Teacher Notes

Extraction and Isolation of Caffeine

Student Laboratory Kit

Materials Included In Kit

Caffeine, 2 g
Ethyl acetate, CH3COOC2H5, 600 mL
Ethyl alcohol, CH3CH2OH, 100 mL
Sodium carbonate, Na2CO3, 50 g
Sodium sulfate, anhydrous, Na2SO4, 50 g
Black tea bags, 50 g
Development jars with lids, 2
Pipets, Beral-type, extra-fine tip, 20
TLC sheet, 20 cm x 10 cm

Additional Materials Required

(for each lab group)
Extraction
Balance, 0.01-g precision*
Beaker, 150-mL
Beakers, 250-mL, 3
Boiling stones
Graduated cylinder, 250-mL
Hot plate
Separatory funnel, 250-mL
Support stand and ring

Purification—Part A. Crystallization of Caffeine
Beaker, 50-mL
Beaker, 250-mL
Filter paper, quantitative
Glass funnel
Hot plate
Support stand and ring
Water–ice mixture

Purification—Part B. Sublimation of Caffeine
Balance, 0.01-g precision*
Beaker, 50-mL
Beaker, 250-mL
Water-ice mixture, 20 mL

Identification
Pencil
Ruler
UV light source*

Prelab Preparation
Beaker, 50-mL
Scissors
Test tube, stoppered
*Shared

Prelab Preparation

The TLC sheets should be cut into 4 cm x 2 cm pieces before use.

Caffeine Standard: Place 0.5 g of caffeine in a beaker. Add 20 mL of ethyl alcohol and stir or swirl the beaker to dissolve (about one minute). All of the solid may not dissolve. Dispense the solution into a labeled stoppered test tube. Close the top of the tube tightly.

Working Groups
Break the student groups into three working teams. All groups will perform the extraction procedure. Select up to three groups to perform the crystallization procedure on their extracted crude caffeine. Select up to three groups to perform the sublimation procedure on their extracted crude caffeine. For TLC, up to four groups can perform this procedure. Select two groups to analyze crystallization samples and two groups to analyze the sublimation samples.

Safety Precautions

The ethyl acetate and ethyl alcohol solvents are extremely flammable. The solvents are volatile, irritating to eyes and skin and have characteristic odors—work in a fume hood or a well-ventilated laboratory only. Caffeine is highly toxic in pure form! Do not touch, taste or ingest any substances in the lab, including the tea extract, the crude caffeine or the purified samples. Never look directly at a UV light as it can be harmful to the eyes. Wear chemical splash goggles, chemical-resistant gloves and a chemical resistant apron. Wash hands thoroughly with soap and water before leaving the laboratory. Please follow all laboratory safety guidelines.

Disposal

Please consult your current Flinn Scientific Catalog/Reference Manual for general guidelines and specific procedures, and review all federal, state and local regulations that may apply, before proceeding. The leftover water extract may be disposed of down the drain with plenty of excess water according to Flinn Suggested Disposal Method #26b.

Lab Hints

  • Enough materials are provided in this kit for 30 students working in groups of three or for 10 groups of students. For best results, plan at least two 50-minute class periods for completing the lab. A convenient stopping point if needed is after extraction and/or evaporation of the ethyl acetate solvent, and before purification of the crude caffeine. The prelaboratory assignment may be completed before coming to lab.
  • Practice strict chemical hygiene and monitor students carefully in the lab. Warn students and make sure they do not touch or taste either the crude caffeine extract or the purified—sublimed or crystallized—product. Caffeine in pure form is highly toxic.
  • Hold the separatory funnel so that the stopper is in the palm of one hand and the stopcock is held with the other. This way leaks are prevented and any pressure built up inside the funnel will not pop the stopper off.
  • A quick way to determine which layer is which, one can simply add distilled water to the separatory funnel. Whichever layer increases in size must be the aqueous layer and the other is the organic layer.
  • In the crystallization procedure, add as small a quantity as possible to fully dissolve the sample. Its better to add too little solvent than too much. More solvent can be added during the heating process, if necessary.
  • Crystals usually begin forming on the bottom of the flask. Its possible to aid crystallization by scratching the flask with a glass rod at the air–solvent junction. The scratch increases the glass surface area, providing a roughened surface on which the solid can crystallize. If doing this, make sure you use these scratched beakers only for subsequent crystallization labs.
  • Sublimation has certain advantages over crystallization: it is a faster process, it requires no solvent, and, in the case of caffeine, separates from any adsorbed water.
  • Visualization of the compounds on TLC plates requires a short-wavelength UV light source—a black light is not high enough energy.
  • The TLC sheets contain a fluorescent powder that glows bright green when placed under a short-wave UV lamp. The spots that contain separated compounds will not glow green and will frequently be dark. Carefully mark the location of the spots using a pencil while the TLC plate is under the UV lamp. Trace an outline of the spots on the plate so a record of the TLC can be kept.
  • When spotting the TLC sheet, keep the spot as small as possible and make sure the spot will be above the solvent line in the developing jar. Briefly and gently touch the top of the micropipet tip to the TLC surface. Let the solvent evaporate before touching the micropipet tip to the TLC plate again. Touch the capillary to the same spot again. Remove the capillary and gently blow on the spot to evaporate the solvent. The spot should not be more than 2 mm in diameter when completed.
  • Carefully place the TLC sheet in the developing jar, making sure that the sample end is down but the spots are above the solvent. The TLC run is stopped when the solvent goes about 80% up the plate.
  • Good TLC technique is required for students to see small, well-separated spots on their sheets. Some of the common causes of poor separation are:
    1. Wrong solvent mixture applied to the TLC sheet.
    2. Too much sample applied to the TLC sheet.
    3. Initial spot too large.
    4. Initial spot is below the solvent level in the developing jar.
  • Allow enough time for the development of the TLC sheets. The sheet must be left in the jar long enough for the solvent to be drawn up to the end of the sheet. Do not stop the development until the solvent front nears the top of the plate. Typical time for development is 10–20 minutes. Give tips and hints on how to complete the activity with the greatest amount of success.

Correlation to Next Generation Science Standards (NGSS)

Science & Engineering Practices

Asking questions and defining problems
Planning and carrying out investigations
Analyzing and interpreting data
Using mathematics and computational thinking
Engaging in argument from evidence

Disciplinary Core Ideas

HS-PS1.A: Structure and Properties of Matter
HS-PS1.B: Chemical Reactions
HS-PS2.B: Types of Interactions

Crosscutting Concepts

Patterns
Cause and effect
Scale, proportion, and quantity
Stability and change

Performance Expectations

HS-PS1-2. Construct and revise an explanation for the outcome of a simple chemical reaction based on the outermost electron states of atoms, trends in the periodic table, and knowledge of the patterns of chemical properties.
HS-PS1-3. Plan and conduct an investigation to gather evidence to compare the structure of substances at the bulk scale to infer the strength of electrical forces between particles.
HS-PS1-7. Use mathematical representations to support the claim that atoms, and therefore mass, are conserved during a chemical reaction.

Answers to Prelab Questions

Carefully read the Background and the entire Procedure, and then answer the following questions.

  1. What two things does the addition of Na2CO3 do to aid the extraction of caffeine?

    This weak base converts caffeine to its less polar form and also converts the tannins to their more ionic form. This lowers the solubility of tannins in ethyl acetate while increasing the solubility of caffeine in ethyl acetate.

  2. What property of an organic solvent determines the position of the immiscible layer it forms with water?

    Its density. If density is less than 1.0 g/mL, the solvent will form a layer above water. If the density is greater than 1.0 g/mL, it forms below water.

  3. What properties should ideally be possessed by a crystallization solvent?

    It should be selective to the materials being extracted for solubility compared to the solubility of the impurities. The solubility of the extracted material should also be much greater at 80 °C than at 0 °C.

  4. How might the melting point of a material differ before and after crystallization?

    Since the materials will contain less “solute” impurities after crystallization, the melting point will be a more narrow range of temperature that is closer to the true value of the material. Since the freezing point depression attributable to the “solute” will be less for the crystallized material, its value should also be higher than that of the crude material.

  5. Your TLC analysis may reveal the presence of several/numerous materials in the isolated sample. What would this observation allow you to conclude about the selectivity of the extraction process?

    The fewer the number of impurities, the more selective the extraction process.

Sample Data

Extraction
Mass of 4 tea bags ___10.060___ g
Mass of tea bag – tea ___0.175___ g
Mass of tea (a – 4b) ___9.360___ g
Mass of beaker + boiling stones ___58.138___ g
Mass of beaker + crude caffeine ___58.229___ g

Crystallization
Mass of filter paper + caffeine crystals ___1.035___ g
Mass of filter paper ___1.005___ g
Mass of caffeine crystals ___0.030___ g

Sublimation

Mass of beaker ___29.881___ g
Mass of beaker + caffeine ___29.842___ g
Mass of sublimed caffeine ___0.031___ g

Thin-Layer Chromatography (TLC)

{12361_Data_Table_1}

Answers to Questions

  1. Tea typically contains 3% caffeine by weight. What percent of the caffeine was obtained by extraction and purification?
    {12361_Answers_Figure_9}
  2. Based on the TLC results, was the purification process selective in isolating caffeine from the crude extract?

    Answers will vary. The fewer impurities that show up in the chromatogram, the better the selectivity.

Student Pages

Extraction and Isolation of Caffeine

Introduction

Caffeine is found in the seeds, leaves or fruits of many plants. Of these, tea leaves and coffee beans are the primary sources for extracting caffeine. The purpose of this lab is to use separation methods for extracting and isolating caffeine from tea leaves, then calculate percent recovery and analyze the recovered caffeine for purity.

Concepts

  • Extraction
  • Sublimation
  • Thin-layer chromatography (TLC)
  • Solubility

Background

Extraction
Caffeine is a naturally occurring heterocyclic compound called an alkaloid. Alkaloids contain at least one nitrogen with lone pair electrons, which gives the compounds their characteristic basic property.

{12361_Background_Figure_1}
Alkaloids often have physiological activity. Other known examples of alkaloids include morphine, quinine, strychnine and nicotine.

The basic nitrogen atoms in caffeine can be used to increase or decrease its water solubility. Acidic conditions will form the conjugate acid salt giving caffeine increased water solubility. On the other hand if caffeine is in a basic environment it takes the neutral form and is only somewhat polar and thus less water soluble.

Caffeine can be extracted easily from tea bags. To make a cup of tea, simply “steep” the tea with hot water just below boiling for about 7 minutes. This extracts most of the caffeine. The solubility of caffeine in water is 2.2 mg/mL at 25 °C, 180 mg/mL at 80 °C and 670 mg/mL at 100 °C.

Caffeine is also quite soluble in ethyl acetate, the solvent used in this experiment to extract the caffeine from tea.
{12361_Background_Figure_2_Ethyl acetate}
In addition to caffeine, several other organic compounds in the tea leaves will be extracted by hot water. These include tannins, which are polyphenolic compounds having molecular weights in the range of 50–20,000 grams per mole. Tannins give brewed teas their dark color.
{12361_Background_Figure_3_Typical tannin structure}
The low molecular weight tannins have similar solublilities to caffeine in both water and slightly polar organic solvents.

Pigments such as chlorophyll are also extracted in hot water. While highly soluble in water, these pigments are only slightly soluble in low polarity solvents.

One more class of biochemicals, saponins, is also extracted from tea leaves. These molecules are amphiphilic, meaning they have polar, water-soluble groups attached to a nonpolar, water insoluble hydrocarbon chain.
{12361_Background_Figure_4_Tea leaf saponin}
Our goal in this laboratory is to extract caffeine from tea leaves, and then separate the caffeine from the other compounds also removed from the tea leaves. We will extract the caffeine from water with ethyl acetate. In order to successfully extract any substance from one solvent into another, we must maximize differences in solubility.

For caffeine, we want to make it much more soluble in ethyl acetate than in water. If base, in the form of sodium carbonate, Na2CO3, is added to the aqueous tea extract, the base converts the caffeine molecule to its non-ionic form. This increases caffeine’s solubility in ethyl acetate compared to its solubility in water.
{12361_Background_Figure_5}
To keep most of the other compounds in the water layer, we need to increase their water solubility while decreasing their solubility in ethyl acetate. Adding the weak base sodium carbonate also facilitates this goal—it increases the solubilities of the tannins and saponins in water while at the same time decreasing their solubilities in the less polar ethyl acetate.
{12361_Background_Figure_6}
Isolation and Identification
Once we have extracted the caffeine we need to remove the solvent to isolate the caffeine. This is accomplished by evaporating the ethyl acetate. The solid that remains is caffeine, along with impurities not removed in the extraction process. To further purify the caffeine, two techniques will be employed.

The first is crystallization. In this process, the crude solid is dissolved in a heated solvent, and then the solvent is cooled, producing purified crystals of the main solid component, in this case, caffeine.

The second process for isolating caffeine is sublimation. Sublimation occurs when a heated solid converts directly to a gas. Caffeine is one such solid. Also, when caffeine vapors are cooled, they condense directly to the solid phase. You will use this property of caffeine to isolate it from the crude extract. A beaker filled with an ice-water mixture is placed inside the beaker containing the crude solid and is positioned slightly above the bottom. The beaker containing the crude solid is slowly heated. As the caffeine sublimes, it is deposited out on the surface of the cold beaker. When all the caffeine has sublimed, the beakers are carefully removed and the purified caffeine is scraped from the bottom surface of the cold beaker.

The isolated caffeine is then identified using the technique of thin-layer chromatography (TLC). TLC is a form of chromatography that uses a thin layer of adsorbent material on an inert support. The TLC sheets used in this experiment contain a thin layer of silica gel on a plastic sheet. The eluent for the TLC is an organic solvent that travels up the TLC plate as it is absorbed by the silica gel.

TLC is frequently used as an analytical method to verify the presence of certain compounds. The use of “known” substances as a baseline for comparison is critical for making a strong case for the composition of unknowns. In order to compare substances collected over different time periods, a relative value called the Rf value is calculated for a given substance under specific chromatographic conditions. Typically, an unknown substance is spotted on a TLC plate alongside known reference substances. Then the solvent is allowed to travel up the TLC plate carrying the substance components up the plate to different levels. The distance a component moves compared to the distance the solvent moves is recorded as a ratio and is called the Rf value.
{12361_Background_Equation_1}
TLC will be used in this lab to identify and determine the purity of the caffeine isolated from tea.

Experiment Overview

Perform separation methods by extracting and isolating caffeine from tea leaves. Calculate percent recovery and then analyze the recovered caffeine for purity.

Materials

Extraction
Ethyl acetate, CH3COOC2H5, 50 mL
Sodium carbonate, Na2CO3, 4 g
Sodium sulfate, Na2SO4, 4 g
Balance, 0.01-g precision
Beakers, 250-mL, 3
Beaker, 100-mL
Boiling stones
Graduated cylinder, 250-mL
Hot plate
Separatory funnel, 250-mL
Support stand and ring
Tea bags, 5
 
Purification—Part A. Crystallization of Caffeine
Ethyl alcohol, CH3CH2OH, 20 mL
Beaker, 50-mL
Beaker, 250-mL
Filter paper, quantitative
Glass funnel
Hot plate
Support stand and ring
Test tube and stopper
Water-ice mixture

Purification—Part B. Sublimation of Caffeine
Balance, 0.01-g precision
Beaker, 50-mL
Beaker, 250-mL
Test tube and stopper
Water–ice mixture, 20 mL

Identification
Caffeine standard solution, 6–10 drops
Ethyl acetate, 25 mL
Development jar with lid
Pencil
Pipets, Beral-type, extra fine tip, 4
Ruler
TLC plate, 4 cm x 2 cm
UV light source

Prelab Questions

Carefully read the Background and the entire Procedure, and then answer the following questions.

  1. What two things does the addition of Na2CO3 do to aid the extraction of caffeine?
  2. What property of an organic solvent determines the position of the immiscible layer it forms with water?
  3. Explain why two extractions using 25 mL of ethyl acetate is more effective than one extraction using 50 mL.
  4. What properties should ideally be possessed by a crystallization solvent?
  5. How might the melting point of a material differ before and after crystallization?
  6. Your TLC analysis may reveal the presence of several compounds in the isolated sample. What would this observation allow you to conclude about the selectivity of the extraction process?

Safety Precautions

The ethyl acetate and ethyl alcohol solvents are extremely flammable. The solvents are volatile, irritating to eyes and skin, and have characteristic odors—work in a fume hood or a well-ventilated laboratory only. Caffeine is highly toxic in pure form! Do not touch, taste or ingest any substances in the lab, including the tea extract, the crude caffeine or the purified samples. Never look directly at a UV light as it can be harmful to the eyes. Wear chemical splash goggles, chemical-resistant gloves and a chemical resistant apron. Wash hands thoroughly with soap and water before leaving the laboratory. Please follow all laboratory safety guidelines.

Procedure

Working Groups
Students will be broken into different groups. Your teacher will assign which groups follow Part A: Crystallization, Part B: Sublimation, or Part C: TLC. Groups will then analyze their results and share with the class.

Extraction of Caffeine

  1. Obtain four unopened tea bags. Weigh the total contents to the nearest 0.1 g and record the mass in the data table.
  2. Obtain another tea bag, remove the staple and open the bag to remove the tea. Weigh the empty tea bag and staple to the nearest 0.1 g and record this mass in the data table.
  3. Using a graduated cylinder, add 100 mL of distilled or deionized water to a 250-mL beaker. Then add the four unopened tea bags to the same beaker.
  4. Weigh out four grams of sodium carbonate, Na2CO3, and add the solid to the beaker. Stir to dissolve.
  5. Set the beaker on the hot plate and heat to just under boiling. Heat for 15 minutes.
  6. Remove from heat and set aside to cool.
  7. Once cooled, use beaker tongs to remove the tea bags from the solution and discard them.
  8. In the hood, using a clean graduated cylinder, measure out 25 mL of ethyl acetate and add this to the solution in the beaker in the hood.
  9. Pour the mixture from the beaker into a 250-mL separatory funnel.
  10. Stopper the funnel and, holding the stopper in place, lightly tip the funnel upsidedown.
  11. While the funnel is inverted, carefully open the stopcock to vent the pressure.
  12. Close the stopcock and place the funnel in the ring attached to the support stand.
  13. Once the two layers separate, place a 250-mL beaker below the stopcock of the separatory funnel and collect the lower (aqueous) layer.
  14. Collect the remaining ethyl acetate layer in a second 250-mL beaker.
  15. Add the aqueous layer back into the separatory funnel.
  16. Add a fresh portion of 25 mL of ethyl acetate to the separatory funnel.
  17. Repeat steps 10–12.
  18. After the layers have separate, again collect the bottom aqueous layer in the same 250-mL beaker.
  19. Collect the remaining ethyl acetate layer again in the second 250-mL beaker. There should be approximately 50 mL of ethyl acetate collected in this beaker.
  20. Weigh out four grams of sodium sulfate and add the solid to the ethyl acetate beaker.
  21. Swirl the ethyl acetate beaker. The crystals of sodium sulfate will clump together as they absorb the water.
  22. Mass a clean, dry 100-mL beaker containing two boiling stones to the nearest 0.01 g. Record this mass in the data table.
  23. Use a glass stir rod to decant the ethyl acetate solution into the 100-mL beaker, leaving the clumped sodium sulfate behind.
  24. Place the 100-mL beaker containing the ethyl acetate solution on a hot plate in the fume hood.
  25. Heat gently at a low setting until the ethyl acetate completely evaporates.
  26. Remove the beaker and allow the beaker to cool to room temperature.
  27. Once cooled, mass the beaker containing the crude caffeine residue on the balance and then record the combined mass in the data table.

Purification of Caffeine

Part A. Crystallization

  1. Use forceps to transfer the boiling stones to a clean 50-mL beaker.
  2. Add 20 mL of 95% ethyl alcohol to the 50-mL beaker.
  3. Place the 50-mL beaker on a hot plate at a low setting and gently heat the ethyl alcohol. Do not allow the solvent to boil.
  4. Once the solution is hot, remove the beaker from the hot plate and set it aside.
  5. Place ice water in a 250-mL beaker to the 50-mL mark.
  6. Pour the hot ethyl alcohol into the 100-mL beaker containing the crude caffeine.
  7. Carefully swirl to mix and dissolve the caffeine.
  8. Place the 100-mL beaker in the 250-mL beaker containing the ice-water mixture. In about 3 minutes crystals should begin to form in the ethyl alcohol solution.
  9. Wait several minutes to allow all of the caffeine to crystallize.
  10. Once crystallization is complete, remove the 100-mL beaker.
  11. Mass a circle of quantitative filter paper and record in the data table.
  12. Set up a gravity filtration with the massed quantitative filter paper, support stand and ring and a glass funnel.
  13. Filter the caffeine from the cold ethyl alcohol.
  14. Once filtration is complete, remove the filter paper and set it aside to dry.
  15. When dry, mass the filter paper and crystallized caffeine and record the mass in the data table.
  16. In a small test tube, add approximately 2 mL of ethyl alcohol. Add the purified caffeine to the test tube. Stopper and mix until caffeine dissolves. Save this solution for Part C.

Part B. Sublimation

  1. Obtain a 50-mL beaker that is clean and dry on the outside.
  2. Mass the beaker. Record this value in the data base.
  3. Add an ice-water mixture to the beaker.
  4. Place the beaker in the 100-mL beaker containing the crude caffeine extracted from the extraction process.
  5. Heat this assembly on the hot plate at a low setting.
  6. As the temperature increases, the caffeine will sublime from the lower beaker and start to deposit on the inner beaker surface as fine white crystals.
  7. Continue heating until the sublimation process is complete and then use beaker tongs remove the beaker assembly from the hot plate. Set the assembly aside to cool.
  8. Carefully remove the inner 50-mL beaker and decant off the ice-water mixture, taking care not to get the crystals wet.
  9. Dry the inside of the 50-mL beaker with paper towels.
  10. Mass the beaker and sublimed caffeine by placing the beaker upside down on the balance. Record this mass in the data table.
  11. Scrape the caffeine crystals from the bottom of the beaker into a filter paper.
  12. In a small test tube, add approximately 2 mL of ethyl alcohol. Add the purified caffeine to the test tube. Stopper and mix until caffeine dissolves. Save this solution for Part C.

Part C. Identification—Thin-Layer Chromatography

  1. Obtain a TLC plate. The plates are fairly fragile and, if cracked or soiled, will yield incorrect results. Handle the plates by the edges only. Do not touch the powdery side of the plate. Place the plate powdery-side up on a piece of clean paper.
  2. Use a pencil and ruler to gently draw a faint line 0.5 cm from the bottom of the plate and make other light markings as shown in Figure 7. Do not dig into the white powder on the plate. Note: Do not use a pen!
    {12361_Procedure_Figure_7_Initial TLC layout}
  3. Obtain test tubes containing the standard solution of caffeine and the purified sample from the tea extraction.
  4. Use the end of a micro-tip plastic pipet to place one small drop of caffeine standard solution on the plate at the CAF location. Let the spot dry completely. Place another drop exactly on top of the first drop and let it dry. Repeat this dropping procedure until 6–8 drops have been placed one on top of each other. Be sure to allow drying time in between each drop application.
  5. Spot the caffeine sample unknown at the appropriate location marked on the TLC plate just like the caffeine standard. Allow each drop to dry before adding another drop.
  6. While the plates are drying, add enough ethyl acetate to a developing jar until the liquid covers the bottom and reaches a depth of 0.3 cm. Do not use too much solvent.
  7. Place the developing jar on a lab bench where it will not be disturbed for approximately 20 minutes A developing jar will be shared with another working group. The TLC plates will be placed in the developing jar in pairs to form a tent-like arrangement to support the plates (see Figure 8). The lid must be on the jar during the developing process.
    {12361_Procedure_Figure_8_Two TLC plates in developing jar in tent-like support}
  8. Carefully open the jar without moving the liquid. Pick up one plate by the top and carefully lower it into the jar so the markings are on the bottom of the jar. Add the second plate into the jar so that the shiny, plastic sides of the plates are back to back toward the center.
  9. Carefully place the lid back on the jar without disturbing the plates. Do not move the jar until the development is complete.
  10. When the ethyl acetate has moved up to within 1 cm of the top of the plates, remove the plates and place them on paper towels (plastic side down) until they are dry. Remove both plates at the same time.
  11. When the plates are removed, use a pencil to mark the solvent front location on the TLC card.
  12. View the plate with a UV light. Your instructor will help with the light and the interpretation of the various spots. Do not look into the UV light directly. Use a pencil to place a dot exactly in the center of each important spot.
  13. Measure the distances in cm from the line at the bottom of the plate (starting line) to the solvent front near the top. Record this distance on the TLC Worksheet.
  14. Measure the distance from the starting line to the center of each spot. Record the distances and calculate the Rf value for each spot on the TLC Worksheet.
  15. Answer the questions on the TLC Worksheet.
  16. Consult your instructor for appropriate disposal procedures.

Student Worksheet PDF

12361_Student1.pdf

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