Approximating Avogadro s Number Using Glass Beads and Monomolecular Film

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1 S T O I 496 modular laboratory program in chemistry program editor: Conrad L. Stanitski Approximating Avogadro s Number Using Glass Beads and Monomolecular Film prepared by Don McMasters, Indiana University, and M. L. Gillette, Indiana University Kokomo Purpose of the Experiment Approximate Avogadro s number, using glass beads. Approximate the size of an oleic acid molecule, using several simple measurements. Approximate the number of oleic acid molecules in one mole of oleic acid. Background Information One Mole = Avogadro s Number of Items Baked potatoes are usually served one at a time, and green beans are normally served in quantities of ten or more. A serving of rice contains a greater number of grains than the items in a serving of potatoes or green beans. Thus, the number of items in a serving usually depends upon the size of the individual items. Of course atoms and molecules are much, much smaller than rice grains. Therefore, in order to deal with atoms or molecules in measurable servings, we must consider a very large number of them. This is why chemists count atoms or molecules in groupings related to , the number of items in one mole. We call this number Avogadro s number. If we make some simple assumptions about the characteristics and behavior of carefully chosen items, we can use these items to experimentally approximate Avogadro s number. In this experiment, you will first work with glass beads, individual items we can see. Then, you will modify the procedure to work with oleic acid molecules, individual items too small to be seen. In each procedure, you will create a monolayer, a layer that is one bead or one molecule thick. You will estimate the dimensions and mass of this layer. Based on these data, along with the given molar mass of the beads or molecules, you will estimate the number of beads or molecules in one mole of the substance. Because Avogadro s number is a counting number, the number of beads in one mole of beads equals the number of molecules in one mole of molecules. Approximating Avogadro s Number Using Glass Beads If we use a Petri dish with a known interior diameter and mass, and put in just enough glass beads to cover the bottom of the dish, we will have created a monolayer of beads. We can determine the mass of beads, using Equation 1. Copyright 1997 by Chemical Education Resources, Inc., P.O. Box 357, 220 S. Railroad, Palmyra, Pennsylvania No part of this laboratory program may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Printed in the United States of America

2 2 STOI 496/Approximating Avogadro s Number Using Glass Beads and Monomolecular Film mass of beads, g mass of dish = plus beads, g mass of (Eq. 1) dish, g We can determine the volume of the beads by adding 25.0 ml of water into a 50-mL graduated cylinder, adding the beads, and reading the new water level. The difference between the original and the new water levels is the volume of the beads, as shown by Equation 2. using Equation 5. We can calculate the height of a cylinder using Equation 7. height of a cylinder, cm volume of cylinder, cm3 = area of cylinder base, cm 2 (Eq. 7) volume of beads, ml = volume of water volume of plus beads, ml water, ml (Eq. 2) We can relate the bead volume to water volume because, at room temperature, 1 ml of water is equivalent to 1 cm 3 of water. From the mass and volume of the beads in cm 3, we can determine the density of the beads, using Equation 3. density, g / cm3 mass, g = (Eq. 3) 3 volume, cm We can determine the area of the bead monolayer in the Petri dish using Equation 4, the equation for the area (A) of a circle, where r is the radius of the circle, and π is approximated at A, cm 2 = πr 2 (Eq. 4) The radius of a circle is equal to half the diameter (d), so we can substitute d/2 for r in Equation 4, giving us Equation 5. A, cm 2 = π(d/2) 2 (Eq. 5) Because the beads are spherical, there are empty spaces in our bead monolayer. Thus, some of the area calculated using Equation 5 is unoccupied space. For purposes of this experiment, we will assume that only 90% of the monolayer area is occupied by the beads. Using this assumption, we can calculate the area occupied by the beads by substituting the area (from Equation 5) into Equation 6. monolayer area occupied = (0.90)(A, cm 2 ) (Eq. 6) by beads, cm 2 In order to determine the height of our bead monolayer, we can begin by thinking of the approximate overall volume occupied by the monolayer as being cylindrical (see Figure 1). The area of the cylinder base equals the overall area of the monolayer calculated Figure 1 The dimensions of a monolayer of glass beads in a Petri dish The height of the cylinder corresponds to the height (or diameter) of a single bead. Thus, we can determine the diameter of a single bead by dividing the total volume of the beads (Equation 2) by the area actually occupied by the beads (Equation 6), using Equation 8. diameter of one bead, cm 3 volume of beads, cm = area occupied by beads, cm 2 (Eq. 8) Once we know the diameter of a single bead, we can compute its volume using Equation 9, the equation for the volume of a sphere. volume of one bead, cm 3 = (4/3)πr 3 = (4/3)π(d/2) 3 (Eq. 9) If we know the mass of one mole of beads, then we can determine the number of beads in one mole of beads, using Equation 10. number of beads per mole molar mass of beads, g / mol = volume of one density of 3 bead, cm beads, g/cm 3 (Eq. 10) The accuracy of your determination will be limited by the accuracy of your measurements and the validity of the assumptions we have made. For example, we can see that the beads are spherical, but have assumed that the beads occupy exactly 90% of the area of the layer. In Part II, in contrast, you will work with molecules so small that we must theorize about their shapes.

3 STOI 496/Approximating Avogadro s Number Using Glass Beads and Monomolecular Film 3 Figure 2 The structure of the oleic acid molecule Approximating Avogadro s Number Using Oleic Acid Molecules The chemical system we use is oleic acid, C 18 H 34 O 2,a long-chain organic acid, dissolved in 95% ethyl alcohol (see Figure 2). If we add a drop of oleic acid ethyl alcohol solution to water, only oleic acid molecules will remain on the water surface, because the ethyl alcohol will evaporate or dissolve in the water. The oleic acid molecule has a nonpolar hydrocarbon portion that is not water soluble, and a water-soluble polar end. Therefore, the molecules will orient themselves in a nearly vertical position, with the polar portion in the water, as shown in Figure 3. The molecules will spread out on the water surface to form the thinnest possible layer, a monolayer. Although glass beads are not mutually attracted, the hydrocarbon portions of oleic acid molecules are attracted to each other. This causes the oleic acid monolayer to occupy the smallest possible area, a circle. Any impurities, such as skin oil, will interfere with the attraction between the oleic acid molecules. In such cases, the oleic acid monolayer will have an irregular shape and contain empty spaces. The diameter of an oleic acid layer is more difficult to measure than that of the glass bead layer, because the acid molecules are not visible on the water. To make the boundary of the acid layer visible, we lightly dust the water surface with lycopodium powder before adding the drop of acid solution. The spreading acid layer pushes away the powder, and the edge of the powder defines the circumference of the acid layer. If too much powder is used, the acid molecules will not be able to spread out in a monolayer, due to excessive resistance from the powder. To determine the volume of oleic acid in one drop of the 0.50% oleic acid solution, we must first determine the average number of drops contained in 1.0 ml of the solution. From this information, we can determine the volume of one drop of solution, using Equation 11. volume of 1.0 ml 1dropofoleic = average number of drops acid solution, ml in 1 ml of oleic acid solution (Eq. 11) Only 0.50% of the volume of one drop of oleic acid solution is oleic acid. Therefore, we can calculate the volume of oleic acid in one drop of solution in cm 3, using Equation 12. Figure 3 The interaction of oleic acid molecules with water

4 4 STOI 496/Approximating Avogadro s Number Using Glass Beads and Monomolecular Film volume of oleic acid per drop of solution, cm 3 = volume of ml oleic acid 1cm3 1dropof solution, ml 1mLofsolution 1mL (Eq. 12) Following the procedure used with the glass beads, we can determine the height of the oleic acid film, using Equations 5 and 7. Because we cannot see individual oleic acid molecules, we must make an assumption about their shape, based upon our best understanding of their molecular behavior. This behavior leads us to assume that the molecules in the monolayer are cubic. Because cubes pack with almost 100% efficiency, we do not need to allow for empty space in the monolayer, as we did for the glass beads. We calculate the volume of a cube by multiplying length times height times width. Because all three dimensions are the same in a cube, we can find the volume of an oleic acid molecule by cubing the height of the oleic acid film, as shown in Equation 13. volume of oleic acid 3 molecule, cm 3 height of = oleic acid film, cm (Eq. 13) Using the calculated volume of one oleic acid molecule, the molar mass of oleic acid ( g/mol), and its density (0.895 g/cm 3 ), we can calculate Avogadro s number of oleic acid molecules, using Equation 14, comparable to Equation 10. percent disagreement, % = log log (theoretical result) (experimental result) log (theoretical result) ( 100%) (Eq. 15) If your calculation of Avogadro s number is within one power of ten of the theoretical value, consider your result acceptable. Preview Procedure Measure interior diameter, and determine mass, of Petri dish Cover bottom of dish with monolayer of glass beads, and determine mass of filled dish Add beads to known volume of water, and determine volume of beads plus water Determine number of drops of oleic acid solution in 1mL Prepare tray by filling with water and dusting with lycopodium powder Measure the diameter of monolayer formed by one drop of oleic acid solution on water in tray number of oleic acid = molecules per mole molar mass of oleic acid, g/mol volume of density of 1 oleic acid oleic acid, molecule, cm 3 g/cm 3 (Eq. 14) Chemical Alert lycopodium powder flammable 0.50% oleic acid in 95% ethyl alcohol solution flammable, toxic, and irritant To evaluate the accuracy of your calculations, you would usually compare your result with the accepted value and determine percent error. However, because the number you will be determining is so large, and because you will be making several assumptions as part of the calculations, you will use a different method for evaluating your results. You will, instead, determine the percent disagreement between your results and the theoretical value of Avogadro s number ( ) by comparing the logarithms of these numbers, as shown in Equation 15. Caution: Wear departmentally approved safety goggles while doing this experiment. I. Approximating Avogadro s Number Using Glass Beads Note: Obtain from your laboratory instructor the molar mass of the beads you are using. Record this value on Data Sheet 1.

5 STOI 496/Approximating Avogadro s Number Using Glass Beads and Monomolecular Film 5 Obtain a clean, dry Petri dish. Measure the interior diameter of the dish to the nearest 0.1 cm. Record this diameter on Data Sheet 1. Determine the mass of the Petri dish to the nearest 0.01 g. Record this mass on Data Sheet 1. Carefully add just enough clean, dry glass beads to the Petri dish to cover the bottom with a monolayer. Tap the dish lightly to make certain that the beads have settled and that you have added the maximum number of beads that will fit in the monolayer. Using forceps, remove any beads that are not resting on the bottom of the dish. Determine the mass of the dish plus beads to the nearest 0.01 g. Record this value on Data Sheet 1. Put approximately 25 ml of tap water into a 50-mL graduated cylinder. Record the volume of water to the nearest 0.1 ml on Data Sheet 1. Using a powder funnel, carefully transfer all the glass beads from the Petri dish into the 50-mL graduated cylinder. Read the new water level and record this volume on Data Sheet 1. If time permits, do a second and third determination using other clean, dry Petri dishes and new groups of glass beads. Following the directions of your laboratory instructor, return all glass beads to the appropriate containers. Wash your graduated cylinder and Petri dish, rinse, and drain to dry. II. Approximating Avogadro s Number Using Oleic Acid Molecules Note: Be very careful not to damage your micropipet. Any such damage will mean that you must repeat all of Part II with an undamaged micropipet. Your laboratory instructor might give you directions for preparing a micropipet. Caution: Oleic acid in ethyl alcohol solution is a mild skin irritant. Wash your hands with soap or detergent after using the solution. Clean up any spills with soap or detergent. The ethyl alcohol in the oleic acid solution and the lycopodium powder are flammable. Do not use these reagents near an open flame. The ethyl alcohol is toxic, as well. Avoid ingestion of the solution. Obtain a micropipet from your laboratory instructor. Using a clean, dry, glass 10-mL graduated cylinder, measure 5 ml of 0.50% oleic acid solution in 95% ethyl alcohol and pour it into a clean, dry test tube. Pour 3 ml more of the oleic acid solution into the graduated cylinder. Note: Drop size will vary if you hold the micropipet at varying angles. Hold the pipet vertically when counting drops and throughout the remainder of the Procedure. Using the micropipet, carefully transfer, drop by drop, exactly 1.0 ml of oleic acid solution from the test tube to the solution in the graduated cylinder. Count the number of drops in 1.0 ml and record this value on Data Sheet 2. Repeat this step three times, or until you obtain four results that are consistent to within three drops. Record all data on Data Sheet 2. Obtain a large tray from your laboratory instructor. Thoroughly clean the tray with soap or detergent and water. Rinse it well with distilled or deionized water. Fill the tray with distilled water to a depth of at least 1 cm, estimating this depth at the center of the tray. When the water surface is calm, lightly and evenly dust it with just enough lycopodium powder to make a visible layer. Figure 4 vertical pipet 1 2 cm above surface (a) (a) Holding pipet vertically over water in tray, and (b) measuring the diameter of circular oleic acid film (b)

6 6 STOI 496/Approximating Avogadro s Number Using Glass Beads and Monomolecular Film Fill your micropipet with some of the oleic acid solution. Allow a few drops of the solution to drain onto a piece of filter paper or other absorbent paper. This will ensure that the drop used to create the monolayer will not contain air and will be representative of the stock solution. Hold the micropipet vertically, with the tip 1 2 cm above the water at the center of the tray, as shown in Figure 4(a). Allow just one drop of the solution to fall onto the water. Wait 10 s until the powder circle shrinks slightly and its size stabilizes. Being careful not to disturb the water, quickly measure the diameter of the circle formed by the oleic acid. Make four such measurements, all to the nearest 0.1 cm, holding the meter stick in the orientations shown in Figure 4(b). Record these measurements on Data Sheet 2. Discard the contents of the tray into a container labeled Discarded Oleic Acid Solution, provided by your laboratory instructor. Thoroughly clean and rinse the tray. Repeat Part II until you get three consistent results. Caution: Wash your hands thoroughly with soap or detergent before leaving the laboratory. Calculations Do the following calculations, and record the results on the appropriate Data Sheet. I. Approximating Avogadro s Number Using Glass Beads 1. Calculate the mass of the beads in your Petri dish, using Equation Determine the volume of beads, using Equation Determine the density of the beads, using Equation Determine the interior area of the Petri dish, using Equation Calculate the monolayer area occupied by the beads, using Equation Determine the height of one bead, using Equation Determine the volume of one bead, using Equation Calculate the number of beads per mole, Avogadro s number, using Equation Determine the percent disagreement between your answer and the accepted value, using Equation 15. II. Approximating Avogadro s Number Using Oleic Acid Molecules 10. Calculate the average number of oleic acid drops per milliliter. 11. Calculate the average diameter of the oleic acid film for each determination, using all four measurements. 12. Calculate the overall average diameter of the film, using the average diameter for each determination. 13. Calculate the average volume of the oleic acid in the film, using Equation Calculate the average area of the oleic acid film, using Equation Calculate the height of the oleic acid film, using Equation 7. Remember that 1 ml = 1 cm Calculate the volume occupied by one oleic acid molecule in the film, using Equation Calculate the number of oleic acid molecules per mole, Avogadro s number, using Equation Determine the percent disagreement between your answer and the accepted value, using Equation 15.

7 STOI 496/Approximating Avogadro s Number Using Glass Beads and Monomolecular Film 7 Post-Laboratory Questions (Use the spaces provided for the answers and additional paper if necessary.) 1. In this experiment, you used an unusual method for comparing your experimentally determined value for Avogadro s number to the theoretical value. (a) Is your experimental result acceptable, according to the standards of the experiment? Briefly explain. 2. Briefly explain why your experimentally determined value for Avogadro s number would be too large, too small, or unaffected if you made the following procedural errors: (a) In Part I, you lost some beads while transferring them from the Petri dish to the graduated cylinder. (b) Calculate the percent error in your determination using the usual expression, shown in Equation 16. theoretical experimental percent result result = error, % theoretical result ( 100%) (b) In Part II, you left your container of oleic acid solution uncovered and some of the ethyl alcohol evaporated before you performed the experiment. (Eq. 16) (c) Compare your calculated percent disagreement with the percent error you calculated in (b). Briefly explain why calculating percent disagreement rather than percent error gives us a more useful measure of the success of this experiment. (c) In Part II, you asked your laboratory partner to drop the oleic acid solution on the water so that you could measure the circle immediately as it formed. name section date

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9 name section date Data Sheet 1 I. Approximating Avogadro s Number Using Glass Beads determination interior diameter of Petri dish, cm mass of Petri dish + beads, g mass of Petri dish, g mass of beads, g volume of water + beads, ml volume of water, ml volume of beads, ml molar mass of beads, g/mol 3 density of beads, g/cm interior area of Petri dish, cm 2 monolayer area occupied by beads, cm 2 height of one bead, cm volume of one bead, cm 3 Avogadro s number, beads/mol percent disagreement, % STOI 496/Approximating Avogadro s Number Using Glass Beads and Monomolecular Film 9

10 10 STOI 496/Approximating Avogadro s Number Using Glass Beads and Monomolecular Film Data Sheet 2 II. Approximating Avogadro s Number Using Oleic Acid Molecules number of drops of oleic acid solution in 1.0 ml determination number of drops/ml average number of drops/ml diameter of oleic acid film, cm determination measurements, cm first second third fourth average overall average diameter, cm average volume of oleic acid in film, ml average area of oleic acid film, cm 2 height of oleic acid film, cm volume of one oleic acid molecule, cm 3 Avogadro s number, oleic acid molecules/mol percent disagreement, %

11 name section date Pre-Laboratory Assignment 1. Briefly explain why you should wash your hands after you complete this experiment. 3. A student performing Part II of this experiment collected the following data: average number of drops/ml = 73.0; overall average diameter of the oleic acid film = 38.0 cm. Use these data to calculate the following: (a) average volume of oleic acid in film 2. The calculations you will make in this experiment are based on certain assumptions. What do we assume about each of the following? (a) the shape of a glass bead (b) volume of oleic acid per drop of solution (b) film the shape of an oleic acid molecule in the (c) average area of oleic acid film (c) surface the shape of the oleic acid film on the water (d) height of oleic acid film (d) beads the monolayer area actually occupied by the (e) volume of one oleic acid molecule STOI 496/Approximating Avogadro s Number Using Glass Beads and Monomolecular Film 11

12 12 STOI 496/Approximating Avogadro s Number Using Glass Beads and Monomolecular Film (f) Avogadro s number (b) What are the smallest and largest acceptable experimental results you could obtain? (g) percent disagreement 4. According to the standards of this experiment, (a) is the experimental result you calculated in Pre-Laboratory Assignment 3 acceptable? Briefly explain. (c) What are the smallest and largest acceptable percent disagreements you could obtain? ISBN