o/avogadro.htm

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1 CH 100 Laboratory Determination of Avogadro s Number Go to the following web sites to see some variations of this experiment: o/avogadro.htm Objectives: 1. To determine Avogadro s number using molecular monolayer techniques 2. To find the number of molecules in a monolayer 3. To find the moles of stearic acid in a monolayer 4. To develop a sensitive technique in preparing a thin film of molecules Avogadro's number, considered one of the few fundamental constants that must be determined independently, is the number of atoms or molecules present in a sample with a mass, expressed in grams, numerically equal to its atomic or molecular mass expressed in amu's or Daltons. It is defined as the number of 12 C atoms in exactly 12 grams of 12 C. NEW SCIENCE Some of the more than twenty different types of experiments used to determine Avogadro's number utilize methods for directly counting the number of molecules present in a sample of a compound with known mass. This is the type of experiment that you will perform. Under appropriately controlled conditions, it is possible to spread a film of a fatty substance only one molecule thick, a monolayer, onto a water surface. The thickness of the monolayer can be calculated from the measured volume of substance required to make the monolayer and the measured area of the surface that is covered.

2 Substances such as stearic acid (C 17 H 35 COOH) are called fatty acids due to their presence in many natural fats. Such molecules include two major fragments: A long hydrocarbon chain and a carboxylic acid group. Stearic Acid, C 17 H 35 COOH CH 3 CH 2 CH 2 CH 2 CH 2 CH 2 CH 2 CH 2 CH 2 CH 2 CH 2 CH 2 CH 2 CH 2 CH 2 CH 2 CH 2 COOH A molecule can be represented by a bond-line drawing where each end or bend in the lines is a carbon atom and hydrogen atoms are not shown but are still present. For example, The polar -COOH acid group is attracted to water molecules where the nonpolar hydrocarbon chain is repelled by water molecules. Stearic acid is not soluble in water so to make a solution, it needs to be dissolved in a different solvent. When a solution of stearic acid in a volatile hydrocarbon solvent is placed on water, the stearic acid spreads out on the surface of the water such that each molecule has its polar COOH group in the water and its nonpolar hydrocarbon chain above the water surface (see Figure 1). The hydrocarbon solvent evaporates quickly, leaving behind a monolayer of stearic acid. Additional aliquots of stearic acid solution will cause the fatty acid molecules to spread and become more compact, adopting a vertical orientation until the entire water surface is covered. This is because each molecule wants to have its polar group in the water and the hydrocarbon chain in the air. The fully compact state of the monolayer is shown schematically in Figure 1.

3 Figure 1 Schematic magnified view of a stearic acid monolayer on a water surface. Only a few of the many molecules are shown for clarity. Subsequent addition of stearic acid solution will cause it to float on top of the existing monolayer forming a lens-shaped droplet that is readily visible. The number of drops of stearic acid solution required to form the monolayer can thus be determined. The mass of stearic acid in the monolayer can be calculated from

4 the measured volume and known concentration of the stearic acid solution. The number of moles of stearic acid in the monolayer is determined using its molar mass. We do not directly know the surface area of the water occupied by each stearic acid molecule. However, we can make guesses based on the molecular geometry of stearic acid. If we assume each stearic acid molecule on the surface has a cubical shape with side length s, it then has a height s and occupies an area s 2. Assuming that there are no spaces between stearic acid molecules in the monolayer, each molecule occupies an area of about 0.21 nm 2. The total number of stearic acid molecules in the monolayer can be determined from s 2 and the measured area of the monolayer. Avogadro s number is obtained by dividing the number of molecules of stearic acid in the monolayer by the number of moles of stearic acid in the layer. In this experiment we will determine an experimental value for Avogadro s number. First, the solution of stearic acid is prepared by dissolving the solid substance in the organic solvent hexane. The solution is then added drop by drop onto the water contained in a watch glass. After each drop is added, the stearic acid molecules spread across the surface of the water forming a single layer, a monolayer. A few seconds after each drop of solution is added, the hexane solvent evaporates and the drop disappears. When enough drops of solution have been added to form a monolayer of stearic acid molecules, one additional drop forms a clear bead or lens.

5 Sample Calculation: The following is a crude but effective way for estimating the order of magnitude of Avogadro s number using stearic acid (C 18 H 36 O 2 ). When stearic acid is added to water, its molecules collect at the surface and form a monolayer; that is, the layer is only one molecule thick. The cross-sectional area of each stearic acid molecule has been measured to be 0.21 nm 2. In one experiment it is found that 1.4 x10-4 g stearic acid is needed to form a monolayer over water in a dish of diameter 20 cm. Based on these measurements, what is Avaogadro s number? The area of a circle of radius r is πr 2.

6 Procedure: A. Calibrating a Dropper Pipet 1. Cut a 15 cm length of 6 mm glass tubing. Heat the tubing and draw it into a fine capillary tip. For best results the dropper calibration exceed 50 drops/ml. 2. Obtain about 3 ml of stearic acid solution in a dry test tube. Calibrate the dropper pipet by adding drops of stearic acid solution into a 10-mL graduated cylinder. Hold the dropper at a 45 o angle, and deliver the drops at a rate of one per second. Record the number of drops to reach the 1 ml mark. 3. Repeat the dropwise calibration procedure twice and find the average for the three trials. B. Calculating Molecules in the Monolayer 1. Measure the diameter of a large watch glass to 0.1 cm. Record the diameter, and calculate the surface area of the monolayer, that is, the surface area of the watchglass. Note: The diameter of a stearic acid monolayer corresponds to the surface area of the watch glass filled with water. 2. Calculate the number of molecules that can occupy a monolayer assuming the area of a stearic acid molecule is 0.21 nm 2. C. Determining Avogadro s number 1. Clean the watchglass carefully with soap and water. Rinse the watchglass thoroughly with distilled water, and do not touch the inside concave surface. 2. Place the convex side of the watchglass on a paper towel on the lab bench. Fill the watch glass completely with distilled water from a wash bottle. 3. Record the concentration of the stearic acid solution. Hold the dropper pipet at a 45 o angle, and slowly deliver drops of solution onto the center of the water surface. Note: A small, persistent, clear lens indicates a monolayer of molecules has formed across the entire surface of the water. 4. In your Data Table, record the number of drops required to form the monolayer. Determine the volume of these drop in ml.

7 5. Using the concentration and molar mass (284 g/mol) of stearic acid, calculate the moles of stearic acid in the monolayer, and determine the experimental value of Avogadro s number. 6. Thoroughly clean and rinse the watchglass and perform a second trial. 7. Thoroughly clean and rinse the watchglass and perform a third trial. Prelaboratory Assignment 1. In your own words, define the following terms: Avogadro s number (N) Molar Mass (MM) Mole (mol) Monolayer Surface area 2. A calibrated pipet (95 drops/ml) delivers 12 drops of stearic acid solution (1.5 x 10-4 g/ml) to give a monolayer with a diameter of 12.5 cm. Calculate the surface area of the monolayer, the number of stearic acid molecules in the monolayer (assuming a molecule occupies 0.21 nm2), the moles of stearic acid (284 g/mol) in the monolayer, and the experimental value for Avogadro s number. 3. What are the sources of error in the experiment? Postlaboratory Assignment 1. Calculate the mass of carbon in a 1 carat diamond that contains 1.00 x atoms of carbon. 2. Calculate the mass of chloroform that contains 1,000,000,000,000 molecules of CHCl What is the mass of one molecule of stearic acid, C 17 H 35 COOH, expressed in grams?

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