This was a favorite of Professor Edward Mason, Newport Rogers Professor Emeritus, Department of Chemistry, Brown University. Please note that Ben did not have any idea about the size of molecules or the concept of monomolecular layers. Lord Rayleigh got this monomolecular layer concept from Edna Pockels.
If you want to cut to the chase and find the relavant data from which, with the assumption of a monolayer dimension and the weight of one mole of oil, you may calculate Avagadro's number,click here
Otherwise go to:
Oil on the Waters, by Benjamin Franklin, 1773
To calculate the number of molecules in a mole we are going to have to make some reasonable assumptions. First we can determine the dimension of a monolayer from the area of the oil and the volume of oil placed on the water. A monolayer is the assumed to be the diameter of a spherical molecule. The second assumption has to do with molecular weight of the oil. Assume about 200 grams per mole. Of course we may measure the density of oil by weighing a measured volume. However we will take the density of oil to be that of Castor oil 0.960-0.967 gm/c.c., or Cod Liver oil 0.922-0.931 gm/c.c., or the hydrocarbon citane C_16H_34 which might be whale oil with density 0.774 gm/c.c. each of which Franklin might have had access to on board ship. We are going to require some conversions between units such as teaspoon and mL.
From the experiments by Franklin and in particular the volume of oil and the area over which it spread (assumed to be a monolayer) please calculate the size (diameter) of a typical oil molecule and the number of molecules of oil on the pond. Using the density of oil and a guess at its molecular weight estimate Avagadro's number. Becareful of units.