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|published in the SHiPS News, Jan. 1994, reprinted with persmission from teh S3TAR News, published by the Center for Math and Science Education, Colorado State Univ.||
How Small is a Molecule?
Colorado State University
In this article I would like to tell you about some rather fortuitous, if not serendipitous research, in the development of a small-scale science module on this topic of molecular dimension. Last fall semester, Usha Herbert was on sabbatical at Colorado State University learning small-scale techniques. She wanted to work on finding a way to make the mole concept, Avogadro's number and the like, understandable for students. I said "O.K., let's go to the library and find out when, why and how these strange notions and names came to be. I certainly don't know!" In the north basement wing of the CSU library we found two or three books on Avogadro and his number. Quite by accident, I noticed on the next shelf a book entitled, Ben Franklin Stilled the Waves, by Charles Tanford. I have always been intrigued by oil on troubled waters, so I checked it out. This wonderful book is not only well-written and very readable for everyone, but it describes the history and development of ideas and experiments on molecular size and biological membranes.
The book starts with a discussion of the experiments carried out by Ben Franklin on the spreading of oil on water. The following is directly from Franklin's paper:
Franklin's thought then turned (but only briefly) to interpretation:
Now in Chapter 8, Tanford does the calculation that Franklin did not do. Since
and one teaspoon is about 2 ml and one-half acre is about 2000 m2, then we arrive at the incredibly small value of 10-7 cm for the thickness of the spread out layer of oil. Now, 10-7 cm is a ten-millionth of a centimeter! Let us assume that Franklin used olive oil (highly probable) anbd let us say that olive oil molecules are spherical, then by using
together with a value for the density of olive oil (a little less than 1.0 gm/l, we can calculate that an olive oil molecule has a mass between 10-22 and 10-21 gram. Try the calculation for yourself. This mass is so incredibly small that it is almost impossible to think about or visualize. The equally mind-boggling corollary is that a teaspoonful of oil must contain about 6x1023 molecules! This, of course, is now known as Avogadro's number, which was not determined with accuracy until 1913. I think it is quite fascinating that the spreading of olive opil on a pond gives one of the most direct and reasonable indications of the size of molecules. Of course, many other intriguing questions arise from this experiment: Why does the oil spread? What is the molecular mechanism for the spreading? What controls the speed of spreading? Why does it stop at a certain point? Which oils spread? Which don't? Why does oil calm the waves? etc.
You don't need a pond. For a small-scale version of Franklin's experiments, just use a plastic petri dish and samples of different oils and detergents. Try filling the petri dish about one-half full with tap water. Then shake some fine ground pepper onto the water's surface. Dip a toothpick into dish-washing liquid and touch the tip to the center of the water surface. Watch what happens. Why? Put the top on the dish and wait . . . something else happens!
Back to the book. Tanford explores the subsequent history of the science of the water surface through the work of Pockels, Rayleigh, Langmuir, etc. up until the early work on biological membranes (Chapter 18). The final chapter, entitled "Gorter and Grendel: A Factor of Two" discusses the truly classic paper that revealed experimentally the exact nature of the structure of biological membranes. Evert Gorter, a professor of pediatrics (who suffered severe rheumatoid arthritis all his life), and his student Grendel, took a sample of blood and under a microscope counted and measured the size of the red blood cells (chromocytes). They could then calculate the total surface area of all the cells. The blood sample was then extracted with acetone to remove all the lipids. The extract was then spread on a trough of water and the area of the spread lipids was determined. It turned out that the area of spread lipid was two times that of the surface area of the blood cells. The first paragraph of the paper published in the Journal of Experimental Medicine in 1925 follows:
We propose to demonstrate in this paper that the chromocytes of different animals are covered by a layer of lipoids just two molecules thick. If chromocytes are taken from an artery or vein, and are separated from the plasma by several washings with saline solution, and after that extracted with pure acetone in large amounts, one obtains a quantity of lipoids that is exactly sufficient to cover the total surface of the chromocytes in a layer that is two molecules thick. Subsequent extraction's with ether or benzene yield only small traces of lipoid substances.
We therefore suppose that every chromocyte is surrounded by a layer of lipoids, of which the polar groups are directed to the inside and to the outside, in much the same way as Bragg (1) supposes the molecules to be oritented in a "crystal" of a fatty acid, and as the molecules of a soap bubble are according to Perrin (2). On the boundary of two phases, one being the watery solution of hemoglobin, and the other the plasma, such an orientation seems a priori to be the most probable one. Any other explanation that does not take account of this constant relation between the surface of the chromocytes and the content of lipoids seems very difficult to sustain.
--And you know what, nobody believed them! It took another 40 years before other experiments firmly established the nature of lipid bilayer membranes.
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