Kinetic Theory and Associated Techniques 3.1. Introduction
3.5. Techniques Associated with the Study of Chemical Kinetics
3.5.1. UV/ Visible Spectrophotometry
UV/Visible spectrophotometry is one of the most powerful[16] and commonly used techniques involved in the kinetic studies.[8] It is a sensitive technique which can detect the sample concentrations ranging from 10-4 to 10-6 M.[21] The key components of a spectrophotometer include the monochromator, light source, detector and the data processer. The photomultiplier tube is a commonly used detector in UV/Visible spectrophotometry. It consists of a cathode which emits electrons when striked by photon of radiation. The light source used is deuterium for UV and tungsten lamp for visible measurements. For UV/Visible region, normally glass prisms are used as
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monochromators.[22] Sample cells (cuvettes) are made up of quartz or fused silica and are transparent.
Radiation of more than one wavelength enters the monochromator and the grating prisms disperse the light into its component wavelengths and the monochromator allows a single wavelength to pass through. The beam then passes through the sample pathway. The photomultiplier detector then measures the transmitted radiation as photons. The photons hit the photoemitive cathode and electrons are kicked out from the cathode which is amplified at the dynodes where a cascade of electrons is produced before they are finally collected at the anode, resulting in a current that is amplified and measured. The UV/Visible spectrophotometer measures the absorbance ranging from 190 nm to 900 nm.
Figure 3.2 Schematic diagram of a UV/Visible spectrophotometry setup.[23]
Modern spectrophotometers are based on a double-beam design where one beam passes through the reference solution while the second beam simultaneously passes through the sample.[22] Outputs from the two are amplified, computed and displayed on the output device. The spectrophotometer measures the transmitted light from the sample. The transmitted light is converted into absorbance which is displayed on the screen.
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The light transmitted from the sample can be represented as
I
T I0 (3.82)
Where I0 = the intensity of the incident light
I = the intensity of the transmitted light The absorbance can then be written as
T
A log (3.83) By applying Beer’s law (Equation 3.84), the concentration of the sample can be determined from its absorbance. Beer’s law states a linear relationship between the absorbance, concentration and the path length.[22]
cl
A (3.84) Where A absorbance
molar absorptivity c concentration in mol dm-3 l path length in cm
UV/Visible absorption spectra often involve broad absorptions that overlap with other species in the solution. Even though this makes the analysis of the product more difficult, kinetic analysis can be done on overlapping absorption spectra.[19]
For a given first-order reaction,
X Y
k1
(3.85) At any time t, the absorption is given by
] [ ]
[X Y
At X Y (3.86) where At = the absorption at any time, t
X, Y= molar absorptivity of X and Y respectively
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When the reaction goes to completion, the absorption is given by
0
0 [ ]
]
[X Y
A X Y (3.87) where A absorbance at infinity
]0
[X and [Y]0 initial concentration of X and Y respectively For the kinetic analysis, the absorbance can be expressed as
t A k
A A A X
X
t o t
o
ln 1
] [
]
ln[ (3.88)
Figure 3.3 shows the reaction profile obtained for the substitution of [Pt{4´-(o-tolyl)- 2,2´:6´,2˝-terpyridine}Cl]CF3SO3 with 1-methylimidazole (Structure given in Figure 5.1). The kinetics for the reaction was studied at 333 nm and the trace obtained for the reaction at 298.15 K is shown as an insert in Figure 3.3. The rate constant for the reaction was obtained by fitting first-order exponential decay function using Origin 5.0®.[24]
Figure 3. 3 Spectrum obtained from Cary UV/Visible spectrophotometer for the substitution of Cl
from [Pt{4´-(o-tolyl)-2,2´:6´,2˝-terpyridine}Cl]CF3SO3 (2.50 x 10-5 mol dm-3) with 1-methylimidazole (5.00 x 10-4 mol dm-3) in methanol solution (I = 0.10 M (0.09 M LiCF3SO3 + 0.01 M NaCl)) at 333 nm and 298.15 K.
300 320 340 360 380 400 420 440
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45
0 500 1000 1500 2000 2500 3000 3500 4000 0.34
0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42
Absorbance vs time at 333 nm
Fit: First order exponential decay k obs : 0.00253 s -1
A b so rb an ce
[1-methylimidazole]/M
333 nm
A b so rb an ce
Wavelength/nm
0 500 1000 1500 2000 2500 3000 3500 4000 0.34
0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42
Absorbance vs time at 333 nm Fit: First-order exponential decay kobs: 0.00253 s-1
Absorbance
[1-methylimidazole]/MTime/ s
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Many chemical reactions occur too rapidly for conventional UV/Visible spectrophotometry.
Such reactions require shorter sampling and mixing time. Often flow methods are used to overcome this problem. Flow methods involve flowing of two reactant solutions rapidly under pressure to a reaction mixing chamber and then to an observation chamber.
Concentrations of the reactants or products are then measured at various positions of the tube at various time intervals. The time scale for mixing of flow methods varies approximately from 1 ms to 10 seconds. Reactions with half- lives of about 10-2 seconds are often studied using such methods.[22] There are two common types of flow methods used namely, continuous flow method and stopped flow method.
Hartridge and Roughton[25] pioneered continuous flow method by designing special mixing chambers to study the rapid reactions in solution.[4] A schematic representation of continuous flow method is given in Figure 3.4. This method works on the principle where the two reacting solution are forced into the mixing chamber by the pistons. The resulting solution then flows through the observation tube, where spectroscopic detection takes place at specific distances downstream from the mixer. This method is normally used to study rapid solution reactions with half- lives of approximately 1 ms or greater.[4] In this technique since a steady state is set up and the observation does not require being rapid. However, a longer observation time requires a larger amount of solutions. This problem can be solved by using stopped-flow technique.[4]
Figure 3. 4 Diagrammatic representation of a continuous flow kinetic system. The letter d represents the distance from the mixture to the point of observation.[11]
A schematic diagram of the stopped-flow technique is shown in Figure 3.5. This technique is designed to study the reaction of two substances where one of the reactant is placed in syringe A and the other in syringe B. The two syringes are kept at constant temperature of choice. In this method the two reacting solutions are rapidly forced into a mixing chamber by pressure. The mixing in stopped-flow takes approximately 0.001 seconds.[22] From the mixing chamber the solution then goes into the reaction cuvette where the solutions
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alternatively get mixed and then stops when the stopping syringe comes against its seating (Figure 3.5). The reaction is then flowed spectrophotometrically.
Figure 3. 5 Diagrammatic representation of stopped-flow apparatus.[20]
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