Coloring Rate of Phenolphthalein by Reaction with Alkaline Solution

May 20, 2015 - ABSTRACT: Many important chemical reactions are induced by ... phenolphthalein (H2PP) by a reaction with NaOH is investigated kinetical...
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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 (H2PP) by a reaction with NaOH is investigated kinetically. Liquid droplets of H2PP/ethanol and NaOH/H2O solutions are made to collide, which induces a reaction that transforms H2PP into a deprotonated form (PP2−). The concentration of PP2− 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 H2PP. This method was shown to be applicable to determine rate constants of rapid chemical reactions between two solutions.

1. INTRODUCTION

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 folding5 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

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 concentrations 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 © 2015 American Chemical Society

Received: April 3, 2015 Revised: May 18, 2015 Published: May 20, 2015 7062

DOI: 10.1021/acs.jpcb.5b03233 J. Phys. Chem. B 2015, 119, 7062−7067

Article

The Journal of Physical Chemistry B

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), H2PP (Tokyo Chemical Industry), and NaOH were used without further purification. We observed droplet collisions of H2PP/EtOH + NaOH/H2O and PP2− solution + water. The H2PP/EtOH, NaOH/H2O, and PP2− solution were prepared as 0.06 M H2PP in EtOH, 1.2 M NaOH in water, and a 30:1 mixture of 0.06 M H2PP in EtOH solution and 12 M NaOH aqueous solution, respectively. The absorption spectrum of PP2− 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.

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 highspeed 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 spectrometry25−28 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.

3. RESULTS Figure 1 shows the droplet-collision sequence of the PP2− solution and pure water, both of whose sizes are 41.6 ± 0.2 μm.

Figure 1. Droplet-collision images of PP2− 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.

2. EXPERIMENTAL SECTION A detailed description of the droplet-collision apparatus has been given previously.19,30 Here, the apparatus and experimental 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-

The collision velocity, the Weber number, and the dimensionless impact parameter are 3.30 ± 0.05 m/s, 4.9 ± 0.2, and 0.05 ± 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 PP2− is observed only in the basic H2PP 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 PP2− 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 H2PP/ EtOH and NaOH/H2O, 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 PP2− solution and pure water (Figure 1). The red color of the PP2− appears at 7063

DOI: 10.1021/acs.jpcb.5b03233 J. Phys. Chem. B 2015, 119, 7062−7067

Article

The Journal of Physical Chemistry B

fitted result has an offset of 460 μs in the elapsed time, which is the time required for the droplets to be homogeneous.

4. DISCUSSION 4.1. Estimation of PP2− Concentration in Droplets. In this paper, we discuss the rate of the reaction H 2PP + 2NaOH → PP2 − + 2Na + + 2H 2O

(1)

which is induced by collision of H2PP/EtOH and NaOH/H2O solution droplets. The colliding droplets exhibit several internal parts after ∼800 μs from the collision. However, each part is considered to be the mixture of H2PP and NaOH, because every part has the red color of PP2−. The parts are likely to differ slightly in the PP2− concentration. We call this a quasihomogeneous state in the present paper. As shown in section 4.2, the kinetics can be discussed under this inhomogeneity, because the experiment is performed in a pseudo-first-order condition and is not so sensitive to the concentration of H2PP. As reaction 1 proceeds, the concentration of PP2−, which exhibits a red color, increases in the droplet. The red color of PP2− originates from green light absorption of PP2− in the droplet. The concentration of PP2− is estimated by color analysis of the CCD image of the PP2− droplet. The color CCD image consists of pixels, each of which has three color values, red (R), green (G), and blue (B). Figure 5a

Figure 2. Absorbance of colliding droplets of PP2− solution and pure water.

Figure 3. Droplet-collision images of H2PP/EtOH (left) and NaOH/ H2O (right) taken at −20 (a), 0 (b), 100 (c), 500 (d), 900 (e), 1800 (f), and 2500 (g) μs after the collision.

∼500 μs and gradually darkens with time. There are both red and colorless regions in the droplet until ∼800 μs, and subsequently the droplet becomes homogeneous. Figure 4 shows the absorbance of PP2− in the colliding droplets of H2PP/EtOH and NaOH/H2O as a function of the

Figure 4. Absorbance of PP2− in colliding droplets of H2PP/EtOH and NaOH/H2O as a function of elapsed time after collision. The right longitudinal axis represents the concentration of PP2− calculated from the absorbance (see text).

Figure 5. Spectral sensitivities of the RGB pixels and the absorption spectrum of PP2−. (a) Spectral sensitivity of the RGB pixels of the CCD camera, (b) emission spectrum of the white LED, (c) the product of the camera sensitivity and the LED emission spectra, and (d) absorption spectrum of PP2−.

elapsed time after the collision. The number of droplets employed for this measurement is 81. The concentration of PP2− in the droplets, [PP2−], is also shown on the right axis (the calculation method is described in detail in section 4.1). The absorbance slightly increases over the elapsed time of 0− 0.5 ms, which indicates that mixing proceeds in the coalesced droplet in this time range. The absorbance continues to increase over time until ∼2 ms and levels off. The solid curve in Figure 4 represents the fitted result with data at ≥800 μs, assuming first-order reaction kinetics (see section 4.2). The

and b show the spectral sensitivities of the RGB pixels of the CCD camera and the emission spectrum of the white LED, respectively, employed in the present study. The effective spectral sensitivity of the present setup is obtained as the product of the camera sensitivity and the LED emission spectra, as shown in Figure 5c. Figure 5d shows the absorption spectrum of PP2−. The PP2− absorption overlaps almost only with the green curve in Figure 5c, which indicates that the 7064

DOI: 10.1021/acs.jpcb.5b03233 J. Phys. Chem. B 2015, 119, 7062−7067

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The Journal of Physical Chemistry B absorption of PP2− can be evaluated by the decrease of the G values in the image. To confirm this point, a line profile of droplets of the PP2−/EtOH solution and pure water is shown in Figure 6. In Figure 6, the RGB values are normalized to the

A = εL[PP2 −]

(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[PP2 −]

(6)

From eqs 4 and 6, [PP ] is finally given as 1 R+B [PP2 −] = log εd 2G 2−

The calculated results are plotted on the left longitudinal axis in Figure 4. We employ a molar absorption coefficient of (3.6 ± 0.6) × 104 M−1 cm−1, which is obtained from absorbance measured by a conventional spectrophotometer. The absorbance is obtained by an extrapolation of the absorbance to time zero (the moment we prepared the solution), because the red color PP2− fades over time by further reaction with OH−.31,32 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

Figure 6. Line profile of droplets of the PP2−/EtOH solution and that of pure water.

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 PP2− droplet. This result indicates that the absorption of green light by PP2− in the droplet decreases the G value in the image. The absorbance of PP2− is calculated from the RGB values of the droplet images as follows. Since the absorption spectrum of PP2− appears at the sensitivity spectrum of G in the RGB values, the absorbance, A, is given as A = −log

G G0

(7)

(2)

where G and G0 represent the sum of the G values inside the image of the droplet with and without PP2−, respectively. It is difficult, however, to obtain comparable G and G0 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 G0 by the average of R and B in the PP2− droplet as R+B G0 = (3) 2 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 PP2− absorption overlaps little with the R and B sensitivity spectra (see Figure 5c). The absorbance is then given as follows. R+B A = log (4) 2G

Figure 7. Two-step deprotonation scheme for phenolphthalein.

opening reaction of the lactone ring, and the second is deprotonation followed by dehydration. The rate constant of the second step, k2, 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 H2PP (0.06 M) in the present experiment. On the other hand, we take into account an offset time, t0, which is the time for the

The concentration of PP2−, [PP2−], is then calculated in the following manner: The absorbance follows the Lambert−Beer law as 7065

DOI: 10.1021/acs.jpcb.5b03233 J. Phys. Chem. B 2015, 119, 7062−7067

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(7) Berger, R. L.; Balko, B.; Chapman, H. F. High Resolution Mixer for the Study of the Kinetics of Rapid Reactions in Solution. Rev. Sci. Instrum. 1968, 39, 493. (8) Lin, Y.; Gerfen, G. J.; Rousseau, D. L.; Yeh, S. Ultrafast Microfluidic Mixer and Freeze-Quenching Device. Anal. Chem. 2003, 75, 5381−5386. (9) Hertzog, D. E.; Michalet, X.; Jäger, M.; Kong, X.; Santiago, J. G.; Weiss, S.; Bakajin, O. Femtomole Mixer for Microsecond Kinetic Studies of Protein Folding. Anal. Chem. 2004, 76, 7169−7178. (10) Bilsel, O.; Kayatekin, C.; Wallace, L. a.; Matthews, C. R. A Microchannel Solution Mixer for Studying Microsecond Protein Folding Reactions. Rev. Sci. Instrum. 2005, 76, 014302. (11) Mortensen, D. N.; Williams, E. R. Theta-Glass Capillaries in Electrospray Ionization: Rapid Mixing and Short Droplet Lifetimes. Anal. Chem. 2014, 86, 9315−9321. (12) Mortensen, D. N.; Williams, E. R. Investigating Protein Folding and Unfolding in Electrospray Nanodrops upon Rapid Mixing Using Theta-Glass Emitters. Anal. Chem. 2015, 87, 1281−1287. (13) Lento, C.; Audette, G. F.; Wilson, D. J. Time-Resolved Electrospray Mass Spectrometry  a Brief History. Can. J. Chem. 2015, 93, 7−12. (14) Orme, M. Experiments on Droplet Collisions, Bounce, Coalescence and Disruption. Prog. Energy Combust. Sci. 1997, 23, 65−79. (15) Qian, J.; Law, C. K. Regimes of Coalescence and Separation in Droplet Collision. J. Fluid Mech. 1997, 331, 59−80. (16) Pan, K.-L.; Law, C. K.; Zhou, B. Experimental and Mechanistic Description of Merging and Bouncing in Head-on Binary Droplet Collision. J. Appl. Phys. 2008, 103, 064901. (17) Ashgriz, N.; Poo, J. Y. Coalescence and Separation in Binary Collisions of Liquid Drops. J. Fluid Mech. 1990, 221, 183−204. (18) Gao, T.-C.; Chen, R.-H.; Pu, J.-Y.; Lin, T.-H. Collision between an Ethanol Drop and a Water Drop. Exp. Fluids 2005, 38, 731−738. (19) Kohno, J.; Kobayashi, M.; Suzuki, T. Protrusion Formation during the Collisional Process of Ethanol and Water Droplets: Capillary Wave Propagation on the Water Droplet. Chem. Phys. Lett. 2013, 578, 15−20. (20) Huebner, A. M.; Abell, C.; Huck, W. T. S.; Baroud, C. N.; Hollfelder, F. Monitoring a Reaction at Submillisecond Resolution in Picoliter Volumes. Anal. Chem. 2011, 83, 1462−1468. (21) Tsuji, K.; Müller, S. C. Chemical Reaction Evolving on a Droplet. J. Phys. Chem. Lett. 2012, 3, 977−980. (22) Simpson, S. F.; Kincaid, J. R.; Holler, F. J. Microdroplet Mixing for Rapid Reaction Kinetics with Raman Spectrometric Detection. Anal. Chem. 1983, 55, 1420−1422. (23) Simpson, S. F.; Kincaid, J. R.; Holler, F. J. Development of a Microdroplet Mixing Technique for the Study of Rapid Reactions by Raman Spectroscopy. Anal. Chem. 1986, 58, 3163−3166. (24) Simpson, S. F.; Holler, F. J. Effects of Experimental Variables on the Mixing of Solutions by Collision of Microdroplets. Anal. Chem. 1988, 60, 2483−2487. (25) Kohno, J.; Toyama, N.; Kondow, T. Ion Formation to the Gas Phase by Laser Ablation on a Droplet Beam. Chem. Phys. Lett. 2006, 420, 146−150. (26) Kohno, J.; Kondow, T. UV Laser Induced Proton-Transfer of Protein Molecule in the Gas Phase Produced by Droplet-Beam Laser Ablation. Chem. Phys. Lett. 2008, 463, 206−210. (27) Kohno, J.; Kondow, T. Trap of Biomolecular Ions in the Gas Phase Produced by IR-laser Ablation of Droplet Beam. Chem. Lett. 2010, 39, 1220−1221. (28) Kohno, J.-Y.; Nabeta, K.; Sasaki, N. Charge State of Lysozyme Molecules in the Gas Phase Produced by IR-Laser Ablation of Droplet Beam. J. Phys. Chem. A 2013, 117, 9−14. (29) Hoshino-nagasaka, M.; Isoda, T.; Takeshima, T.; Kohno, J. Scanning Cavity-Enhanced Droplet Spectroscopy: Tuning of the Excitation Laser for Obtaining a Continuous Raman Spectrum. Chem. Phys. Lett. 2012, 539−540, 229−233. (30) Suzuki, T.; Kohno, J. Simultaneous Detection of Images and Raman Spectra of Colliding Droplets: Composition Analysis of

system to be settled in a quasi-homogeneous state. Then, the rate equation d[PP2 −] = k1[H 2PP][NaOH] dt

(8)

is integrated as [PP2 −] = [H 2PP]0 (1 − e−k1[NaOH]0 (t − t0))

(9)

where [H2PP]0 and [NaOH]0 represent initial solution concentrations of H2PP 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 t0 and k1 values as (4.6 ± 0.1) × 102 μs and (2.2 ± 0.7) × 103 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 k1 value is significantly smaller than that of the second step, k2, which validates the analysis as well as the assumption that the first step, the lactone opening, is the ratedetermining step for the coloring reaction of phenolphthalein in alkaline solution.

5. CONCLUSION In summary, we observed a chemical reaction induced by droplet collision of H2PP/EtOH and NaOH/H2O. The concentration of deprotonated phenolphthalein, PP2−, produced 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.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +81-3-3986-0221. Fax: +81-3-5992-1029. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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DOI: 10.1021/acs.jpcb.5b03233 J. Phys. Chem. B 2015, 119, 7062−7067