The Dimensions of a Molecule

Purpose

The purpose of this experiment is to determine the length and cross sectional area of a molecule of stearic acid.

Introduction

Stearic acid has the molecular formula, C₁₈H₃₆O₂. Its structure is shown below:

The molecule contains a long hydrocarbon-like chain bonded to a carboxyl group. The three-dimensional arrangement of the atoms is shown by the ball and stick model:

Ball and stick model of stearic acid

An alternative, more realistic, depiction of the structure is the space filling model below:

A space filling model of stearic acid

The hydrocarbon-like chain is nonpolar, has a small attraction for water, and has a low tendency to dissolve in water. The carboxyl group is polar, is attracted to water molecules and has a strong tendency to dissolve in water. A short-hand representation of stearic acid is:

The stearic acid molecule

When stearic acid is added to water its molecules tend to accumulate on the surface of the water with the carboxyl group dissolved in water and the hydrocarbon end pointing away from the surface. If the amount of acid added is just sufficient to cover the water's surface it forms a layer which is just one molecule thick, and is referred to as a "monolayer". In the monolayer the molecules are arranged as shown in the figure below:

A magnified view of a stearic acid monolayer

The thickness of the monolayer is equal to the length of the stearic acid molecule.

Method In this experiment, a solution of stearic acid in hexane of known concentration will be added to water surface of known area. the amount added will be just enough to form a monolayer. Once the solution is added the hexane solvent evaporates leaving a film of pure stearic acid on the water surface.

If V is the volume, in mL (or cm³), of the stearic acid-hexane solution needed to form a monolayer, and c is its concentration in g/cm³, then the mass of stearic acid in grams, m, in the monolayer is:

m = cV

If we assume that the density of the stearic acid in the film is the same as that of bulk stearic acid, d_sa = 0.85 g/mL( or g/cm³), then the volume of the film, V_film, in cm³, is

V_film = m/ d_sa

The volume of the film is also given by the product of the film thickness, t, in cm( which is also the molecular length), and its area, A, in cm²:

V_film = tA

Equating the two expression for the film volume and solving for t gives:

molecular length = t = m/(A d_sa)

The cross sectional area of a stearic acid molecule is obtained from the total area of the film and the number of molecules in the film.

The number of molcules in the film = N = mN_A / (MM_sa)

where N_A is Avogadro's number( 6.022x10²³) and MM_sa is the molar mass of stearic acid.

The cross sectional area of a molecule is equal to the total film area, A, in cm², divided by the number of molecules in the film:

molecular cross sectional area in cm² = A/ N

Procedure

Special supplies:  

• 14 cm watch glasses will be soaking in a tub of methanolic NaOH in one of the hoods. They have been there overnight or at least two hours. When you are done with them, rinse them with deionized water and put them back in the tub for the next class. 
• A glass pipet drawn to a fine capillary tip ( see instructions below). 
• Hexane 
• A solution of stearic acid in hexane containing 0.12 to 0.15 g/L stearic acid. Write down the actual value. Do not waste this. Take only 5ml from the stock bottle.

Preparation and calibration of the pipet: The stearic acid-hexane solution will be added to the water with a calibrated pipet. Your instructor will demonstrate how to pull the tip of a disposable pipet to a fine point. After your pipet has cooled(CAUTION, a hot pipet looks the same as a cool one!) calibrate it with hexane. While holding the pipet vertically, count the number of drops that must be expressed into a 10 -mL graduated cylinder to equal one mL. Do this by filling the cylinder to a milliliter mark and then counting the drops needed to reach the next milliliter mark. Between 100 and 150 drops should be required. If fewer than 100 drops are needed, ask your instructor for help in preparing another pipet. Repeat the calibration until successive trials agree to within 4 to 5 drops. The size of the drops will be affected by the angle from the vertical at which your pipet is held. Keep your pipet as vertical as possible when it is being used.

Preparing the watch glass: Obtain a 14 cm watch glass which has been treated as described in the "Special Supplies" section above. Wash it with detergent; NOT SOAP. Any trace of soap will form a film on the water surface and prevent the stearic acid film from spreading. Rinse the detergent off completely under a full stream of cold tap water for 1 minute, and then rinse with distilled water. Once the watch glass has been given its final rinse it must be handled only by its edges. Any grease or dirt from your hands will contaminate the surface and prevent the stearic acid film from spreading.

Measurement of the volume of stearic acid solution needed to cover the water surface:

Support the watch glass firmly in a horizontal position on an iron ring attached to a ring stand, and add water to it until it is filled to the brim. Measure as precisely as possible, the diameter of the water surface. Quickly rinse your calibrated pipet several times with the stearic acid-hexane solution. The rinsing must be done quickly to avoid the evaporation of hexane and a subsequent increase in the solution's concentration. Be careful to keep the solution from contacting the rubber pipet bulb, as this may dissolve some of the rubber and ruin the experiment.

Add the stearic acid-hexane solution to the water surface drop by drop with your calibrated pipet. Count the drops and remember to keep the pipet vertical. Wait 5 to 10 seconds between drops. Initially, you will notice that the solution will spread rapidly over the surface. As more solution is added the rate of spreading will decrease. Finally when the surface is covered with a monolayer an added drop will not spread but remain on the surface as a small lens. When the lens persists for about 20 seconds, you can assume that you have added one more drop than is necessary to form a monolayer. Record the number of drops added in your notebook.

Thoroughly clean the watch glass, as before, and repeat the measurement. Successive trials should agree to within 3 or 4 drops. Additional trials should be performed as time allows to achieve the required precision. Base your calculations on the average of your consistent values.

Use the following table to guide your data collection.

Data Table

Calculations

Clearly show all of the calculations below for each trial

h) The average length of a stearic acid molecule (cm) .

i) The average cross sectional area of a stearic acid molecule (cm²) .

Compare your data with the calculated value:

Assuming that the length of a stearic acid molecule is approximately the same as that of a hydrocarbon molecule containing 18 carbon atoms, estimate the length of the stearic acid molecule, and compare the result to your experimental value.  What is the % error of your value from the calculated value?

Hint: In a hydrocarbon in which all of the carbon - carbon bonds are single bonds, the hybridization on each carbon atom is sp³, the bond angle is 109.5^o and the averageC - C bond length is 154 pm. The fully extended molecule has its carbon atoms in a zig-zag arrangement:

Thus, there are 8.5 "triangles for each stearic acid molecule.  The length of each triangle calculated by

sin 54.5 = x/154 

where 2x = length of the triangle

8.5 *2*x = length of the stearic acid molecule

Clearly show your calculations.

Conclusion

Report your experimental values for the length and cross sectional area of a stearic acid molecule.  Compare your experimental value for the length of stearic acid with the calculated value.  Clearly describe the sources of error in this experiment.