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 and compare the experimental length to a value estimated from the known structure.

References:

 Chemistry, 4th ed, by J. McMurry and R. Fay. Prentice Hall, 2004, Sections 7.9, 10.2, 23.1-4,14

Introduction

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

The molecule contains a long hydrocarbon-like chain bonded to a carboxyl group. The three-dimensional arrangement of the atoms is better 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, and so has little affinity for polar water molecules, and a low solubility in water. The carboxyl group is polar, is attracted to water molecules and has a strong tendency to dissolve in water. A shorthand representation of stearic acid is:

The Stearic Acid Molecule  - Shorthand View

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 as the nonpolar ends are attracted to each other but are uncomfortable in the water.. If the amount of the stearic acid added is just sufficient to cover the water's surface it forms a layer which is just one molecule thick.  This 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 with a known concentration is added to water to just cover the surface.  Once the solution is added the hexane solvent evaporates leaving a film of pure stearic acid on the water surface as a monolayer.

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, dsa = 0.85 g/mL( or g/cm3), then the volume of the film, Vfilm, in cm3, is

Vfilm = m/ dsa

The volume of the film, in cm3,  is also given by the product of the film thickness, t, in cm (the molecular length), and its area, A, in cm2:

Vfilm = tA

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

molecular length = t = m/(A dsa)

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 from the expression;

 number of molecules in the film = N = mNA / (MMsa)

where NA is Avogadro's number( 6.022x1023atoms/mole) and MMsa is the molar mass of stearic acid (grams/mole)..

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:  

Glass Petri dishes that are soaking in a tub of methanolic NaOH, in one of the hoods.  
A glass pipet drawn to a fine capillary tip (you'll do this). 
Hexane 
A solution of stearic acid in hexane containing 0.12 to 0.15 g/L. Record the actual value from the label in your notebook. Please do not waste this solution. Take only 5ml from the stock bottle and keep it covered to prevent evaporation.

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 pure hexane. Add a small amount of the hexane to a 10-mL graduated cylinder, read and record the volume paying special attention the the significant figures in your value..  While holding your  pipet vertically, count the number of drops needed  to equal a volume of about 1 mL. Carefully read and record the final volume. Between 100 and 150 drops should be required. If fewer than 100 drops are needed, ask your instructor for help in preparing another pipet. Calculate and record the number of drops per mL.  Repeat the calibration until successive trials agree to within 4 to 5 drops/mL. The size of the drops will be affected by the angle from the vertical at which your pipet is held so keep your pipet as vertical as possible when adding drops.

Preparing the Petri dish:  

For this part, wear disposable gloves for safety.  Obtain a Petri dish  which has been treated as described in the "Special Supplies" section above. Wash it with lab detergent.  Rinse the detergent off completely under a full stream of cold tap water for at least one minute and then rinse it with distilled water. Once the Petri dish 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 and forming a film.  Measure and record the outer diameter of the dish by making several measurements of the maximum outer diameter.

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

Add water to the Petri dish until it is filled to the brim and the water level is visible just above the glass edge.  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 needed to form the monolayer.

Rinse the Petri dish with tap and deionized water, as before, and repeat the measurement. Successive trials should agree to within 3 or 4 drops.  Base your calculations below on the values of your consistent measurements.  When you are completely finished collecting data, rinse your Petri dish again with deionized water and place  it back in the tub of methanolic NaOH for the next class. Thank you.

Use the following table to guide your data collection, but make your own table using Excel.

Data Table

 

Trial 1

Trial 2

Trial 3

 etc.

Average.

Calibration of pipet

        -
a) drops ( ?)         -
b) volume of hexane  ( ?)  (mL)           -
c) average drop volume ( ?)  (mL/drop)

-

-

-

-

 
           

Molecular Dimensions

         
a) Diameter of water surface ( ?) (cm)

-

-

-

-

 
b) number of drops needed to cover surface ( ?)         -
c) The mass of stearic acid ( ?)  (g)         -
d) The volume of stearic acid in the monolayer ( ?) (cm3)         -
e) The area of the monolayer ( ?) (cm2).         -
f) Thickness of the monolayer ( ?) (cm).         -
g) Length of the molecules ( ?) (pm)         -
h) Number of molecules in film.( ?)         -
i) Cross sectional area of a stearic acid molecule  ( ?) (pm2)         -

 

Average length   ( ?) (pm)  
Average cross-sectional area  ( ?) (pm2)  

 

Clearly show all of the calculations in your notebook  for the entries in your Table

Conclusion

Report your experimental values for the length and cross sectional area of a stearic acid molecule with the relative standard deviations.  Are your significant figures consistent with your absolute standard deviations?  Briefly discuss any discrepancies.

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.  Be sure you show your calculations and pay attention to significant figures.

The following will be useful in making your estimation   In a hydrocarbon in which all of the carbon - carbon bonds are single bonds,  the bond angle is 109.5o and the average C - C bond length is 154 pm. The fully extended molecule has its carbon atoms in a zig-zag arrangement with the geometry shown below.