Determination of the Gas-Law Constant (R) using CO2 EXPERIMENT 11 Prepared by Edward L. Brown and Miranda Raines, Lee University The student will become familiar with ideal gases and how their properties are related to the ideal gas constant. OBJECTIVE ring stand A P P A R A T U S 2 ml disposable pipette 2 2L soda bottles bent glass tubing 3 2-hole stoppers rubber tubing clamps 50 ml Erlenmeyer flask 1000 ml beaker (or 1L soda bottle) APPARATUS AND CHEMICALS Sodium Bicarbonate (baking soda) Citric Acid C H E M I C A L S Many gases at room temperature and atmospheric pressure are ideal and obey the ideal gas law (PV = nrt). An ideal gas is one that has no intermolecular attractive forces present between its atoms (for elemental gases like He, Ne, etc) or molecules (for molecular gases like O 2, CO 2, etc). Intermolecular attractive forces cause atoms and molecules to deviate from gaseous behavior and to begin to possess properties common to liquids. These forces are strongest when molecules are forced close to one another (high pressures) and when molecules move slowly past one another (low temperatures). To account for the non-ideal behavior of gases, an equation based on experimental observations was derived by Johannes Diderik van der Waals, called the van der Waals equation [Equation 1]. Copyright 2005 Chem21 LLC. No part of this work may be reproduced, transcribed, or used in any form by any means graphic, electronic, or mechanical, including, but not limited to, photocopying, recording, taping, Web distribution, or information storage or retrieval systems without the prior written permission of the publisher. For permission to use material from this work, contact us at info@chem21labs.com. Printed in United States of America.
P + 2 na V 2 V - nb = nrt Equation 1 where a and b are constants that have been determined for a given gas. In this experiment, you will determine the value of R using both the ideal gas equation and van der Waals equation. The gas constant will be determined in units of atm-l/mole-k. The gas that will be used is carbon dioxide, generated from the neutralization / decomposition of NaHCO 3, baking soda. The temperature, pressure, volume and grams of carbon dioxide will be measured and placed in the ideal gas equation and in van der Waals equation (a = 3.592 L 2 -atm/mole 2 and b = 42.67 cm 3 /mole for CO 2) to determine the value of R. The first three measurements will be made directly on an enclosed sample of CO 2, the number of moles of carbon dioxide contained in the sample will be determined from the mass of CO 2 that left the following reaction: NaHCO 3 (s) + HCl (aq) NaCl (aq) + H2 O (l) + CO2 (g) Equation 2 Since carbon dioxide is the only product that can escape the test tube, an accurate weight of the test tube and its contents before and after the experiment reveals the mass of CO 2 generated. The temperature of the gas is determined by measuring the temperature of the water that is displaced by the gas. The volume of the gas is determined by weighing the displaced water and using the density of water to determine the volume. The pressure of the CO 2 will equal the atmospheric pressure if the displaced water level is the same height as the water level in the 2-L bottle. Only when the water levels are equal will the pressure above the water be equal to the atmospheric pressure. In this experiment, it is critical that the measurements contain the largest number of significant figures possible from the instruments available. For example, the temperature of the water / CO 2 can be determined to within 0.2 ºC using thermometers common in most laboratories. In addition, the volume of the CO 2 is more accurately obtained by measuring the mass of the displaced water and then using the density of water to convert mass into volume. The use of a beaker or graduated cylinder to measure the volume of the displaced water directly will give values that contain fewer significant figures and are less accurate. When possible, always select instruments and methods that give the greatest accuracy an instrument s accuracy depends on how well it has been calibrated prior to its use. The density of water, corresponding to the range of temperatures in which this experiment should be performed, is found in Table 3. Use this information to convert the mass of water displaced into milliliters of CO 2 produced. Experiment 11 11-2
The water in the collection beaker and the carbon dioxide gas are related by the fact that their volumes are the same. The mass of water collected is converted into liters of CO 2 produced in the reaction. This number is used in the ideal gas equation (along with pressure, moles and temperature) and in van der Waals experimental equation [Equation 1] to find the value of R. The apparatus used to collect CO 2 [Figure 1] overcomes a problem that plagues this particular gas. Common gases are routinely collected by bubbling them into an inverted waterfilled container or by generating them inside a closed system where their expansion pushes water out of the system. Carbon dioxide gas, however, cannot be collected quantitatively in these systems since it is very soluble in water. Figure 1 depicts an experimental setup where the generated CO 2 never physically contacts the water, so no CO 2 gas is Figure 1 removed (by dissolution) once it is formed. The density of CO 2 makes this possible CO 2 is much denser than other common gases (air included) and will sink to the bottom of its container. The mixing of CO 2 and air is minimized by directing the generated CO 2 to the bottom of the left soda bottle. This gas accumulates in the bottom and pushes air out the top of the first soda bottle and into the top of the right soda bottle. Carbon dioxide gas is sequestered in the first soda bottle and never contacts the water in the second soda bottle Did you know that the density of CO 2 is greater than the densities of other common gases like O 2, N 2, H 2, or He? It is because it has a greater molar mass than the other gases. At room temperature and pressure, these gases are fairly ideal and adhere to the ideal gas equation. Substitution of mass (g) divided by molar mass (MM) for moles (n) and rearrangement will give an equation that can be used to find the density of an ideal gas [Equation 3]. Table 1 lists the molar mass (MM) of these gases and uses Equation 3 to find their density. g Density = L P(MM) RT Equation 3 Experiment 11 11-3
Chemical Formula Molar Mass (g/mole) Density (g/l) O 2 31.9988 1.309 N 2 28.0134 1.146 H 2 2.0158 0.0824 He 4.0026 0.1637 CO 2 44.0098 1. 9797 Table 1 Carbon dioxide gas has the greatest density among the gases listed because it has the largest molar mass. Carbon dioxide is also denser than air (a 21 : 78 mixture of O 2 : N 2). Hydrogen gained the attention of early chemists because it is the most buoyant gas known. Hydrogen was used in early dirigibles like the Hindenburg, but its flammability and explosive nature prevents its use in this industry. Being unreactive, helium is now used to give buoyancy to objects such as balloons, blimps, and zeppelins. Work In Pairs PROCEDURE 1. The apparatus will be assembled prior to lab. Make sure the apparatus is airtight by filling the right soda bottle with water up to the ring clamp, clamping the tubing on the left, raising the beaker on the lab jack so that its water level is higher than the water level in the right soda bottle. If the water level in the right soda bottle does not rise within 30 seconds, the system is air-tight. Air-filled Clamp Water Level 2. Note that small segments of rubber tubing (~0.15 cm) have been cut and placed on the glass tubing prior to attaching longer segments of tubing. This small piece of tubing is then rolled over the outside of the larger tubing to ensure an airtight connection. 3. Obtain a 5 ml disposable pipette that has been filled with water and heat-sealed at the tip. Remove the 2-hole stopper from the Erlenmeyer flask and insert one of the pipettes snugly into the stopper. Push the pipette in firmly to avoid gas leaks! Experiment 11 11-4
4. Place ~ 3.5 g NaHCO 3 and ~ 3 g citric acid in the Erlenmeyer flask (these weights are not recorded but must be 0.1 g). Weigh the flask, stopper, NaHCO 3, citric acid, pipette containing the water and the bent tubing [Data Sheet Q1]. 5. Fill the collection beaker ¼ full with water (or remove water until is it ¼ full) and adjust the height of the collection beaker so that water in it is at the same level as the water in the soda bottle. 6. Create a siphon by removing the air in the tubing between the right soda bottle and the collection beaker. To do this, pinch the tubing between the two soda bottles between the fingers of your left hand and gently squeeze the middle of the right soda bottle with your right hand. Squeeze slowly and continuously until no more air bubbles exit from the tube in the collection beaker only water is exiting the tube. 7. Release the pressure on the soda bottle and remove any dents in the soda bottle. 8. Finally, release the tube in your left hand. 9. If the 2-L soda bottle containing the water is not filled with water up to the level of the ring clamp, fill the collection beaker with water and raise it with the lab jack. 10. Once the water level in the 2-L soda bottle is even with the ring clamp, lower the collection beaker so that its water level equals the water level in the soda bottle. 11. At the Erlenmeyer flask, attach the rubber tubing leading to the first soda bottle and make certain the connection is airtight by rolling the segment of rubber tubing over the longer section of rubber tubing. 12. Cut the very tip of the pipette with a pair of scissors and allow this piece of plastic to fall into the Erlenmeyer flask. 13. Snugly replace the rubber stopper. Do Not Add Any of the Water Yet!! 14. Use hemostats to clamp the very end of the rubber tubing in the collection beaker - you can use your fingers to pinch it closed and then clamp it with the hemostats. 15. Empty the water in the collection beaker and dry the beaker with a paper towel before placing the tubing back into the beaker. Your Air Water Level No Water Clamp lab setup should look like the picture to the right. NaHCO3 + Citric Acid Experiment 11 11-5
Start the Experiment... 16. Remove the clamp and place the rubber tubing into the collection beaker it s ok if some water from the tubing collects in the beaker. 17. Squeeze the bulb of the disposable pipette to drip a few drops water onto the baking soda / citric acid. Proceed slowly to ensure that only CO 2 gas (no foam or liquid) exits the Erlenmeyer flask and enters the first soda bottle. 18. Continue adding water dropwise until no more CO 2 is generated from the reaction in the flask (~ 10 15 minutes). The solution in the Erlenmeyer flask will stop bubbling and become clear. You can speed up the reaction by increasing the temperature - hold the flask in your hand. 19. As water is pushed into the collection beaker, adjust the height of this beaker so that its water level is the same as the water level in the water-filled soda bottle. 20. With the two water levels equal, let the experiment sit for 5 minutes after the reaction has ceased to allow the system to return to room temperature. Adjust the water levels during this time as needed to keep them equal. 21. Place a thermometer in the water in the collection beaker during this 5 minute period record the temperature (ºC) of the water / CO 2 gas to the nearest 0.2 ºC [Data Sheet Q2]. 22. Convert the Celsius temperature to the absolute temperature (use 273.2 in your conversion) [Online Report Sheet Q3]. 23. Record the barometric pressure in Pascals [Data Sheet Q4] your instructor may give this to you or you can find it at http://www.wunderground.com or at another website. 24. Convert Pascals to atmospheres (atm) [Online Report Sheet Q5]. 25. Round the temperature in Data Sheet Q2 to the nearest whole number and report the vapor pressure of water at that temperature using Table 2 [Online Report Sheet Q6]. 26. Determine the pressure of the CO 2 gas by subtracting the vapor pressure of water from the barometric pressure [Online Report Sheet Q7]. 27. Pinch the end of the tube in the collection beaker and clamp it at the end. Determine the mass of the water in the collection beaker [Data Sheet Q8] you will need to tare a Styrofoam cup, add 250 290 g water, and record exactly this mass. Pour the water into the sink, re-tare the balance, and add Temperature ( C) Vapor Pressure (mm Hg) 18 15.5 19 16.5 20 17.5 21 18.6 22 19.8 23 21.1 24 22.4 25 23.8 26 25.2 27 26.7 28 28.4 29 30.0 Table 2 Experiment 11 11-6
another 250 290 g of water to the Styrofoam cup. Continue until you have weighed all the water. Sum these masses of water to determine the total mass of water collected. 28. Round the temperature in Data Sheet Q2 to the nearest whole number and report the density of water at that temperature using Table 3 [Online Report Sheet Q9]. 29. 30. Determine the volume (in ml) of water displaced [Online Report Sheet Q10]. Temperature ( C) Density (g/ml) 18 0.9986 19 0.9984 20 0.9982 21 0.9980 22 0.9978 23 0.9975 24 0.9972 31. Determine the volume (in L) of CO 2 formed [Online Report Sheet Q11]. 32. Remove the rubber stopper from the Erlenmeyer flask and blow air into the flask for 5 seconds to remove any CO 2 gas this is critical to obtain an accurate mass of CO 2, since CO 2 weighs more than air. The first mass of the flask [Data Sheet Q1] was done with air in the flask this second weighing must also be done with air in the flask. Once the CO 2 is replaced with air, weigh the flask, stopper, product mixture, bent tubing, and pipette [Data Sheet Q12]. 33. Calculate the mass of CO 2 generated in the reaction [Online Report Sheet Q13]. 34. Calculate the moles of CO 2 generated in the reaction [Online Report Sheet Q14]. 35. Calculate the value of R using the ideal gas equation [Online Report Sheet Q15]. 36. Calculate the value of R using van der Waals equation [Online Report Sheet Q16]. 37. Repeat the experiment. Make sure the water level in the right soda bottle is even with the ring clamp before starting Step 1. 25 0.9970 26 0.9968 27 0.9965 28 0.9962 29 0.9959 Table 3 Waste Disposal: The sodium bicarbonate / citric acid solution can be flushed down the sink with plenty of water. Online Lab Report @ chem21labs.com Experiment 11 11-7
Laboratory 11 Student Data Sheet Trial 1 Trial 2 1. Mass of flask / Citric acid / NaHCO 3 / stopper / tubing / pipette g g 2. Temperature of water / CO 2 gas C C 4. Barometric Pressure Pa 6. Vapor Pressure H2O at Temperature in Q2 (look up value in Table 2) mmhg mm Hg 8. Mass of water displaced by the CO 2 gas g g 9. Density H2O at Temperature in Q2 (look up value in Table 3) g/ml g/ml 12. Mass of flask / stopper / tubing / pipette without CO 2 g g Laboratory 11 Instructor Data Sheet Name: Partner: Trial 1 Trial 2 1. Mass of flask / Citric acid / NaHCO 3 / stopper / tubing / pipette g g 2. Temperature of water / CO 2 gas C C 4. Barometric Pressure Pa 6. Vapor Pressure H2O at Temperature in Q2 (look up value in Table 2) mmhg mm Hg 8. Mass of water displaced by the CO 2 gas g g 9. Density H2O at Temperature in Q2 (look up value in Table 3) g/ml g/ml 12. Mass of flask / stopper / tubing / pipette without CO 2 g g Experiment 11 11-8