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Estimating Avogadro’s Number Nathaniel Morales Oct 26, 2023

1 PURPOSE STATEMENT: This experiment aims to find Avogadro's number using stearic acid and understand how molecules behave at the air-water interface. Data Data Table 1 Trial 1 Trial 2 Length of Thread Used Note: Measure after the loop is made. This will be the circumference of the circle. MEASURE TO 0.01cm 17.0 cm 22.0 cm Radius of Loop Circumference = 2π r π = 3.14 r=LENGTH OF STRING/2π d= 5.8 cm r=2.9 cm Circumference=18.2 cm d= 7cm r=3.5 Circumference=21.9 cm Area of Loop Area = π r 2 26.4 cm 38.5 cm Initial Volume of Stearic Acid Solution in Syringe [mL] MEASURED TO 0.1mL 1 mL 1 mL Final Volume of Stearic Acid Solution in Syringe [mL] MEASURED TO 0.1mL 0.59 mL 0.45 mL Volume of Stearic Acid Dispensed [mL] = FINAL - INITIAL 0.41 mL 0.55 mL Concentration of Stearic Acid in Hexane 0.1g/L 0.1g/L Mass of Stearic Acid Mass = concentration × volume/1000mL/L 0.041 g 0.055 g Moles of Stearic Acid Moles = mass / mol weight Mol Weight = 284.5 g / mol 0.000144 mol 0.000193 mol Area of Stearic Acid Area of Stearic Acid = Area of Loop 26.4 cm 38.5 cm Area of One Stearic Acid Given in the lab manual 20.7 × 10 Up -16 cm2 20.7 × 10 Up -16 cm2 Number of Stearic Acid Molecules Area of Stearic Acid / Area of One Stearic Acid Molecule 1.28 x 10 Up -16 1.86 x 10 Up -16 Avogadro’s Number Number of Stearic Acid Molecules / Moles of Stearic Acid 8.89 x 10 Up -13 mol 9.64 x 10 Up -13 mol Lab Questions: © 2016 Carolina Biological Supply Company

2 1. Describe the appearance of the monolayer and the thread, as the first drops of stearic acid were added to the water. When you add stearic acid to water, it forms a thin, shiny layer on the water's surface. As you add more, small clumps or threads of stearic acid can appear on the water, looking a bit thicker and less transparent. This is because stearic acid doesn't mix well with water and tends to form these structures at the surface. Scientists use this to study how molecules behave at the water's surface. 2. Describe the appearance of the monolayer and thread as the last drops of stearic acid were added to the water. When you add the last drops of stearic acid to water, the shiny layer on the water gets thicker and smoother. Any separate clumps or threads you saw before disappear because there's no space left for them. The water looks even and glossy. 3. If some the hexane had evaporated from the stearic acid solution, what effect (if any) would it have on the experimental value of Avogadro’s number? Why? The evaporation of hexane from the stearic acid solution won't affect the value of Avogadro's number. Avogadro's number is a fixed value and doesn't change with alterations in the solution's concentration or solvent. 4. What assumptions are made in the stearic acid experiment to calculate the value of Avogadro’s number? In the stearic acid experiment to find Avogadro's number, we assume ideal behavior, perfect monolayer formation, complete molecule transfer, minimal hexane evaporation, equal molecular areas, negligible interactions, and a smooth water surface for simplified calculations, even though real-world conditions can be more complex. 5. What is the percent error for your experimental determination of Avogadro’s number? Make sure you include the calculation. Trial 1: Calculate the error: © 2016 Carolina Biological Supply Company

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3 Error = Experimental Value - Accepted Value Error = 9.64 x 10^23 - 6.022 x 10^23 Error = 3.618 x 10^23 Now, divide the error by the accepted value: Error / Accepted Value = (3.618 x 10^23) / (6.022 x 10^23) = 0.6 Finally, multiply by 100% to get the percent error: Percent Error = 0.6 * 100% = 60% So, the correct percent error is 60%, not 8.47%. 6. What are three possible sources of error in the stearic acid experiment? Solvent Evaporation: This means that if the liquid used (hexane) starts to disappear or evaporate during the experiment, it can mess up the results because the concentration of the stearic acid changes. Monolayer Imperfections: Imagine trying to make a perfect, even layer of stearic acid on the water, but it's really hard to make it perfectly smooth. Imperfections in this layer can affect the experiment's accuracy. Material Contamination or Loss: If any stearic acid gets dirty or goes missing while you're working with it, it can cause errors in the final results. You want to keep the stearic acid pure and not lose any during the process. Calculations: Radius; d = 7cm r = d/2 r = 7cm/2 © 2016 Carolina Biological Supply Company

4 r = 3.5cm Circumference = 2π rd = 7cm r = 3.5cm π=3.14 2r = 2(3.14)(3.5cm) = 21.98cm =21.9cm Area of LoopArea = π r2 π=3.14 r = 3.5 A = (3.14)(3.5)= 38.47cm =38.5cm 2π=3.14 r = 2.9 A = (3.14)(2.9)2= 26.4074cm =26.4cm The volume of Stearic Acid Dispensed [mL] Starting Volume - Final Volume = volume of dispensed Starting volume = 1mL Final volume = 0.45mL 1mL - 0.45mL =0.55mL Starting volume = 1mL Final volume = 0.59mL 1mL - 0.59mL =0.41mL Mass of Stearic Acid Mass = concentration × volume 0.1 g/mol x 0.55mL = 0.055g0.1 g/mol x 0.41mL = 0.041g Moles of Stearic AcidMoles = mass / mol weight Mol Weight = 284.5 g / mol 0.055g / 284.5 g / mol = 0.00019332mol =0.000193mol 0.041g / 284.5 g / mol = 0.00014411mol =0.000144mol Photos: © 2016 Carolina Biological Supply Company

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10 CONCLUSION: In this experiment, we used stearic acid to figure out Avogadro's number. We saw that when we added stearic acid to water, it formed a thin, shiny layer on the water's surface, and as we added more, it got thicker and smoother. The earlier threads or clumps disappeared. We calculated a 60% error compared to the accepted value for Avogadro's number, which means our result was quite different. We also found possible errors like solvent evaporation, making the layer not perfect, and losing or dirtying the stearic acid. In the end, this experiment taught us about stearic acid behavior and the need to be careful about errors when calculating Avogadro's number. © 2016 Carolina Biological Supply Company

11 REFERENCES: Estimating Avogadro's Number Investigation Manual. (n.d.). https://media.ccconline.org/ccco/CarolinaLabs/CHE101/7_EstimatingAvogadrosNumber_ADA. pdf © 2016 Carolina Biological Supply Company

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