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Coloring Rate of Phenolphthalein by Reaction with Alkaline Solution
Observed by Liquid-Droplet Collision
Yuuka Takano, Shigenori Kikkawa, Tomoko Suzuki, and Jun-ya Kohno*
Department of Chemistry, Faculty of Science, Gakushuin University, 1-5-1 Mejiro, Toshima-ku, Tokyo 171-8588, Japan
ABSTRACT: Many important chemical reactions are induced by mixing two solutions. This paper presents a new way to measure rates of rapid chemical reactions induced by mixing two reactant solutions using a liquid-droplet collision. The coloring reaction of phenolphthalein (H 2 PP) by a reaction with NaOH is investigated kinetically. Liquid droplets of H 2 PP/ethanol and NaOH/H 2 O solutions are made to collide, which induces a reaction that transforms H 2 PP into a deprotonated form (PP 2 −). The concentration of PP 2 −^ is evaluated from the RGB values of pixels in the colored droplet images, and is measured as a function of the elapsed time from the collision. The obtained rate constant is (2.2 ± 0.7) × 103 M−^1 s−^1 , which is the rate constant for the rate-determining step of the coloring reaction of H 2 PP. This method was shown to be applicable to determine rate constants of rapid chemical reactions between two solutions.
1. INTRODUCTION
Reactions in solutions play a central role in chemistry. Most synthetic reactions, as well as biochemical reactions, proceed in organic and/or aqueous solutions. Reaction kinetics and dynamics in solution have been extensively studied by spectroscopic methods. Especially, studies with ultrafast pump−probe techniques reveal the dynamics of molecules down to the femtosecond time range. 1,2^ Such studies, however, have been limited to chemical reactions triggered by photon absorption in homogeneous media. The reaction kinetics have also been investigated by a chemical relaxation method, in which one observes the rate from one chemical equilibrium to another after an instantaneous jump in temperature. 3,4^ The temperature jump method can be executed by pulsed laser irradiation. However, this method is limited to investigations of reversible reactions in solutions, and hence is also limited to those in homogeneous media. Moreover, the temperature-jump method gives a rate constant of a reaction in a direct equilibrium with the molecules under observation even if the reaction is a part of a multistep reaction, which prevent determining the rate of an important reaction step not directly in equilibrium with the molecules under observation. Chemical reactions induced by mixing two solutions have more importance than those in homogeneous solution, because, to maintain control of the reaction, the two reactant species are usually separated in different solutions before the reaction. Kinetic measurements of reactions in solutions can be performed by observing the time evolution of the concen- trations of species of interest in the solution. The reaction rate induced by mixing two solutions is measured by sampling a part of the solution and analyzing the concentration of the reactant and/or products as a function of the evolved time after mixing. However, this method requires a certain amount of time for the
mixed solutions to settle into a homogeneous state, which results in dead time in the measurement. A stopped-flow method was employed to obtain kinetic information on rapid chemical reactions induced by mixing two solutions, where two reactant solutions are pumped to a mixer and the composition of the output mixed solution is analyzed as a function of the distance from the mixer, which corresponds with the reaction time. The stopped-flow method is widely used for investigations of various processes such as protein folding 5 and the association of two species. 6 The stopped-flow method has a dead time of usually more than 1 ms to mix the two solutions to form a homogeneous solution. It is necessary to decrease the dead time to observe the rates of more rapid chemical reactions. Technical advances allowing enhanced techniques to mix the two solutions have reduced the dead time to several tens of microseconds. 7 −^10 Recently, the mixing technique has been applied to mass spectrometry. 11 −^13 For example, Mortensen et al. have performed an electrospray mass-spectrometric observation of solutions mixed in the needle ion source, which yields kinetic information by varying the distance from the tip of the needle to the detection region of the mass spectrometer. 11 The morphological dynamics of liquid droplets, especially outcomes following a collision of two droplets, have been investigated extensively with a focus toward meteorological and industrial interests, such as raindrop formation and spray combustion in engines, respectively. The collision outcomes can be classified by two parameters: the Weber number and the impact parameter. 14 −^18 We also investigated collisions between ethanol and water droplets: 19 A protrusion is produced in the
Received: April 3, 2015 Revised: May 18, 2015 Published: May 20, 2015
Article pubs.acs.org/JPCB
© 2015 American Chemical Society 7062 DOI: 10.1021/acs.jpcb.5b
course of the collision, which is explained by propagation of a capillary wave on the droplet surface. It is revealed that droplet collision enables precise observation of the time evolution of the two merging solutions and is applicable to the observation of chemical reactions induced by mixing two solutions. Novel approaches using liquid droplets have been proposed to measure the rate of rapid chemical reactions induced by mixing two solutions. Huebner et al. trapped two reactant droplets in a liquid and observed the chemical reaction following the merger of the droplets at sub-millisecond time resolution. 20 Tsuji et al. have observed a chemical reaction induced by a droplet falling on a liquid surface using a high- speed camera. 21 Aerosol droplets have also been used to investigate chemical reactions. Simpson et al. have used droplet collisions to observe chemical reactions, where two droplet streams merge into a single stream, which is analyzed by Raman spectroscopy. 22 −^24 The composition of the droplet stream is analyzed as a function of the time from the merger. However, we believe that a more microscopic analysis of the droplets will yield more detailed information on the reaction. To analyze the droplets, we have developed sensitive methods based on mass spectrometry 25 −^28 or cavity enhanced spectroscopy. 29 The spectroscopic method was applied to elucidate the mechanism of protrusions formed in collisions of ethanol and water droplets. 30 The droplet-collision dynamics have been elucidated by time-resolved observation under irradiation of a pulsed laser onto the colliding droplets. This method has proven to be particularly appropriate to investigate the mixing dynamics of different droplets. In the present paper, we apply the droplet-collision technique to observe the coloring reaction of phenolphthalein induced by mixing two solutions. A reaction rate constant is obtained by color analysis of the image of the red phenolphthalein droplets.
2. EXPERIMENTAL SECTION
A detailed description of the droplet-collision apparatus has been given previously. 19,30^ Here, the apparatus and exper- imental procedures employed in the present study are described briefly. The apparatus was constructed on a microscope stage to observe the colliding droplets having sizes of tens of micrometers. Liquid droplets were produced by a set of piezo-driven nozzles (Microdrop MD-K-130), which were triggered independently by electric pulses supplied from a pulse generator. A white-light-emitting diode (LED, Nichia NSPW500GS) was employed as a strobe light to collect droplet-collision images in red, green, and blue (RGB) colors. The LED mounted under the collision region of the droplet illuminated the colliding droplets from the bottom to the top, where the objective lens of the microscope collected the shadow images of the droplets. We employed a triggerable color CCD camera (The Imaging source, DBK-41BU02) for image detection. The duration of the LED pulse was set to 1 μs, which was the time resolution of the measurement. The pulse generator employed to trigger droplet generation was also synchronized to the LED with a variable delay. A series of droplet-collision images was recorded by changing the timing of the LED strobe light with respect to that of the droplet generation. Because the images in the series showed different droplets, we did not follow the fate of particular droplets. However, the series of images allowed us to follow the collision dynamics of the droplets, because the images are sufficiently reproducible owing to the short timing jitter of the droplet generation. The recorded images were taken as laboratory-
frame images, and were then transferred into a center-of-mass frame by extracting part of the image using a method described in a previous paper. 19 Deionized and distilled water was used as the solvent, and ethanol (EtOH, Wako Pure Chemical Industries), H 2 PP (Tokyo Chemical Industry), and NaOH were used without further purification. We observed droplet collisions of H 2 PP/EtOH + NaOH/H 2 O and PP 2 −^ solution + water. The H 2 PP/EtOH, NaOH/H 2 O, and PP 2 −^ solution were prepared as 0.06 M H 2 PP in EtOH, 1.2 M NaOH in water, and a 30:1 mixture of 0.06 M H 2 PP in EtOH solution and 12 M NaOH aqueous solution, respectively. The absorption spectrum of PP 2 −^ and emission spectrum of the white LED were obtained with a spectrophotometer (JASCO V-530) and a photonic multichannel spectral analyzer (Hamamatsu, PMA-11), respectively.
3. RESULTS
Figure 1 shows the droplet-collision sequence of the PP 2 − solution and pure water, both of whose sizes are 41.6 ± 0.2 μm.
The collision velocity, the Weber number, and the dimension- less impact parameter are 3.30 ± 0.05 m/s, 4.9 ± 0.2, and 0. ± 0.05, where the outcome of collisions is predicted to be coalescence. 14 −^18 In fact, the droplets coalesce during collision, and become spherical ∼ 500 μs after the collision. The red color of PP 2 −^ is observed only in the basic H 2 PP side of the coalesced droplet, and the other side remains colorless immediately after collision. The red and colorless parts gradually mix, and all the parts of the colliding droplets become red at ∼ 800 μs. The circumference of the droplet cannot be observed because the back-illuminated LED light focuses on the center of the droplet by a lens effect, which shadows the droplet circumference. Figure 2 shows the absorbance of the colliding droplets of the PP 2 −^ solution and pure water calculated from the RGB values of the images (see section 4.1). The number of droplets employed for this measurement is 83. The absorbance increases as a function of the elapsed time from the collision until ∼ 800 μs and levels off, which coincides with our observation that the droplet images become homogeneous at an elapsed time of ∼ 800 μs (Figure 1). Figure 3 shows the droplet-collision sequence of H 2 PP/ EtOH and NaOH/H 2 O, whose sizes are 36.0 ± 0.2 and 37.8 ± 0.2 μm, respectively. The collision velocity, the Weber number, and the dimensionless impact parameter are 2.71 ± 0.05 m/s, 3.7 ± 0.2, and 0.02 ± 0.05, where the outcome of collisions is predicted to be coalescence. 14 −^18 The morphological change is similar to that observed for the collision of PP 2 −^ solution and pure water (Figure 1). The red color of the PP 2 −^ appears at
Figure 1. Droplet-collision images of PP 2 −^ solution (left) and pure water (right) taken at −20 (a), 0 (b), 50 (c), 300 (d), 600 (e), 800 (f), and 1000 (g) μs after the collision.
DOI: 10.1021/acs.jpcb.5b 7063
absorption of PP 2 −^ can be evaluated by the decrease of the G values in the image. To confirm this point, a line profile of droplets of the PP 2 −/EtOH solution and pure water is shown in Figure 6. In Figure 6, the RGB values are normalized to the
background. The normalization factors are 1.28, 1.15, and 1 for R, G, and B, respectively. In the droplet image, the peripheries of the droplet shadows and the center are brighter than the background, because the back-illuminated LED light is focused into the center by a lens effect of the droplet. The RGB values are almost the same for the water (colorless) droplet, whereas the G value is significantly smaller than the R and B values for the PP 2 −^ droplet. This result indicates that the absorption of green light by PP 2 −^ in the droplet decreases the G value in the image. The absorbance of PP 2 −^ is calculated from the RGB values of the droplet images as follows. Since the absorption spectrum of PP 2 −^ appears at the sensitivity spectrum of G in the RGB values, the absorbance, A, is given as
A = −
G
G
log 0 (2)
where G and G 0 represent the sum of the G values inside the image of the droplet with and without PP 2 −, respectively. It is difficult, however, to obtain comparable G and G 0 values for each droplet, because (1) each droplet slightly differs in size and/or traveling velocity and (2) the illuminating LED intensities differ in position, and hence differ in the illumination timing. Then, instead of observing the G 0 value, we approximate G 0 by the average of R and B in the PP 2 −^ droplet as
=
G
R B
where R and B represent the sum of the R and B values inside the image of the droplet. This approximation is likely to work well because the PP 2 −^ absorption overlaps little with the R and B sensitivity spectra (see Figure 5c). The absorbance is then given as follows.
=
A
R B
G
log 2 (4)
The concentration of PP 2 −, [PP^2 −], is then calculated in the following manner: The absorbance follows the Lambert−Beer law as
A = εL [PP 2 −] (5)
where ε and L represent the molar absorption coefficient and absorption length, respectively. The absorption length of the incoming light is dependent on the offset from the center of the droplet. The light coming into the center of the droplet has an absorption length equal to the droplet diameter, d. Our simple refraction calculation gives that the light grazing the edge of the droplet shows the shortest absorption length equal to 0.66d. Then, we approximate the absorption length to be the diameter of the droplet, which gives the upper limit with an error less than 34%. On this assumption, one obtains
A = εd [PP 2 −^ ] (6)
From eqs 4 and 6, [PP^2 −] is finally given as
ε
d
R B
G
[PP ]
log 2
2 (7) The calculated results are plotted on the left longitudinal axis in Figure 4. We employ a molar absorption coefficient of (3.6 ± 0.6) × 10 4 M−^1 cm−^1 , which is obtained from absorbance measured by a conventional spectrophotometer. The absorb- ance is obtained by an extrapolation of the absorbance to time zero (the moment we prepared the solution), because the red color PP 2 −^ fades over time by further reaction with OH−. 31, 4.2. Coloring Rate of Phenolphthalein. As described in section 4.1, the phenolphthalein molecules exhibit their red color upon release of two protons. The deprotonation reaction has two steps, as shown in Figure 7. 33 The first step is the
opening reaction of the lactone ring, and the second is deprotonation followed by dehydration. The rate constant of the second step, k 2 , is reported to be 1.7 × 109 M−^1 s−^1 , as measured by a chemical relaxation method. 33 We analyze the kinetic data obtained in Figure 4 on the assumption that the first step of the reaction is the rate-determining step of the reaction. A pseudo-first-order reaction rate analysis is applied for the first step of the reaction, because the concentration of OH−, which equals that of NaOH (1.2 M), is much larger than that of H 2 PP (0.06 M) in the present experiment. On the other hand, we take into account an offset time, t 0 , which is the time for the
Figure 6. Line profile of droplets of the PP 2 −/EtOH solution and that of pure water.
Figure 7. Two-step deprotonation scheme for phenolphthalein.
DOI: 10.1021/acs.jpcb.5b 7065
system to be settled in a quasi-homogeneous state. Then, the rate equation
−
t
k
d[PP ] d
[H PP][NaOH]
2 (^1 2) (8)
is integrated as
[PP 2 −^ ] = [H PP] (1 2 0 −e− k^^1 [NaOH] (^0 t^ −^ t^0 )^ ) (9)
where [H 2 PP] 0 and [NaOH] 0 represent initial solution concentrations of H 2 PP and NaOH, respectively, and t is the time elapsed from the collision. A fit of eq 9 to the data shown in Figure 4 yields t 0 and k 1 values as (4.6 ± 0.1) × 10 2 μs and (2.2 ± 0.7) × 10 3 M−^1 s−^1 , respectively. The obtained offset time almost coincides with the start of the quasi-homogeneous state formation, and hence supports the validity of the present analysis. Moreover, the k 1 value is significantly smaller than that of the second step, k 2 , which validates the analysis as well as the assumption that the first step, the lactone opening, is the rate- determining step for the coloring reaction of phenolphthalein in alkaline solution.
5. CONCLUSION
In summary, we observed a chemical reaction induced by droplet collision of H 2 PP/EtOH and NaOH/H 2 O. The concentration of deprotonated phenolphthalein, PP 2 −, pro- duced in the collided droplets is evaluated by the RGB values of the color CCD images. The obtained rate constant for the first (rate-determining) step of the coloring reaction is (2.2 ± 0.7) × 103 M−^1 s−^1. This work demonstrates a novel method to observe rapid reactions induced by mixing two solutions and to analyze the absorption of the product species by conventional color CCD images.
■ AUTHOR INFORMATION
Corresponding Author *Phone: +81-3-3986-0221. Fax: +81-3-5992-1029. E-mail: jun- ya.kohno@gakushuin.ac.jp.
Notes The authors declare no competing financial interest.
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