#### Introduction

Atoms and molecules are incredible tiny and weigh hardly anything, so scientists usually count them in terms of moles, which is 6.022140857 x 1023 particles. Why? For the same reason that we measure distance in terms of miles and donuts in terms of dozens: when you are counting to big numbers, it is easier to use big units. When eating donuts, it makes more sense to count in dozens than attempt to count individual donuts, and it is simpler to tell someone that you live 5 miles down the road than 26,400 feet.

Avogadro’s number is named to honor Amedeo Avogadro who pioneered some of the molecular theory that led to the discovery of Avogadro’s number. In this lab, you will estimate the number of molecules in a monolayer of stearic acid in order to calculate Avogadro’s number.

#### Background

To estimate Avogadro’s number, you must count the number of molecules. Most of the time, chemists simply use the mass to count molecules because molar mass relates mass and number of molecules:

mass of carbon (g) / molar mass of carbon (g/mole) = number of moles of carbon

number of moles of carbon (moles) x 6.022 x 1023 atoms per mole (atoms/mole) = number of atoms of carbon

However, this approach assumes you know Avogadro’s number, so we have to get a little more creative.

When measuring lots of little things, it helps to have a lot of them piled up.

Remember that molecules are physical things that take up space. One molecule is a very little thing that takes up just a little space (microscopic), but if you have a lot of them all lined up, they take up enough space for you to measure (macroscopic). When the dimensions of the stearic acid molecule are known, we can effectively count stearic acid molecules by measuring a volume of stearic acid.

Stearic acid is a non-polar hydrocarbon chain that has a polar carboxylic acid end. When you add it to water, each molecule aligns with the polar end pointing towards the water and the non-polar portion pointing up, and the molecules form a monolayer on top of the water. You can picture each molecule like a tall, skinny rectangle with dimensions 1:5.44, and the monolayer can be approximated as a cylinder. By measuring the volume and surface area of the stearic acid layer, you will be able to calculate the dimensions of the individual molecules via geometry, which is all you need to calculate the volume of the individual molecule. Comparing the volume of the monolayer to the volume of an individual molecule gives you the number of molecules in the monolayer. Since the monolayer has a known mass, and stearic acid has a known molar mass, you can calculate Avogadro’s number. Step-by-step instructions for completing the calculations are on the worksheet.

#### Procedure

Note: this should all take place in a hood to protect you from fumes.

##### Calibration of a pipet

I. Wash a 10 mL beaker (or the smallest beaker you have).

1. Wash with soap and water.
2. Rinse with ~1 mL of ammonia solution three times. Put the rinsate in the ammonia waste container.
3. Rinse with DIH2O three times.
4. Rinse with ~1 mL of acetone. Put the rinsate in the acetone waste container. Wait for the beaker to dry (a minute or two).
5. Rinse the beaker with ~1/2 mL of hexane [CAUTION!] three times. Put the rinsate in the hexane waste container.

II. Wash a 10 mL graduated cylinder.

1. Wash with soap and water.
2. Rinse with ~1 mL of acetone. Wait for it to dry.

III. Calibrate the pipet

1. Put approximately 3 mL of hexane into the clean beaker.
2. Use the pipet and the hexane in the beaker to fill the graduated cylinder up to exactly 1.0 mL. Count the number of drops it takes to fill it to 1 mL. Record the number of drops. Tips to ensure consistent drop size:
• Have one designated dropper. Preferably whoever has steadier hands.
• Be sure to hold the pipet straight up and down.
• Make sure no drops stick to the side of the graduated cylinder.
• Don’t let the dropper touch the sides of the cylinder.
• Work slowly and be patient.
3. Pour the hexane out of the graduated cylinder and into the hexane waste container. Wait for the graduated cylinder to dry. Blowing nitrogen on the glassware will help it dry faster.
4. Repeat the calibration procedure again. Record the number of drops in 1 mL.
5. Repeat again if the first two calibration measurements are not within 10% of one another (example: 20 and 22 drops would be acceptable, but 20 and 25 drops would warrant another calibration).
##### Make a stearic acid monolayer

I. Prepare a large watch glass

1. Measure and record the diameter of the watch glass with your ruler.
2. Wash the watch glass with soap and water.
3. Rinse with ammonia solution. Put rinsate in the ammonia waste container.
4. Rinse thoroughly with DIH2O. Wait for it to dry.
5. Once clean, be sure to avoid getting fingerprints on it. Handle wearing gloves, and hold it on the edges.
6. Place the watch glass on a 400 mL beaker, which will simply hold it steady for you. Make sure the watch glass is parallel to the bench top.

II. Form the monolayer

1. Using your wash bottle, fill the watch glass to the brim with DIH2O.
2. Pour about 3 mL of the stearic acid solution into the clean 10 mL beaker.
3. Fill the pipet with the stearic acid solution. Holding it straight up and down, add one drop of stearic acid solution to the water-filled watch glass. If the watch glass is sufficiently clean, the drop should disappear quickly.
4. Add the stearic acid solution drop wise until the last drop, which will remain a lens and not disappear. Record the number of drops you used. You will know you are close when you see a circular pattern forming. If you see a second lens forming, you added too much stearic acid and no longer have a monolayer.