英文实验 油膜法测阿伏伽德罗常数

ESTIMATION OF AVOGADRO’S NUMBER This experiment is designed to extend your measurement capabilities and to determine the value of the constant Avogadro’s number. In many situations where quantitative measurements are needed, direct measurement such as laying a ruler next to the object is not possible when the object is too large or too small. In such situations a common procedure is to use some method of indirect measurement. The determination of Avogadro’s number is an example where this indirect metho d is needed because its magnitude is much too large to determine by direct counting or other methods available in an introductory level laboratory.

If one considers the units for Avogadro’s number, mole-1 , it is the number of any item per mole. One possible item is molecules per mole which gives the units “molecules mole-1”for this constant. These units may also be expressed in the format "molecules/mole". It is possible to determine the value of Avogadro’s number from a property such as the mass or volume of a system which may be experimentally determined for one molecule as well as one mole of the molecules. When this is possible, the value of Avogadro’s number is calculated by obtaining the ratio of this property on a mole basis to that same property on a molecule basis. For example, if the mass of one molecule of substance A is m A and the mass of a mole of A is M A the value of the ratio (N o) is calculated by the expression:

N o = M A/m A = (grams/mole)/ (grams/ molecule)

= molecules/mole = 6.02 x 10 23 molecules/mole

In this experiment, the property measured is the volume instead of the mass and the substance that will be used is Oleic Acid (C18H34O2 ). The value of Avogadro’s number is to be determined by obtaining the ratio of the volume per mole of Oleic Acid (V A) to the volume per molecule of the acid (v A ) as shown below.

N o = V A/v A = (cm3/mole) / (cm3/molecule)

= molecules/mole = Avogadro’s number

The volume of one mole of oleic acid, V A, is determined by dividing the molar mass by the density which is 0.873 g/cm3 (V A = M A/ρ). The molar mass of Oleic Acid is obtained from the molecular formula given above and the atomic weights of the elements in grams.

The use of indirect measurement comes into use in determining the volume of one molecule of oleic acid. When Oleic Acid is placed on the surface of water the acid spreads out on the surface in a film one molecule thick. The acid end of the molecule, –CO2H, is soluble in water but the rest of the molecule is not. This cause

the molecules to orient themselves vertically with respect to the water surface forming a mono-molecular film with a thickness equal to the length of one molecule. From a general idea of the shape of the molecule, long and narrow, it is possible to estimate the volume of the molecule as the size of a cylinder or rectangular box that this molecule would just fit into. Thus, the molecular volume is approximated as the volume of the container required to hold one molecule. The value of Avogadro’s number obtained will depend on how well the volume is modeled by the shape of the container chosen and how well one can determine the thickness of the Oleic Acid film on the surface of the water.

Since the thickness of the film will be determined by the area and the volume of acid used, it is necessary to know the volume of acid that is place on the surface. However, if pure Oleic Acid was used the film would be too big to measure in the laboratory. The acid is dissolved in methyl alcohol and this solution is dropped on the surface of the water from an eyedropper. The alcohol is soluble in the water and goes into solution leaving the Oleic Acid on the surface. The concentration of the acid is 0.50% by volume in methyl alcohol. The volume of the acid used in each trial is therefore 0.0050 * V drop used. The acid will form a circular film on the surface and its area may be determine by measuring the diameter of the circle (D) and using the standard equation for the area of a circle A = πR2 where R is the radius of the surface film (R=D/2). The thickness of the film is obtained by dividing the volume of acid in one drop by the area calculated for the circular film this drop makes on the water [t = V A/A = V A/πR2 ] since the shape of the layer of acid is approximately an extremely short cylinder. V is the volume of the Oleic acid in one drop and R is the radius of the surface film of Oleic Acid.

The volume of the molecule may be reasonably approximated by two models, a cylinder and a rectangular box, as shown below:

The value of the length of the molecule is the thickness of the film t for both models. The radius, r, is calculated as t/12 for the cylinder and the edge is t/6 for the rectangular box model.

You will calculate Avogad ro’s number with both models and compare the calculated values with the accepted value of 6.02 x10 23 molecules/mole.

It is also possible to obtain an approximate value for the radius of a carbon atom from the length of the molecule. Oleic acid is eighteen carbon atoms long and this length is, therefore, approximately 18 times the diameter of the carbon atom. This gives the radius of the carbon atom as t/36 since the diameter is twice the radius.