniques of UV/visible absorption spectrophotometry and the stopped-flow method would be highlighted in this thesis.
2.4.3.1 UV/visible Spectrophotometry
A substitution reaction which is slow (a reaction which generally takes longer than 16 minutes) are monitored using UV/visible spectrophotometer. UV/visible spectrophotometry is a sensitive technique14b which can detect the sample concentrations ranging from 10-4 to 10-6 mol dm-3.32 The instrument comprises of two light sources, one in the visible (tungsten lamp, 800 to 400 nm) and the other in ultra- violet (deuterium lam, 400 - 200 nm), monochromator, reference and sample compartment, temperature control unit, detector, the data processer and the output- readout system.31 The commonly used detector is a photomultiplier tube. In a UV/visible spectrophotometer, radiation from the light sources is passed through a monochromator. The light gets dispersed by the grating prisms and the monochromator allows a particular wavelength to pass through. The light of the single wavelength with intensity,
I
0, passes through the sample cell called a cuvette of length, l where the sample absorbs some light. Modern spectrophotometers are based on a double-beam design where it manages the light alternatively to pass through the sample cell and the reference cell using a chopper which is a motor that rotates a16
mirror into and out of the light path.31,33 The basic set-up of the UV/visible spectrophotometer is illustrated in Figure 2.5 while the photograph is as shown in Figure 2.6.34
Figure 2.5 Schematic diagram of a UV/visible spectrophotometry setup.34
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Figure 2.6 Photograph of a double-beam-in-space Varian Cary 100 Bio UV/visible spectrophotometer used by the University of KwaZulu Natal, Pietermaritzburg campus kinetics research group.
The spectrophotometer measures the transmitted light (T) from the sample which can be represented as
I
T I0 (2.28)
where I0 is the intensity of the incident light and I is the intensity of the transmitted light.
The transmittance is converted into absorbance by use of Equation 2.29 and is displayed on the screen.
AlogT (2.29) In Beer’s law (Equation 2.30), concentration of the sample is directly proportional to the absorbance and thus, can be determined from its absorbance.31
Acl (2.30) where A is the absorbance, ε is the molar absorptivity in mol-1 dm3 cm-1, c is the concentration in
mol dm-3 and l is the path length in cm (1 cm).
18 For a simple first-order reaction,
X Y k1
(2.31) The absorption at any time t, (At) is
At
X[X]
Y[Y] (2.32) where
X,
Y= molar absorptivity of X and Y respectivelyUpon completion of the reaction, the absorption is given by
A
X[X]0
Y[Y]0 (2.33) where A absorbance at infinity]
0[ X
and [Y]0 initial concentration of X and Y respectivelyFor the kinetic analysis, absorbance can be obtained from the following equation
t A k
A A A X
X
t o t
o
ln 1
] [
]
ln[
(2.34)
The observed rate constant for the reaction can be obtained by a least squares fit of the observed absorbance versus time trace at a specific wavelength. The second-order rate constant for the reaction is obtained by monitoring the reaction at different concentrations. The reactions can also be performed at different temperatures to determine the activation parameters.
Figure 2.7 shows the reaction profile obtained for the substitution of [ClPt(tppz)Ru(tppz)PtCl](PF6)4 (where tppz = tetra-2-pyridyl-1,4-pyrazine) with thiourea. The kinetics for the reaction was studied at 383 nm and the kinetic trace obtained for the reaction at 298 K is shown as an inset in Figure 2.7. The rate constant for the reaction was obtained by fitting first-order exponential decay function using Origin 7.5®.35
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250 300 350 400 450 500 550 600 650 700
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0 20 40 60 80 100 120
0.15 0.20 0.25 0.30 0.35
Absorbance
time, minutes
= 383 nm
Absorbance
Wavelength, nm
Figure 2.7 Spectrum obtained from Cary UV/visible spectrophotometer for the substitution of Clˉ from [ClPt(tppz)Ru(tppz)PtCl](PF6)4 (2.0 x 10-5 M) by thiourea (0.0004 M) in methanol solution (I = 0.02 M (adjusted with LiCF3SO3 and LiCl) at 383 nm and 298 K.
Apart from its use in the direct monitoring of conventionally slow kinetics of ligand substitution reactions, UV/visible spectroscopy is also used to perform UV/visible spectroscopic titrations to determine the pKa values of the coordinated protic ligands such as aqua ligands. In such titrations, the aqua complex is titrated against a suitable strong base and the resulting change in the absorbance is spectroscopically monitored.
By analysing the data obtained at a specific wavelength, the pKa values for the complex are obtained. Such thermodynamic pKa values of the coordinated aqua ligands are important for probing the electrophilicity of the metal complexes as reported by Jaganyi et al.36 and van Eldik et al.29,36a,b,37 An example of a spectroscopic titration spectrum is given in Chapter 4, Figure 4.2.