In the Laboratory
Determinations of pKa from Luminescence Quenching Data An Undergraduate Laboratory Experiment Héctor E. Gsponer* Departamento de Química y Física, Facultad de Ciencias Exactas, Fisicoquímicas y Naturales Universidad Nacional de Río Cuarto, Estafeta No 9, 5800 Río Cuarto, Argentina Gustavo A. Argüello and Gerardo A. Argüello* INFIQC, Departamento de Físico-Química, Facultad de Ciencias Químicas Universidad Nacional de Córdoba, C.C. 61 - A.P. 4, 5000 Córdoba, Argentina The experiment that we describe in this article is designed to study the acid–base equilibrium in aqueous solution of a phenolic compound and to determine the acid dissociation constant (Ka) according to the following general reaction AH
A{ + H +
(1)
This is achieved by studying the effect of pH on the luminescence quenching of tris(2,2′-bipyridine)ruthenium(II) (Ru(bpy)32+ ) either by 4-bromo-2,6-dimethylphenol (4-Br2,6-DMP) or 2,6-dimethylphenol (2,6-DMP). The Stern– Volmer quenching constant (KSV) at different pH values was measured, and from these data the KaSV and Kb SV (or kaq and kb q ), the Stern–Volmer constants (or bimolecular quenching rate constants) for the species AH and A {, respectively, and Ka for each quencher can be evaluated. As a consequence, such measurements constitute an appropriate experiment for the physical chemistry laboratory. Background Interest has been centered for years on the possibility of obtaining quantitative values of acid dissociation constants and on their analytical implications. Therefore, many different techniques have been employed to study the equilibrium of the reaction given in eq 1. In recent years, a great deal of enthusiasm has arisen for the study of the properties of electronically excited states in order to better understand the mechanism responsible for energy and charge transfer processes (1). The fact that a photoexcited entity can be more oxidizing or more reductive than its fundamental state is useful for converting optical energy (light) into chemical or electrical energy. In this context luminescence techniques have been extensively used because they give information about these states, as absorption techniques give information corresponding to the fundamental states. Several systems that consist of complexes of transition elements have been studied. One of these is Ru(bpy) 32+ owing to a special set of properties that make it one of the most suitable species (2) for studying photochemical processes in solution. It is readily manageable in the laboratory, it is safe to work with, its excited-state lifetime is long enough to permit the use of easily affordable equipment, it emits visible light, and above all, it is commercially available. Furthermore, fluorescence spectroscopy is a technique ideally suited for the undergraduate laboratory curriculum. Several papers designing experiments for this laboratory and using fluorescence measurements have been published (3). Our objective is to propose a laboratory experiment enabling undergraduates to become familiar with the fluores*Corresponding authors.
968
cence technique and the principles of photochemistry. They will be able to produce the excited state of Ru(bpy)3 2+, to observe and measure how either the luminescence intensity (I) or excited state lifetime (τ) change with the addition of a luminescence quencher, to extract from these data the bimolecular quenching rate constant (kq ); and to observe that for a certain analytical concentration of a quencher, that is itself an acid base pair, the kq changes with the pH of the solution. To obtain kq values (kq = KSV/τ0) through I measurements we must first know the lifetime in absence of the quencher (τ0). However, to get the variation of kq with pH from the KSV values at different pH’s obtained by I measurements, τ0 must be pH-independent. The complex ion Ru(bpy)32+ meets this condition (4, 5) and the student is encourage to perform time-resolved experiments. Then, Ka of the quencher can be obtained. From the analysis of the acid–base equilibrium of the quencher, the quenching mechanism, the KSV values at different pH’s, and τ0, Ka can be obtained either by an analytic or a graphic method. This result can be corroborated using any commercial nonlinear least-squares fitting software and a personal computer allowing KaSV, KbSV, and Ka to be adjustable parameters and observing the coincidence. Principles The following general scheme is given in order to understand the nature of some processes that lead to the deactivation of an electronically excited species: Ia
A + hν → *A kr
*A → products k nr
*A → A k
l *A → A + hν′
k
r *A + Q → quenching
(2) (3) (4) (5) (6)
The absorption of a photon by the species A produces an excited species *A. This species has several ways to get rid of the excess energy—for example, unimolecular processes such as decomposition to form products (eq 3), conversion of energy into heat (radiationless deactivation, eq 4), emission of light (luminescence, eq 5) or interaction with other species present in the solution (bimolecular quenching process, eq 6). A relatively long lifetime of the excited state is important to facilitate the efficiency of the quenching process.
Journal of Chemical Education • Vol. 74 No. 8 August 1997
In the Laboratory Thus the quencher molecule can reach the excited species during its lifetime and produce a shortening of excited state lifetime through the bimolecular reaction (6) shown in eq 6. Some of the most important bimolecular processes are energy transfer (eq 6a) and electron transfer. The latter may lead either to oxidation (eq 6b) or reduction (eq 6c) of the excited state. *A + Q → A + *Q {
(6a)
*A + Q → A + Q
Oxidative
(6b)
{ *A + Q → A + Q+
Reductive
(6c)
+
For the systems studied in the experiments described below, luminescence quenching of Ru(bpy) 32+ by phenolic compounds such as 4-bromo-2,6-dimethylphenol and 2,6dimethylphenol, the quenching mechanism is formulated by eq 6c (5). Applying the steady-state approximation for *A: d[*A]/dt = I a – k r[*A] – knr[*A] – kl[*A] – kq[*A] [Q] = 0 Its concentration is given by: [*A] = Ia / (kr + knr + kl + kq[Q])
(7)
The quantum yield of luminescence is defined as φ = I l / Ia = k l[*A] / Ia
(8)
where Il and Ia are the rates of emission and absorption of radiation, respectively. Replacing [*A] in eq 8 we obtain φ = k l / (kr + knr + kl + k q[Q]) = klτ
(9)
τ = 1 / (kr + knr + kl + kq[Q])
(10)
where and τ is the lifetime of the excited state. When no quencher is added to the solution (that means [Q] = 0), the luminescence is the highest and the lifetime is the longest attainable provided all other conditions for the system remain constant. Thus, the quantum yield of luminescence and the excited state lifetime in absence of Q is given by eqs 11 and 12: φ0 = kl / (k r + knr + k l) = kl τ0
(11)
τ0 = 1 / (k r + knr + kl)
(12)
The general mechanism shown above predicts that the quantum yield of luminescence varies with the quencher concentration as φ0 / φ = 1 + kqτ0[Q]
(13)
From eqs 10 and 12, it is also true that τ0 / τ = 1 + kqτ0[Q]
(14)
Combining eqs 13 and 14 we obtain φ0 / φ = τ0 / τ = 1 + K SV[Q]
(15)
It is important to note that the quantum yields ratio (φ0 / φ) in eq 15 is equal to the lifetime’s ratio (τ0 / τ) only if the quenching occurs by a dynamic process (eq 6).1 However, in a general sense, the quenching mechanism can occur also by a solely static process or both static and dynamic processes. In this sense, L. K. Fraiji et al. (3c) described and discussed a series of experiments for the undergraduate laboratory on luminescence quenching that exhibits static, dynamic, and both static and dynamic quenching mechanisms. Equations 13 and 14, the so called Stern–Volmer equations (7), predict a straight line having unity intercept and a slope of kqτ0 = KSV, the Stern–Volmer constant. This is the magnitude experimentally determined.
Experimental Procedure The absorption spectra of Ru(bpy)32+ and phenols were recorded in a Shimadzu UV 1602 spectrophotometer. The pH control could be carried out by using a pH meter providing an accuracy of 0.02 units and temperature control. We controlled the pH with a pH/ISE EA 940 Orion Research pH meter using two glass-combined electrodes.
Luminescence Intensity and Lifetime Measurements This experiment can be fulfilled according to the equipment available. For steady-state measurements (luminescence intensity), the instrumentation required can be found in any laboratory even modestly equipped. For time-resolved measurements (lifetime), a nanosecond flash fluorescence system is required. We used a Farrand Mark I coupled with a Nicolet Explorer III digital oscilloscope and a personal computer. Time-resolved experiments were carried out with a homemade N 2 laser (337.2 nm) of ca. 140 µJ and 10 ns pulse. The laser beam was focused and passed across a 1cm fused silica cell. The emission signal collected at 90° was picked up with a Hamamatsu R928 photomultiplier tube and digitized in an HP 54200A oscilloscope. Materials and Procedure Tris(2,2′-bipyridine)ruthenium(II) was purchased from Baker and used as received. The 4-bromo-2,6dimethylphenol and 2,6-dimethylphenol were supplied by Sigma and purified by vacuum sublimation. All other reactants were used as received without further purification. The deionized water used to prepare the solutions was obtained with a Milli Q System (Millipore Co.). The Ru(bpy)3 2+ solution was made using Britton– Robinson buffer (10{2 M, equimolar in NaCH3COO, BO3 H3, Na2HPO4) in 1.0 M NaCl or NaClO 4 to maintain constant ionic strength. This solution was used as solvent to prepare the quencher. The concentrations of 4-Br-2,6-DMP and 2,6-DMP were 1 × 10{5 to 1 × 10{2 M according to their solubilities in acid media and the expected efficiency as quenchers, whereas the concentration of Ru(bpy)32+ was in the 1.0–3.0 × 10{5 M range. In most experiments, we started at basic pH, which was decreased by adding small volumes of concentratred phosphoric acid. The pH’s of Ru(bpy)32+ and Ru(bpy)3 2+ + Q solutions were adjusted separately before the solutions were mixed to run an experiment. Although the great stability of the ruthenium complex is known, it is recommended to use fresh solutions for each run. In all cases aerated solutions were used. To obtain the Stern–Volmer plot, luminescence spectra were taken in absence and in presence of the quencher (at least five different concentrations), keeping the same experimental conditions (22 ± 2 °C, ionic strength 1.0 M) for each pH. The intensity of luminescence was read at the same wavelength (λ em = 610 nm), corresponding to the maximum of emission band. Data Acquisition and Handling Although a PC attached to a digital oscilloscope was used for the luminescence intensity measurements, a conventional xt plotter can be helpful too. Moreover, it is not absolutely necessary to record a complete luminescence spectrum; a simple measure of intensity at a fixed wavelength (610 nm) may be equally precise. The pKa values were adjusted by using a nonlinear least-squares weighed fitting algorithm, taking KSV’s of the phenol and the phenolate ion (KaSV and KbSV) as adjustable parameters too.
Vol. 74 No. 8 August 1997 • Journal of Chemical Education
969
In the Laboratory
12
7
1.0
pH
6 10
0.8
9.83 10.14 10.54
5
3
0.4
Io/I
O.D.
4
Emision Intensity (Arbitrary units)
8
0.6
6
4
2 0.2 1
0.0 300
400
500
600
700
2
0 800
0 0.000
λ(nm)
Figure 1. Absorption and emission spectra of 5 × 10{5 M Ru(bpy) 32+ at pH 7.36. Temperature 22 ± 2 °C and ionic strength 1 M.
0.005
0.010
0.015
0.020
0.025
[2,6DMP] M
Figure 3. Stern–Volmer plots for the luminescence quenching of Ru(bpy)32+ by 2,6-DMP at three pH values. Temperature 22 ± 2 °C; ionic strength 1 M.
1.0
Acid Basic
0.8
Table 1. Stern–Volmer Constants for Luminescence Quenching of Ru(bpy)32+ by Phenolsa 2,6-DMP pH
O.D.
0.6
0.4
N 2 Laser
0.2
0.0
260
280
300
320
340
λ(nm) {
Figure 2. Absorption spectra of 10{ 4 M 2,6-DMP. Basic form (A ) (---) and acid form (AH) (—). Temperature 22 ± 2 °C, ionic strength 1 M.
Results and Discussion Figure 1 shows the absorption and emission spectra of Ru(bpy)3 2+ and Figure 2, the corresponding absorption spectra of 2,6-DMP in basic and acid media. The spectra of 4-Br-2,6-DMP (not shown) are similar to those given in Figure 2. From these figures we see that λex = 450 nm is the suitable wavelength to perform steady-state experiments in acid medium as well as in basic medium. It can also be seen that the laser pulse (337.2 nm) does not overlap with the absorption bands of the phenols. Equation 13 applies for steady-state measurements. To obtain the kq constants, τ0 = 480 ns (the excited state lifetime of the metallic complex in solutions not deoxygenated and in absence of phenol) was taken from previous experiments (5). Using the time resolved technique and rearrang-
970
a
4-Br-2,6-DMP
KSV
pH
KSV
8.02
99.9
8.21
314
8.35
99.9
9.21
494
8.85
113
9.45
491
9.29
111
9.76
668
9.83
133
10.02
868
10.13
316
10.36
1.07 × 103
10.14
280
10.62
1.10 × 103
10.54
490
11.07
11.05
1.18 × 103
1.04 ×
103
11.91
1.23 × 103
11.45
1.14 ×
103
12.09
1.24 × 103
12.52
1.31 ×
103
12.39
1.30 × 103
Temperature = 22 ± 2 °C; ionic strength = 1 M.
ing eq 14, it is possible to obtain kq from the slope of a plot of 1 / τ vs. [Q]. Figure 3 shows some Stern–Volmer plots, φ0/φ vs. [Q], obtained at different pH’s for 2,6-DMP as quencher. Table 1 lists the values of KSV vs. pH obtained for 2,6-DMP and 4-Br-2,6-DMP. In general, the Stern–Volmer quenching constant increases with pH (Fig. 3 and Table 1). The variation of KSV with the pH of the solution shows the variation of the rate constant kq , since τ0 is virtually independent of the medium pH as stated above. These results could be explained assuming that the reactivity of the functional group is affected by the reaction given in eq 1. Therefore, the treatment of the results can be put on a simple quantitative basis in this equilibrium reaction. In addition, the quenching of *Ru(bpy)3 2+ by both species was taken into account. Then, the term KSV[Q] in eq 15
Journal of Chemical Education • Vol. 74 No. 8 August 1997
In the Laboratory 4Br.2.6diMe
1400
K
a
K
b
286
SV
1.28E3
Ka pKa
1200
3.2
SV
1.28E-10 9.89
4Br.2.6diMe
3.0
1000
2.8
KSV
log KSV
800
600
2.6
2.4 2.6diMe
400
2.6diMe
200
K
a
K
b
2.2 SV
69.2
SV
1.37E3
Ka pKa
1.67E-11 10.78
2.0
0 6
7
8
9
10
11
12
13
14
6
7
8
9
10
11
12
13
14
pH
pH
Figure 4. Plots of experimental data and calculated curve of KSV vs. pH. j = 4Br-2,6-DMP and s = 2,6-DMP. Temperature 22 ± 2 °C; ionic strength 1 M.
Figure 5. Plots of experimental data and calculated curve of log KSV vs. pH. j = 4Br-2,6-DMP and s = 2,6-DMP. Temperature 22 ± 2 °C; ionic strength 1 M.
can be expressed as the sum of the contributions of the acid form AH and the basic form A{:
the knowledge of KaSV and KbSV (graphical method). Finally, a nonlinear least-squares method can be applied to the data in Table 1 taking KaSV, KbSV, and Ka as adjustable parameters. On account of these findings, it may be interesting for students to compare the results obtained by either the analytical or graphical method with those obtained by the fitting method. In the present work, the fitting of data from Table 1 gives the results shown in Table 2 together with the bimolecular quenching rate constants (k aq and k bq ). The pKa values thus obtained are in good agreement with bibliographic data (5, 8) (Table 2).
KSV[Q] = K aSV[AH] + K bSV[A { ] = K SV [AH]t
(16)
where [AH] and [A{ ] are the concentrations of phenol and phenolate species, respectively, and [AH]t is the analytical concentration of the phenolic compound. If eq 16 is divided by [AH] t and substituted by the eqs d and e,2 we obtain: +
a
K SV = K SV
Ka [H ] b + + K SV + K a + [H ] K a + [H ]
(17)
where KSV is expressed as a function of [H+] and the constants to be evaluated. In the logarithmic form, this equation can be written as: a
+
b
+
log K SV = log K SV [H ] + K SV K a – log K a + [H ]
(18)
In Figures 4 and 5 are plotted KSV and log KSV vs. pH; values are taken from steady-state quenching data. Some of these results can be confirmed by time-resolved experiments. KaSV and KbSV can be directly obtained from the slopes of plots of eq 15 at low and high pH, respectively. Then, Ka can be obtained by solving eq 17 at a pH where both species are present (analytical method). When pH = pKa, eq 17 reduces to KSV = (KaSV + KbSV) / 2. Consequently the pKa value can be directly determined from the plot in Figure 4 and
Conclusion This experiment provides training in techniques such as absorption and fluorescence spectroscopy and time-resolved fluorescence. The absorption, excitation, and emission spectra of Ru(bpy) 32+ must be recorded. The absorption spectra of the phenols in acid medium and basic media must also be recorded in order to analyze the shifting of UV absorption bands. The appropriate excitation wavelength of the ruthenium complex has to be chosen. It should be corroborated that in using the N 2 laser, the sample is irradiated where no absorption of phenols occurs. Furthermore, through a single time-resolved experiment we can observe how the luminescence lifetime of Ru(bpy)32+ increases when nitrogen is continuously bubbled in the sample cell, and thus show that oxygen is a quencher of the excited state of the metallic complex. How this experiment is accomplished depends on the equipment available for the students.
Table 2. Stern–Volmer and Bimolecular Quenching Rate Constants and pKa 's for 2,6-DMP and 4-Br-2,6-DMPa Phenol 2,6-DMP 4-Br-2,6-DMP
Constant
KaSV (M{1)
KbSV (M{1)
k qa (M{1s{1)
k bq (M{1s{1)
pKa (exp)
pKa (lit)
69.2
1.37× 103
1.44× 108
2.85× 109
10.78
10.63b
1.28× 103
6.00× 108
2.67× 109
9.89
9.98c
286
Temperature = 22 ± 2 °C; ionic strength = 1 M. bRef 8. cRef 5.
a
Vol. 74 No. 8 August 1997 • Journal of Chemical Education
971
In the Laboratory Acknowledgments
The fraction of the analytical concentration present as anion (the degree of dissocation of the acid) is
We thank the Consejo Nacional de Investigaciones Científicas y Técnicas de Argentina (CONICET), the Consejo de Investigaciones de la Provincia de Córdoba (CONICOR), and the Secretarías de Ciencia y Técnica de las Universidades de Río Cuarto and Córdoba for financial support.
{
αA { =
(d)
and the fraction of the analytical concentration present as undissociated form (the degree of formation of the acid from its ions) is given by
Notes
+
1. The quantum yield ratio φ°/φ is equal to the ratio of luminescence intensities I t°/ I t (I °/ I in the plot of Fig. 3) in experiments in which Ia is the same in absence or presence of quenchers— that is, the quencher does not absorb. This condition is fully met in our system and this was actually measured. 2. If the pH of the solution is known, the concentration of all the species in solution can be easily calculated. The concentration of weak acid and its anion are related by the mass balance [AH]t = [A {] + [AH]
(a)
and the equilibrium constant expression +
Ka =
{
[H ] [A ] [AH]
(b)
Equation b can be solved for [AH] in terms of [H+ ] and [A{] and substituted in the mass balance to give {
[AH]t = [A ] +
972
Ka [A ] = [AH]t K a + [H+]
+
{
[H ] [A ] [K a]
(c)
αAH =
[H ] [AH] = [AH]t K a + [H+]
(e)
Literatured Cited 1. Sutin, N.; Creutz, C. J. Chem. Educ. 1983, 60, 809–814; Scandola, F.; Balzani, V. J. Chem. Educ. 1983, 60, 814–823; Meyer, T. J. Prog. Inorg. Chem. 1983, 30, 389–440. 2. Juris, A.; Balzani, V.; Barigelletti, F.; Campagna, S.; Belser, P.; Von Zelewsky, A. Coord. Chem. Rev. 1988, 84, 85–277. 3. (a) Sacksteder, L.; Ballew, R, M.; Brown, E. A.; Demas, J. N.; Nesselrodt, D.; DeGraff, B. A. J. Chem. Educ. 1990, 67, 1065–1067; (b) Byron, C. M.; Werner, T. C. J. Chem. Educ. 1991, 68, 433–436; (c) Fraiji, L. K.; Hayes, D. M.; Werner, T. C. J. Chem. Educ. 1992, 69, 424–428. 4. Xu, J. G.; Porter, G. B. Can. J. Chem. 1982, 60, 2856–2858. 5. Vera, D. M.; Argüello, Gustavo A.; Argüello, Gerardo A.; Gsponer,H. E. J. Photochem. Photobiol. A: Chem. 1993, 76, 13–19. 6. Balzani, V.; Moggi, I.; Manfrin, M. F.; Bolletta, F. Coord. Chem. Rev. 1975, 15, 321–433. 7. Stern O.; Volmer, M. Phys. Z. 1919, 20, 183. 8. Foye, W. O.; Principios de Química Farmaceútica, ed. reverté, Barcelona, 1984.
Journal of Chemical Education • Vol. 74 No. 8 August 1997
