Using Beads and Divided Containers To Study Kinetic and Equilibrium

Laboratory Experiment pubs.acs.org/jchemeduc

Using Beads and Divided Containers To Study Kinetic and Equilibrium Isotope Effects in the Laboratory and in the Classroom Dean J. Campbell,* Emily R. Brewer, Keri A. Martinez, and Tamara J. Fitzjarrald Mund-Lagowski Department of Chemistry and Biochemisty, Bradley University, Peoria, Illinois 61625, United States S Supporting Information *

ABSTRACT: The purpose of this laboratory experiment is to study fundamental concepts of kinetics and equilibria and the isotope effects associated with both of these concepts. The concepts of isotopes in introductory and general chemistry courses are typically used within the contexts of atomic weights and radioactivity. Kinetic and equilibrium isotope effects are typically covered in upper-level courses in the chemistry curriculum, but the concepts behind these isotope effects are also relevant to introductory chemistry. Beads (specifically “airsoft” pellets) of the same size but with two different masses can be used to represent isotopes of two different masses in classroom activities. Plastic Petri dishes with dividers can be modified so that the chambers can represent different states of matter or different chemical species. When the Petri dishes containing a number of beads of each mass are shaken, the beads will be distributed among the chambers in a manner similar to isotope distributions in matter. The bead/Petri dish shakers have been used as a chemistry demonstration and as a chemistry laboratory activity. Additionally, LEGO-based models containing chambers separated by dividers can be used to demonstrate the phenomena of kinetics and equilibria. The laboratory experiments can be performed in one laboratory period and are designed to touch on a variety of topics relevant for general chemistry students, although the lab could also be easily used for students with more or less advanced backgrounds. KEYWORDS: General Public, High School/Introductory Chemistry, First-Year Undergraduate/General, Laboratory Instruction, Demonstrations, Environmental Chemistry, Hands-On Learning/Manipulatives, Equilibrium, Isotopes, Kinetics

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INTRODUCTION Concepts associated with kinetics and equilibria are undoubtedly essential to a proper understanding of chemistry. Many concepts associated with kinetics and equilibria can be illustrated with energy diagrams that describe the energies of chemical species as functions of reaction progress. Many models, ranging from physical to abstract models and including models of energy diagrams, have been used to describe kinetics and equilibria.1−17 The energy diagram models help to demonstrate how chemical species distributions are affected by time and energy in a chemical system. Figure 1 shows the energy diagram models or “shakers” that have been developed for this laboratory activity. In the activity, the models are oriented such that the vertical direction (along the y axis of an energy diagram) represents energy and the horizontal direction (along the x axis of an energy diagram) represents reaction progress. The models contain chambers that are separated by vertical dividers, which represent activation energy barriers. Beads placed in the chambers represent the chemical species themselves and can move from chamber to chamber over the vertical dividers when the model is shaken. In addition to being able to model energy diagrams for a single chemical reactant species, the shakers can also model isotope effects. In many collegiate general chemistry textbooks, discussion of isotopes often occurs within the first couple chapters, near other discussions of atomic structure, atomic © XXXX American Chemical Society and Division of Chemical Education, Inc.

masses, atomic and molecular weights, and stoichiometry. Isotopes are typically not covered further in general chemistry until coverage of nuclear chemistry, when discussing isotopic decay tendencies. In organic chemistry, isotopes play in important role in NMR spectroscopy (only some isotopes are NMR-active) and mass spectrometry (isotopic distributions can aid in identifying elements in compounds). Other courses might cover the influence of isotopes on vibrational frequencies in infrared spectroscopy or mention the impact of the kinetic isotope effect in various chemical and biochemical processes. The shakers described in this paper easily demonstrate the kinetic isotope effect as well as the equilibrium isotope effect. Both of these isotope effects can be studied by measuring the distribution of isotopes of a particular element between different phases or chemical species. Isotope concentration differences from an established standard isotope distribution can be expressed as a δ value (eq 1):18−20 ⎡⎛ heavy isotopes ⎤ ⎞ ⎢⎜ light isotopes in sample ⎟ ⎥ δ = ⎢⎜ heavy isotopes ⎟⎟ − 1⎥ × 1000 ⎜ in standard ⎠ ⎥⎦ ⎣⎢⎝ light isotopes

(1)

Received: January 1, 2017 Revised: May 4, 2017

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DOI: 10.1021/acs.jchemed.6b01004 J. Chem. Educ. XXXX, XXX, XXX−XXX

Journal of Chemical Education

Laboratory Experiment

the δ values for the starting LIQUID side chamber are averaged, as are those for the opposite GAS side chamber, to minimize the impact of one or two spurious trials. For the kinetic isotope effect shakers (Figure 1A), the chamber floors are all at the same height, although this is not strictly necessary. In these experiments, the shaking intensity can represent the reaction temperature. When the shaker is shaken for 10 seconds in a gentle, slow manner (representing cooler temperatures), most trials result in the light beads moving over the vertical barrier at a higher rate than the heavy beads. This on average produces significantly positive δ values in the starting LIQUID side chamber and significantly negative δ values in the opposite GAS side chamber. When the shaker is shaken for 10 seconds in a hard, fast manner (representing warmer temperatures), both the light beads and the heavy beads move over the barrier at higher rates. On average, the starting LIQUID side chamber might still have a positive δ value and the opposite GAS side chamber a negative value, but the magnitudes of these values tend to be less than those produced by gentle shaking. Regardless of the shaking intensity, shaking the kinetic shakers for an infinite amount of time should yield average δ values of zero in each chamber, since the chamber floors have the same height relative to the energy barrier and each other. For the shakers used to demonstrate the equilibrium isotope effect (Figure 1B), the floors of the different chambers are at different heights. All of the beads start in one chamber for 10 trials and then in the other chamber for 10 trials. The shaker is shaken hard and fast in each trial for 20 s to determine whether the starting location has any real effect on the final distribution of beads. The students run several trials to obtain average δ values. Calculation of δ values for the trials shows that on average there is not much difference due to starting location: on average, the beads in the high GAS side chamber attain a negative δ value and the beads in the low LIQUID side chamber attain a positive δ value. Aggregated δ values from two courses that used this laboratory activity are described in the instructor guide in the Supporting Information. To minimize the possible influence of human bias and check the impact of the shaking speed on the kinetic isotope shakers, a kinetic isotope shaker was affixed to the oscillating platform of a variable-speed Vortex Genie 2 (Scientific Industries). The shaker was oscillated for 15 s trials, each with ten 0.12 g beads and ten 0.28 g beads starting in one chamber. The average final δ values for the beads in the starting side chamber and the other side chamber are shown in Table 1. On rare occasions, a trial produced a bead arrangement that required division by zero to calculate δ; those rare trials were not included. It should be noted that at higher shaking speeds, the difference between the δ values for the chambers decreased. This is consistent with what was observed by hand shaking.

Figure 1. Isotope effect shakers produced from divided Petri dishes used in this laboratory activity. (A) The kinetic isotope effect shaker must be held horizontally while the dish is shaken horizontally (left and right from the perspective of this photograph). (B) The equilibrium isotope effect shaker must be held vertically while the dish is shaken horizontally (left and right from the perspective of this photograph).

The shakers demonstrate the isotope effects by using two sets of beads of the same size but different mass. A variety of beads can be used, but airsoft ammunition is particularly effective in that the beads are all the same size but are available in a variety of different masses (e.g., 0.12 g/bead and 0.28 g/bead). The δ values can also be used to describe relative numbers of beads. In describing the bead enrichment ratio relative to an initial equal number of light and heavy beads, the expression for δ simplifies to eq 2: ⎡⎛ average heavy bead count ⎞ ⎤ δ = ⎢⎜ ⎟ − 1⎥ × 1000 ⎢⎣⎝ average light bead count ⎠ ⎥⎦

(2)

Shakers using beads of two different masses have been used both as a laboratory activity and as demonstration activities in outreach events, as described below. The laboratory activity easily fits within a three-hour lab period and is designed to be placed into any location in the general chemistry sequence after the students are introduced to the concept of isotopes.

Table 1. Mechanical Shaking Trials on a Kinetic Isotope Shaker

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Average Final δ Values

EXPERIMENT In the laboratory activity, the shakers are used to model water evaporation from the oceans, although many other processes could be modeled. Each shaking experiment is run with all of the beads starting in the same LIQUID side chamber, which has an initial δ value of zero since there are equal numbers of light and heavy beads. The shaker is shaken for 10 trials, and B

Shaking Speed (Hz)

Number of 15 s Trials

Starting Side Chamber

Opposite Side Chamber

1880 1900 2600 2900

28 59 30 30

2176 2298 331 142

−803 −785 192 67



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HAZARDS There are no significant hazards associated with these experiments. If the shaker boxes break open, the beads could be swallowed by small children, or a large number of loose beads on the floor could possibly present a slipping hazard.

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shaken is highly recommended. Differing groups of people can then be prompted either to shake gently or vigorously. Alternatively, the directions can be presented as a challenge to the groups to try to shake the shakers in such a way as to separate the two colors of beads as much as possible and to let the groups discover on their own that gentle shaking produces the best separation. Occasionally, gentle shaking will produce the statistically less likely result of high proportions of the heavy beads ending in the GAS side chamber. However, when the majority of shakers are taken into account, the difference between gentle and vigorous shaking should become apparent. If the shakers can be carefully collected so that their bead arrangements are not disrupted, they can be stacked so that each shaker simulates a layer in an ice or sediment profile. Shakers with high proportions of light beads in the GAS side chambers correspond to ice layers produced during times of cool ocean temperatures; shakers with low proportions of light beads in the GAS side chambers correspond to ice layers produced during times of warm ocean temperatures. An illustration of a shaker stack representing an ice and a sediment profile is shown in Figure 2.

DISCUSSION

Modeling the Measurement of Global Temperatures in the Past

A number of chemical and physical processes can be influenced by isotope effects,21−26 but this laboratory activity uses the shakers to illustrate how water isotopic distributions can be used to estimate how the earth’s temperature has varied over time. In a simplified view of the water cycle, liquid water in the ocean evaporates into the gas phase and is blown about by the wind. Light water molecules move into the gas phase more quickly than the heavy water molecules, an example of the kinetic isotope effect.19,20,27,28 The equilibrium isotope effect also plays a role, as heavy isotopes are more likely to be distributed into the lower-energy liquid phase than the gas phase.19,20,27 Some of the water vapor that has evaporated from the ocean and is depleted in heavy water moves over land before it condenses and falls out as rain or snow. Much of the precipitation that falls on the land finds its way via rivers back to the ocean, but some of the snow accumulates in deposits such as glaciers and polar ice caps, sometimes producing thousands of years of layered ice deposits. The water in the snow is depleted in heavy isotopes relative to the ocean, so it has a negative δ value for isotopes such as oxygen-18 relative to ocean water. Both the kinetic and equilibrium isotope effects, and the resulting global isotope distributions in water, can be influenced by temperature. At lower ocean temperatures, the light isotopes escape from the liquid ocean water into the gas phase more readily than the heavy isotopes. At higher ocean temperatures, the light and heavy isotopes escape from the liquid ocean water into the gas phase at a more equal pace. As a result, ice accumulating at the poles is more depleted in heavy isotopes such as oxygen-18 (and have more negative δ values) when the ocean temperatures are cooler. A complementary pattern is observed in ocean sediments, as the oxygen in carbonate compounds in small animal shells and coral can come from ocean water. At cooler global temperatures, the sediments are enriched in oxygen-18 (and have more positive δ values) compared with when the ocean is warmer.27,28 Ice can be sampled from accumulated ice cap deposits, or sediment can be sampled from the ocean floor, and the isotopic composition of each layer of ice or sediment can be measured. This laboratory activity can thus be connected to concepts of geological stratigraphy such as the law of superposition in addition to the chemical principles discussed. What emerges from the isotope measurements of the layers is a temporal profile of the layers with respect to δ values and, ultimately, ocean temperatures. For example, isotopic analyses of ice layers corresponding to glacial advances in the past exhibit rather negative δ values, and interglacial warm periods exhibit less negative values. Isotope distributions have therefore been used to monitor global climate change. The aforementioned concepts behind global temperature measurement can also be demonstrated to participants in outreach events. Kinetic isotope shakers can be handed out to small groups of people with directions on how they are to be shaken. An actual demonstration of how the shakers should be

Figure 2. A shaker stack representing an ice profile and a sediment profile produced by the same variations in ocean temperature.

Modeling the Loss of Water from Mars

The kinetic isotope effect shakers can also be used to explain the history behind some of the current conditions on the surface of Mars. It is hypothesized that Mars had much more water at its surface in the distant past. Over time, much of this water was lost when radiation from the sun broke apart water molecules in the atmosphere and some of the molecular fragments escaped into space. One piece of evidence supporting this comes from measurements of the hydrogen isotope distribution on Mars. The relatively high abundance of heavy hydrogen isotopes on Mars compared with Earth can be explained by the ability of lighter hydrogen isotopes to escape the Martian atmosphere more quickly than heavier hydrogen isotopes.29 It has also been hypothesized that when the lighter hydrogen atoms were lost more readily than the heavier oxygen atoms, the Martian atmosphere became more oxygen-rich for a time, enabling the formation of iron oxides and manganese oxides that have been observed on the surface of Mars.30 The loss of the lighter atoms relative to the heavier atoms can be easily simulated by the kinetic isotope effect shaker with slow, gentle shaking (Figure 3A). The light beads represent light hydrogen atoms, and the heavy beads represent heavy hydrogen atoms or even oxygen atoms. C




the same mass. The beads all start on one side of the barrier (here the left side), and a single shake is all it usually takes to illustrate that the beads tend to move more easily over the smaller divider. Modeling Isotope Effects Using LEGO Bricks

An alternative to using divided Petri dishes to model energy diagrams is the use of LEGO bricks (Figure 4). LEGO bricks have been used to build many structures used to model chemistry, ranging from molecules to larger chemical structures

Figure 3. Additional shakers produced from divided Petri dishes used in this laboratory activity. (A) A shaker demonstrating the preferential loss of light atoms (represented by orange beads) over heavy atoms (represented by white beads) from Mars (left side of the shaker) to space (right side of the shaker). (B) A pair of shakers used to demonstrate the relation between reaction catalysis and activation energy.

Demonstrating Reaction Catalysis

The model shown in Figure 3B is used to demonstrate both uncatalyzed and catalyzed reactions. The divided plastic Petri dish shakers representing the reactions are attached to a cardboard panel on a handle. A portion of each Petri dish divider has been removed, and the remaining divider is highlighted with colored tape. The shaker with the larger divider represents an uncatalyzed system with a higher activation energy, and the shaker with the smaller divider represents a catalyzed system with a lower activation energy. Both sets of chambers have beads (e.g., airsoft ammunition) of

Figure 4. Shaker produced from LEGO bricks that have varying barrier heights. (A) A model with sets of chambers to illustrate twostep reactions. (B) A model with multiple pairs of chambers to demonstrate the kinetic isotope effect. D




to instrumentation.31,32 An advantage to using LEGO bricks in modeling is that structures can be readily modified by adding and removing bricks. For example, the floors of the chambers and the activation barriers can be raised or lowered by changing the numbers of bricks in the model. Additionally, the LEGO structure shown here is large enough that multiple energy diagram situations can be demonstrated at the same time. Beads are still used to represent chemical species, and those beads are made visible within the LEGO chambers by using a transparent plastic plate such as a CD or DVD case as a front panel (which can be held in place using rubber bands). As with the Petri dish models, the demonstrations begin with all of the beads in one chamber and the model is shaken horizontally to distribute the beads throughout the chambers. A LEGO model with sets of chambers to illustrate two-step reactions is shown in Figure 4A. Beads beginning from the leftmost chambers move more easily over the lower barriers than the higher barriers, regardless of whether the barriers are for the first or second step of the process. A LEGO model with sets of chambers that can be used to demonstrate the kinetic isotope effect is shown in Figure 4B. The lighter-weight orange beads tend to have an easier time crossing left to right over the barriers than the heavier-weight white beads regardless of the barrier height. Detailed instructions for the construction and possible applications of these models are described in the Supporting Information.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Dean J. Campbell: 0000-0002-2216-4642 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful to Bradley University for funding through the Sherry, Special Emphasis, and Building Excellent Scientists for Tomorrow Programs. We also thank the Illinois Space Grant Consortium and the Illinois Heartland Section of the American Chemical Society for support. We are grateful for contributions from Kristine and Kathryn Campbell, Shreya Bellur and Vishwaarth Vijayakumar, and Max Palmer and Dannielle Wentzel. We thank the students in various chemistry laboratories in the Mund-Lagowski Department of Chemistry and Biochemistry at Bradley University and participants in outreach events held by the Bradley University Chemistry Club Demo Crew.

Other Simple Analogies of the Kinetic Isotope Effect

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A low-tech, low-cost, cross-cultural analogy of the kinetic isotope effect can be illustrated by the process of winnowing grain. This process, done in various ways for thousands of years, separates seeds of grain from chaff. One of the ways winnowing can be performed is to toss both seeds and chaff into the wind from a container such as a basket. The heavier-weight seeds of grain fall back to the container, and the lighter-weight chaff is blown about by the wind. In this analogy, the edge of the basket represents the activation barrier, the seeds represent the heavier isotopes, and the chaff represents the lighter isotopes. One could imagine that if the basket were shaken hard enough, both the seeds and the chaff would be moved out of the basket, providing an illustration of the impact of temperature on the kinetic isotope effect. Another analogy could be based on the process of panning for gold, where gold grains represent the heavier isotopes, much of the non-gold sediment minerals represent the lighter isotopes, and the edge of the pan represents the activation barrier. The student laboratory procedure in the Supporting Information contains these types of questions (and the instructor notes contain the answers). As written, the laboratory procedure is designed for first-year undergraduate students. However, with appropriate supervision, high school and middle school students could also perform these relatively simple simulations and therefore experience some of the subtleties of the kinetic and equilibrium isotope effects.

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Labels for the shaker models (PDF, DOCX)

REFERENCES

(1) Meyer, E. F.; Glass, E. Demonstrating the Relation between Rate Constants and the Equilibrium Constant. J. Chem. Educ. 1970, 47, 646. (2) Alden, T. A.; Schmuckler, J. S. The Design and Use of an Equilibrium Machine. J. Chem. Educ. 1972, 49, 509. (3) Hambly, G. F. Equilibrium - A Novel Classroom Demonstration. J. Chem. Educ. 1975, 52, 519. (4) Birk, J. P.; Gunter, K. K. Water Dipping Kinetics. J. Chem. Educ. 1977, 54, 557. (5) Harsch, G. Kinetics and Mechanism − A Games Approach. J. Chem. Educ. 1984, 61, 1039. (6) Cullen, J. F., Jr. Computer Simulation of Chemical Equilibrium. J. Chem. Educ. 1989, 66, 1023. (7) Sawyer, D. J.; Martens, T. E. An Equilibrium Machine. J. Chem. Educ. 1992, 69, 551. (8) Schultz, E. Dice-Shaking as an Analogy for Radioactive Decay and First-Order Kinetics. J. Chem. Educ. 1997, 74, 505. (9) Garritz, A. The Painting-Sponging Analogy for Chemical Equilibrium. J. Chem. Educ. 1997, 74, 544. (10) Wilson, A. H. Equilibrium: A Teaching/Learning Activity. J. Chem. Educ. 1998, 75, 1176. (11) Edmonson, L. J.; Lewis, D. L. Equilibrium Principles: A Game for Students. J. Chem. Educ. 1999, 76, 502. (12) Huddle, P. A.; White, M. W.; Rogers, F. Simulations for Teaching Chemical Equilibrium. J. Chem. Educ. 2000, 77, 920. (13) Hanson, R. M. Playing Card Equilibrium. J. Chem. Educ. 2003, 80, 1271. (14) Schultz, E. Simple Dynamic Models for Hydrogen Bonding Using Velcro-Polarized Molecular Models. J. Chem. Educ. 2005, 82, 401. (15) Bartholow, M. Modeling Dynamic Equilibrium with Coins. J. Chem. Educ. 2006, 83, 48A. (16) Ellis, B. E.; Ellis, D. C. An Experimental Approach to Teaching and Learning Elementary Statistical Mechanics. J. Chem. Educ. 2008, 85, 78. (17) Schultz, E. An Updated Equilibrium Machine. J. Chem. Educ. 2008, 85, 1131. (18) Eby, G. N. Principles of Environmental Geochemistry; Brooks/ Cole-Thomson Learning: Pacific Grove, CA, 2004.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.6b01004. Student laboratory procedures (PDF, DOCX) Instructor guide and instructions for building Petri dish shaker models (PDF, DOCX) Instructions for building and use of LEGO shaker models (PDF, DOCX) E




(19) Kendall, C.; Caldwell, E. A. Chapter 2: Fundamentals of Isotope Geochemistry. In Isotope Tracers in Catchment Hydrology; Kendall, C., McDonnell, J. J., Eds.; Elsevier: Amsterdam, 1998; pp 51−84. (20) USGS. Resources on Isotopes. http://wwwrcamnl.wr.usgs.gov/ isoig/res/funda.html (accessed May 2017). (21) O’leary, M. H.; Madhavan, S.; Paneth, P. Physical And Chemical Basis of Carbon Isotope Fractionation in Plants. Plant, Cell Environ. 1992, 15, 1099−1104. (22) Wilson, E. K. New Direction for Isotope Chemistry. Chem. Eng. News 2015, 93 (24), 28−29. (23) Halford, B. Deuterium switcheroo breathes life into old drugs. Chem. Eng. News 2016, 94 (27), 32−36. (24) Squires, A. M. The Fractionation of Isotopes. J. Chem. Educ. 1946, 23, 538−541. (25) Wang, L.; Goodey, N. M.; Benkovic, S. J.; Kohen, A. The role of enzyme dynamics and tunnelling in catalysing hydride transfer: studies of distal mutants of dihydrofolate reductase. Philos. Trans. R. Soc., B 2006, 361, 1307−1315. (26) Ž emva, P.; Lesar, A.; Senegačnik, M.; Kobal, I. Nitrogen-15 and oxygen-18 kinetic isotope effects in the catalytic decomposition of N2O over MgO. Phys. Chem. Chem. Phys. 2000, 2, 3319−3325. (27) Kump, L. R.; Kasting, J. F.; Crane, R. G. The Earth System, 2nd ed.; Pearson Education: Upper Saddle River, NJ, 2004. (28) Past Climates on Earth. http://www.globalchange.umich.edu/ globalchange1/current/lectures/kling/paleoclimate/paleoclimate.html (accessed May 2017). (29) Wilson, R. M. New Hydrogen-Isotope Measurements Refine the Picture of Water on Mars. Phys. Today 2015, 68, 12−14. (30) Jet Propulsion Laboratory. NASA Rover Findings Point to a More Earth-like Martian Past. http://www.jpl.nasa.gov/news/news. php?feature=6544 (accessed May 2017). (31) Campbell, D. J.; Freidinger, E. R.; Querns, M.; Swanson, S.; Ellis, A. B.; Kuech, T. F.; Payne, A.; Socie, B.; Condren, S. M.; Lisensky, G. C.; Rassmussen, R. Exploring the Nanoworld with LEGO® Bricks; Bradley University: Peoria, IL, 2012; available online for download at http://mrsec.wisc.edu/edetc/LEGO/index.html. (32) Campbell, D. J.; Miller, J. D.; Bannon, S. J.; Obermaier, L. M. An Exploration of the Nanoworld with LEGO® Bricks. J. Chem. Educ. 2011, 88, 602−606.

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Using Beads and Divided Containers To Study Kinetic and Equilibrium

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