IUP Fluorescence Lifetimes and Quenching Introduction

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EXPERIMENTAL
PHYSICAL CHEMISTRY
–
——-
A laboratory Textbook
THIRD EDITION
Arthur’ M. Halpern
Indiana State University
George C. McBane
Grand Valley State University
·=
W. H. FREEMAN AND COMPANY
New York
——
ISBN-13: 97807167-1735-5
ISBN-10: 0-7167-1735-2
© 2006 by W . H. Freeman and Company
All rights reserved.
Printed in the United States of America
Second printing
W. H . Freeman and Company
41 Madison Avenue
New York, NY 10010
Houndmills, Basingstoke RG21 6XS England
www.whfreeman.com
Contents
Experiment 13
Solid-Liquid Equilibrium in a Binary System
Experiment 14
Liquid-Vapor Equilibrium in a Binary System
Experiment 15
Henry’s Law Constant Determined by Headspace
Chromatography
Experiment 16
Surface Tension Properties of Liquids
Part 6
vii
Transport Properties and Chemical Kinetics
Experiment 17
Viscosity of Liquids, Part I: Low Viscosities
Experiment 18:
Viscosity of Liquids, Part II: High Viscosities
Experiment 19:
Determination of Collision Diameters from Gas Viscosities
Experiment 20:
Kinetics of a Homogeneous Reaction in Soluti on
Experiment 21:
Kinetics of a Diffusion-Controlled Reaction
Experiment 22:
Kinetics of a Reversible, First-Order, Consecutive
Reaction: The Reduction of Cr(VI) by Glutathione
Experiment 23:
Kinetics of an Enzyme-Catalyzed Reaction
Experiment 24:
Kinetics and Thermodynamics of a Heterogeneous Gas
Phase Reaction: Reversible Dissociation of Ammonium
Carbamate
Experiment 25:
Kinetics and Mechanism of a Heterogenous Reaction: Oxidation
of Magnesium by Hydrochloric Acid
Experiment 26:
Laser Kinetics, Part I: Luminescence Quenching of the
Uranyl Ion by the Chloride Ion
Experiment 27:
Laser Kinetics, Part II: Photochromism of Mercury(ll)
Dithizonate
Experiment 28:
Laser Kinetics, Part III: Viscosity Effects on Lumjnescence
Quenching Rate Constants
Part 7
Colloidal Systems: Micelles
Experiment 29:
Determination of the Critical Micelle Concentration
Experiment 30:
Determination of the Mean Aggregation Number of a
Micellar System
Part 8
Polymers
Experiment 31:
Molecular Weight and Monomer Linkage Properties of
Poly(vinyl alcohol)
Experiment 32:
Thermodynamic Properties of Elastomers
Part 9-
Photophysics and Molecular Spectroscopy
Experiment 33:
Excited-State Properties of 2-Naphthol, Part I: Excited-State
Acidity Constant
viii
Contents
Experiment 34:
Excited-State Properties of 2-Naphthol, Part II: Deprotonation
and Protonation Rate Constants
Experiment 35:
Enthalpy and Entropy of Excimer Formation
Experiment 36:
Rotational-Vibrational Spectrum of HCl
Experiment 37:
Vibrational Spectrum of Sulfur Dioxide
Experiment 38:
Analysis of a Flame using Emission Spectroscopy
Experiment 39:
Absorption Spectra of Conjugated Dyes
Part 10
Computational Chemistry
Experiment 40:
Computational Chemistry: The Calculation of LirG 0 , LirH 0 ,
and LirS0 for the Reaction N104 ~ 2 N02
Experiment 41:
Computational Determination of the Molecular Constants
of HCl
Photophysics and Molecular
Spectroscopy
EXPERIMENT 33
Excited State Properties of 2-Naphthol
Part I: Excited State Acidity Constant
Objective
To determine the acidity constants of the ground and lowest electronica lly excited states of 2-naphthol in aqueous solution.
Introduction
The electronic structure of a molecule determines such physical and chemical properties as its charge distribution, geometry (therefore dipole moment), ionization
potential, electron affinity, and general chemical reactivity. If the electronic structure of a molecule is changed, therefore, we would expect its physical and chemical properties to be altered. Such a rearrangement in electronic strucrure can, in
fact, be brought about (and very rapidly, -10- 13 s) if the molecule is raised to
an electronically excited state by the absorption of a quantum of light (a photon)
whose energy matches the gap between the molecular ground and excited-state
energy levels.
For most orga nic molecules that contain an even number of electrons, the
ground state is characterized by the pairing of all electron spins; the net spin angular momentum is zero, and this arrangement is called a singlet state. When considered in terms of molecular orbitals (MO), electronic excitation involves the
promotion of an electron from a filled MO to a higher, vacant MO. This new
orbital configuration, which characterizes the electronically excited state, may be
one in which the two electrons in the singly occupied MOs have opposite spins.
Accordingly, this electronically excited state is also a singlet. The ground and lowest electronicalJy excited singlet states are often denoted So and S1, respectively.
Higher excited singlet states are referred to as S2 , S3, … , S,,. This experiment
deals with excited singlet states.
Although measurements of the physical and chemical properties of a molecule
in its ground state can be carried out at leisure, more or less (assuming that the
molecule is thermally stable), the examination of these properties in its excited
states is severely hampered because these states are very short-lived. For most
molecules, S1 states have lifetimes ranging from 10- 6 to 10- 11 s. Excited states
are metastable; they undergo decay processes that dissipate the energy they possess relative to more stable products. For example, the excited state of a molecule may in general spontaneously return to the ground state via photon emission (fl uorescence), convert electronic excitation into ground-state vibrational
energy (heat), or undergo bond dissociation or rearrangement or a change in elec-
tron spin multiplicity. Because sp o ntaneous emission from an excited state (that
is, fluorescence) takes place very rapidly, fluorescence can be used as a probe, or
measurement, of excited-state concentration. In addition, fluo rescence studies can
provide information about the physical an d chemical properties of these shortlived singlet states. This field of experimentation is ca lled photophysics.
In this experiment, you will determine some ground- and excited-state properties of the organic molecule 2-naphthol (ArOH ).
2-Naphthol (A rOH)
In aq ueous solution, ArOH behaves as a weak acid, fo rming its conjugate base
naphthoxy ion Aro – and the h ydronium ion.
It is instructive to measure the acidity constant of ArOH in its lowest excited
electronic state, denoted as K~, and to compare this value with that of the ground
state Ka. This information indicates how the change .in electronic structure alters
the charge density at the oxygen atom. The experimental method is best introduced in terms of the energy-level diagram shown in Figure 1.
-~~~r—~~~-A-ro—*—–~s,
s,-~—–~~
ArOH*
Figure 1. Schematic
diagram of the ground
and first excited singlet
state energies of free
naphthol and its
conjugate base, the
naphthoxy ion, in
aqueous solution.
50 _ ..___ _
~-~-1~-~— -~~ –~—~–A-r_O___+_H_+–~ So
ArOH
The relative energies of the free acid and its conjugate base (the naphthoxy
io n ) are indicated for both the electronic ground (So) and (lowest} excited (Si)
states in aqueous solution. Each anion is elevated with respect to its free acid by
a n energy, !1H a nd !1H’:·, r espective ly. These are the entha lp ies of deprotonation.
Both the ground-state acid and its conjugate base can be transformed to their respective excited states via the absorption of photons of energy hv A r OH and hv ArO – .
For simplicity, these absorptive transitions are shown to be equa l to the fluorescence from the excited to the ground states of the acid and conjugate base. (The
ground- and excited-state vibrational levels involved in the transitions a re not
indi cated.)
Experiment 33
33-3
We can express the free energy of deprotonation of ArOH in terms of the enthalpy and entropy of deprotonation and the equilibrium (ionization) constants
6. G = 6.H – T 6.S = – RT ln K0
(1)
and
(2)
for the So and 5 1 states, respectively. If we make the assumption that the entropies
of dissoci ation of ArOH and (ArOH)’:- are equal, it follows that
6.H- 6.H’:- =-RT ln
~ ,
(K”)
Note: a “+”
– sign is removed,
corrected by Jun Han
(3)
and thus from Figure 1, it can be deduced that
(4 )
where his Planck’s constant. Avogadro’s number NA has been included to put each
energy term on a molar basis. Combining equations (4) and (3) and rearranging,
Note: a negative sign is added.
(5) Corrected by Jun Han
_
Thus knowledge of the energy gap between the ground and first excited states
for both the free acid and its conjugate base leads to an estimate of K~, if K 0 is
known. The analysis presented here, which accounts for the observed thermodynamic and spectroscopic energy differences, was first’ developed by Th. Forster
(1949, 1950). This approach is thus often referred to as a Forster cycle. Equation (5) can be recast into a more convenient form:
[v
PKa’:- = pKa – 2 .NAhc
30 3 RT ArOH –
vAro – ] ,
(6)
where c, the speed of light, ha s been incorporated in the expression to express
the transition energies of ArOH and Aro – into wavenumbers (cm- 1), a common
spectroscopic energy unit, rather than Hz (s- 1 ). The acidity constants are expressed as pK values. The 2.303 is needed in the denominator because the pK’s
are defined as – log 1o K.
The question now is how to obtain the spectroscopic energy difference (-VArO- VArOH), or 6.v, pertinenr to the Forster cycle in 2-naphthol. Three approaches can
be considered. The first is to base the measurement on the absorption maxima of
the free acid and conjugate base. The second is to use the fluorescence maxima
of the two species, and the third is to use what is called the 0-0 energies of ArOH
and Aro- . The first two methods are somewhat more straightforward. Obtaining 6.v from absorption data has the advantage that the energy difference that is
obtained does not require an instrumental wavelength correction. Although obtaining 6.v from the fluorescence maxima seems simple enough, fluorimeters usually produce spectra that are distorted by the wavelength response of the monochromator/photomultiplier combination. Thus, unless these spectra are corrected
for this sensitivity distortion, the recorded fluorescence maxima will depend (al-
33-4
PART 9 Photophysics and Molecular Spectroscopy
though perhaps subtly) on the particular instrument used and thus wi ll nor represent the “true” or absolute spectroscopic properties of the ArOH/Aro- system.
The third approach provides the value of Liv that best represents the energy
difference between S1 and So implied in the Forster cycle, Li1Jo.o. Unfortunately
LiiJo.0 cannot be determined directl y in all cases (such as ArOH), but it can be estimated from an analysis of both the absorption and fluorescence spectra. It is
shown schematically in Figure 2 for a single species (ArOH or ArO – ).
iimax (abs)
t
Figure 2. Schematic
diagram of the
absorption and
fluorescence spectra of a
molecule. It is assumed
that these transitions are
between the same t wo
electronic states, that is,
\
\
\
\
_
‘, … ,.-,’Mirror image of fluorescence
”
So~S1 .
”
”
ii –
. The absorption and (preferably instrument-corrected) fluorescence spectra are
both plotted on a common energy axis. Furthermore, the spectra are presented
so that each has the same peak max imum value. The point of intersection of these
spectra gives an estimate of the 0-0 energy gap between So and S1• This approach
does not apply to cases in wh ich the S0-S 1 transition is distorted by a nearby (and
especia lly more intensely absorbing) So to 52 transition.
Whichever method is used to determine Liv, it should be used consistently with
both species ArOH and Aro – .
Safety Precautions
•
Always wear safety goggles in the laboratory. Ultraviolet-light-absorbing
eye protection is required. Some plastic safety goggles do nor completely
a bsorb ultraviolet radiation.
•
2-Naphthol is an irritant. If you are to prepare the solutions from solid
material, you must wear gloves; if possible, work in a fume hood.
•
Be sure you h ave been instructed to use the proper p ipetting techniques
when handling 2-naphthol soluti ons. Never piper using suction by mouth.
•
If you a re to obta in fluorescence spectra, be sure that a ny ozone produced
by the ultraviolet sou rce is vented. O zone is a noxious, dangerous gas that
has an acrid odor. If you detect this gas, leave the vicinity, inform your
instructor, and increase air circulation at o nce.
Procedure .
In this experiment, you will determine Ka from the pH dependence of rhe absorption spectrum of aqueous 2-naphrhol.
1. Obtain the absorption spectra of two solutions of ArOH (each at
– 2 x 10- 4 M; the actua l concentration must be accurately known). In one
Experiment 33
MJ:I
solution, the free acid must predominate (low pH), and in the other, the
conjugate base must be the major naphtha! component (high pH). Use
stock solutions of HCI and Na OH (for example, 0.10 M) to create [H + ]
and [OH- ] of 0.02 M, respectively. It is important that the ArOH
concentration be the same in each case. Label and save these solutions.
Record or display these spectra on a common wavelength axis so that the
spectra overlap.
2. Now o btain absorption spectra of ArOH (a lso ~2 x 10- 4 M) at
intermediate pH values . Adjust pH levels using ammonium ch loride buffer
solutions (NH 40H/NH4Cl), for example, 0.1 M/0.1 M, 0.1/0.2, or 0.2/0.1.
These solutions can be conveniently prepared from 1.00 M stock solutions
of NH40H and NH4Cl. Obtain at least three spectra and scan the entire
wavelength range as in step 1. These spectra will display both free acid and
conjugate base a bsorption . If necessary, choose appropriate ratios of the
NH40H and NH4Cl stock solutions to produce a satisfactory series of
ArOH/Aro – spectra. It is essential that the 2-naphthol concentrations be
identical and accurately known in each case. Immediately after recording
each spectrum, measure the actual pH of the solution using a calibra ted
pH meter. Label and save these solutions. It is instructive to display or
overlap each spectrum on a common axis. Make sure that the temperature
of the samples is constant (to w ithin 1°C) or otherwise controlled
throughout the experiment. If the bulk ArOH concentration, for example,
[ArOH] + [Aro – ], is invariant, the spectra, when properly overlapped,
should intersect at a common wavelength called the isosbestic (equal
absorption) point. The presence of an isos bestic point indicates that there is
a closed system (as a function of the variable, pH ) consisting of two species
in equilibrium.
3. Using the same solutions in step 1, obta in the fluorescence spectra of
naphtha! and its conjugate base. If possible, correct the spectra fo r the
monochromator/photomultiplier response of the fluorimeter.
4. If possible, display the fluorescence spectra of the intermediate pH solutions
on the same wavelength axis so that the spectra overlap. Again, you sho uld
observe a com mon wavelength where the spectra overlap. This is sometimes
referred to as an isostilbic (equal brightness) point. Likewise, the presence
of an isostilbic point indicates that there are two excited-state species that,
aside from emitting light, interconvert only with each o ther .
Calculations
Because the bulk nap hthol concentrations [ArOH]o are identical in each of the
solutions studied, the following material balance applies :
rArOH]o = [ArOH] + [Aro-].
(7)
Under the conditions that (a) both the free acid and conjugate base a bsorb at
AmaxArOH, the wavelength of maximum absorption for ArO H, and (b) Beer’s
law holds,
A(A.maxArOH
) = EArOH [-Ar OH] + EArO – [Ar O – ],
f
(8)
llt!td I PART 9 Photophysics and Molecul ar Spectroscopy
e
w here A is the a bsorbance, is the path length, and EArOH and EArO are the molar absorptivity coefficients of the free aci d a nd conjugate base at Am:ix(ArOH),
respectively. Combin ing eq uations (7) and (8) produces
A(A,mxArOH)
.’e
= { EA,-()1-1 –
EArO }lA r OH]
+ { EArO }[A rOH] O·
(9)
This relation allows IArOHl to be determined under equilibrium conditi o ns. Once
it is known, the va lue of IArQ – ] at the sa me pH can be o bta ined from eq uation
(7). Because the acidity constant is
K = IH30+][Aro-1
a
[ArOH]
( 10)
(assuming that the activity coefficient ra tio is unity in these dilute solutio ns), you
can obtain the pK0 va lue for ArOH from a linear regression of pH versus
log([ArO-]/[ArOH]):
_
pH – pKa
+1
[Aro- 1
og [ArOH].
(11 )
You can obtain the va lu es of [ArOHJ and [Aro-1 for each solution from equati01~s (9) and (7), respectively. Report the standard deviation in pK0 • Compare
yo ur results w ith literature values.
Calculate pK~· for (ArOHr- from equation (6) using th e pK0 va lue you obta ined and w h atever method (s) you choose to determine (vArOH – VA.-0 ). Compa re these values and perform an error ana lysis. Discuss the errors that the prim ary measurements have on the d erived value of pK~.
Other molecules that you ca n study using this procedure are 2-naphtho ic acid,
acridine, and quinoline. Their solubilities in water a re limited but sufficient to allow you to prepare the dilute solutions needed for t he experiments.
0
OOC-OH
II
©LOO 00
N
2 -Naph thoic acid
Acridine
N
Qu inoli ne
Q!lestions_ and BJ rther Thoughts
1. In com paring the va lues o f K,1 and K~”, what can you deduce abou t the change in electron density at the 0 atom in 2-naphthol in the electronica lly excited state relative to the
ground state? If you have access to a molecu lar orbital program , such as HyperChem,
MOPAC, or Gaussian, perform a suitable MO calculation on the grou nd and first excited singlet states of 2-naphthol. The AM l Hamiltonian is appropriate, and a configuration interaction calculation in volving at least the hig hest-filled and lowest-unfilled
molecular orbitals is required for the excited-state property. These calculations wil l provide the atomic electronic charges.
2. If pK~· < pKa (the excited-state species is a stronger acid), ca n you comment o n th e relative (a bsolute) magn itudes of t he enthalpies of deprotonation? See Figure 1. Experiment 33 33-7 3. On what basis can we justify the assumption that the entropies of deprotonation of the ground- and excited-state 2-naphthol molecules are equal [see equations (1)-(3)]. Can yo u think of another possibility in which this assumption is a poor one? 4. Other molecu les that can be studied using this technique are 2-naphthoic acid, acridine, and quinoline (see the last paragraph in the Calcu lations section). Indicate the protolytic reactions for these molecu les, i.e., write the aqueous acid-base reactions. 5. Can yo u predict before doing an experiment whether the excited state of a molecule is a stronger or weaker acid than its respective ground state? What information would yo u need to perform such an assessment? further Readings General P. Atkins and J. de Paula, Physical Chemistry, 8th ed., pp. 492--494, W. H. Freeman (New York), 2006. I. N. Levine, Physical Chemistry, 5th ed., pp. 777-780, McGraw-Hill (New York), 2002 . R. J. Silbey, R . A. Alberty, and M. G. Bawendi, Physical Chemistry, 4th ed., pp. 519- 522, Wiley (Hoboken, NJ), 2005. Forster Cycle and Excited-State Acidity T h. fo rster, Naturwiss. , 36:1 86 (1949 ). Th. forster, Z . Electrochem., 54:531 (1950). C. Parker, Photoluminescence of Solutions, pp. 328-341, Elsevier (Amsterdam), 1968. ]. Van Stam and J.E. Loefroth,]. Chem. Educ., 63 :181 (1986) . A. Weller, in G. Porter, ed., Progress in Reaction Kinetics, vol. 1, pp. 189-214, Pergamon (New York), 1961. Fluorescence and Photophysics ]. B. Birks, Photophysics of Aromatic Molecules, Wiley-Interscience (London), 1970. ]. R. Lakowicz, Principles of Fluorescence Spectroscopy, Plenum Press (New York), 1983. N . J. Turro, Modern Molecular Photochemistry, Benjam in/Cummi ngs (Menlo Park, CA), 1978. EXPERIMENT 34 Excited-State Properties of 2-Naphthol Part II: Deprotonation and Protonat ion Rate Constant s Objective To determine the deprotonation and protonation rate constants of 2-naphthol in its lowest excited singlet state in aqueous solution. Introduction In the previous experiment, we determined acidity constants for aqueous 2-n aphtho l (ArOH) for both the ground and lowest excited (singlet) states. These constants perta in to the equilibrium (1) where the rate consta nts for the forward (deprotonation) and reverse (protonation ) reactions are indicated as kp and kd, respectively. A similar equilibrium can be w ritten for the electronica lly excited-state species, which is produced via photon absorption: ArOH'' + H ,O ~ Aro ->!· + H 30 +,
k;,
(2)
in which the values of the forward- and reverse-rate constants may be different
from those in the ground state because of differences in the properties of the
2-na phthol in these two states (for exa mple, different Ka values).
We can express the ratio of the concentra tions of free acid and the conjugate
base as a function of the pH:
[Ar0H1) _
log ( [ArO – l – pKa – pH,
(3a)
where we use molar concentrations to a pproximate activities. An analogous
equation,
log
[ArOH•:·l )
= pK’-· – pH
a
,
( [Aro – ::·1
(3b)
applies to excited state species. Equations (3a) and (3 b) show that if the pH of
the solution is less than pKa of 2-naphthol (in either electronic state), the free acid
form will predominate over that of the conjugate base: [ArOH] >> [Aro- ]. Likewise, if pH > pKa, then [Aro- 1 > [Ar0H1.
Suppose that by using a suitable buffer, the pH of the medium is established
to be less than pKa but greater than pK~. The ground state of the system will
then consist primarily of Ar OH. Electronic excitation via light absorption will instantaneously (~10 – 13 s) transform ArOH into ArOH •!· . We may assume that in
this experiment, the buffer holds the pH of the medium constant during and after electronic excitation. This is a va lid assumption because the number of photons absorbed per unit volume is much less than the ground-state concentration
•tfW PART 9 Photophysics and Mo lecular Spectroscopy
of ArOH. Thu s IArOH’:·]