Avogadro and all that  (Page 3/3)

4. Estimation of Avogadro's number

Briefly, as a group with your TA, you will make an approximate (order of magnitude) estimate of Avogadro's number by determining the amount of stearic acid that it takes to form a single layer (called a monolayer) on the surface of water. By making simple assumptions about the way the stearic acid molecules pack together to form the monolayer, we can determine its thickness, and from that thickness we can estimate the size of a carbon atom. Knowing the size of a carbon atom, we can compute its volume; and if we know the volume occupied by a mole of carbon (in the form of a diamond), we can divide the volume of a mole of carbon by the volume of an atom of carbon to get an estimate of Avogadro's number.

Procedure

Special Supplies: 14 cm watch glass; cm ruler; polyethylene transfer pipets; 1-mL syringes; pure distilled water free of surface active materials; disposable rubber gloves (for cleaning own watch glasses in 0.1 M NaOH in 50:50 methanol/water): 13 $$ 100 mm test tubes with rubber stoppers to fit.

Chemicals: pure hexane, 0.108 g/L stearic acid (purified grade) solution in hexane. 0.1 M NaOH in 50:50 methanol/water used for washing the watch glasses, dye.

SAFETY PRECAUTIONS: Hexane is flammable! There must be no open flames in the laboratory while hexane is being used.

WASTE COLLECTION: At the end of the experiment, unused hexane solvent and stearic acid in hexane solution should be placed in a waste container, marked "Waste hexane/stearic acid solution in hexane."

Measurement of the volume of stearic acid solution required to cover the water surface

Your TA will do this as a group demonstration:

1. Fill the clean watch glass to brim with deionized water. One recommended way to do this is to set up your 25 mL burette on a ring stand.
2. Using a transfer pipette, obtain about 3-4 mL 0.108 g/L stearic acid solution in hexane in a clean, dry 13 $$ 100 mm test tube. Keep the tube corked when not in use.
3. Obtain more distilled water and fill the burette. Place your watch glass directly under the burette (about 1 inch or less from the tip) and dispense the water until the entire watch glass is full. You may have to refill the burette 4 or 5 times to do this. With careful dispensing, the surface tension of the water should allow you to fill the entire watch glass with relative ease.
4. Carefully measure the diameter of the water surface with a centimeter ruler. It should be close to 14 cm, + or - a couple of millimeters. Next, rinse and fill your 1 mL syringe with stearic acid solution, taking care to eliminate bubbles in the solution inside the syringe.
5. Read and record the initial volume of the syringe (1 mL is always a good place to start.)
6. Then add the stearic acid solution drop by drop to the water surface. Initially, the solution will spread across the entire surface, and it will continue to do so until a complete monolayer of stearic acid has been formed. If your first few drops do not spread and evaporate quickly, either your water or watch glass is still dirty. As this point is approached, the spreading will become slower and slower, until finally a drop will not spread out but will instead sit on the surface of the water (looking like a little contact lens). If this "lens" persists for at least 30 s, you can safely conclude that you have added 1 drop more than is required to form a complete monolayer.
7. Now, read and record the final volume reading of the syringe.

When you have completed all of your measurements, rinse your syringe with pure hexane, and dispose of all the hexane-containing solutions in the waste collection bottle provided.

Calculation of Avogadro's Number

The calculation proceeds in several steps.

• We calculate the volume of stearic acid solution in hexane required to deliver enough stearic acid to form a monolayer.
• All of the hexane evaporates, leaving only the thin monolayer film of stearic acid, so we next calculate the actual mass of pure stearic acid in the monolayer.
• We calculate the thickness of the stearic acid monolayer, using the known density of stearic acid and the area of the monolayer.
• Assuming the stearic acid molecules are stacked on end and are tightly packed, and knowing that there are 18 carbon atoms linked together in the stearic acid molecule, calculate the diameter and volume of a carbon atom.
• Calculate the volume of a mole of carbon atoms in diamond; divide the molar volume of carbon (diamond) by the volume of a single carbon atom to obtain an estimate of Avogadro's number. Remember that the units of Avogadro’s number are mol ${}^{-1}$ , so you can use unit analysis to check your answer.