Molecular Weight Of Substances In Solutions : Brownian Movement

An obvious step from the gaseous theory of solution is to identify osmotic pressure with molecular bombardment by the dissolved substance. Boltzmann showed, on the assumption that the solute molecules had the same mean kinetic energy as gas molecules, that the laws of osmotic pressure followed from the kinetic theory. His calculation met with some opposition and gradually dropped out of sight, until it was revived on the basis of the fascinating researches of Jean Perrin, professor at the Sorbonne.

If an aqueous suspension of gamboge, a gum-resin familiar to painters in water-colour, is examined under the microscope the particles are seen to be in motion, each performing little excursions in an apparently erratic manner and moving in a zigzag path. This motion was first observed with suspensions in grains of pollen by the botanist Robert Brown in 1827; it is shown by all suspensions if the particles are sufficiently small and is known as the Brownian movement.

The cause of the Brownian movement was ascribed by C. Wiener in 1863 to bombardment of the suspended particles by the molecules of the liquid. This was confirmed by Svedberg in 1906; he found that the length of the path described agrees with that calculated from the kinetic theory by Einstein (1905) and Smoluchowski (1906).

Perrin found that in a gamboge emulsion examined by the microscope there was a gradation in the density of distribution of the particles with height. Near the surface, a rise of 1/20 mm. halved the number of gamboge particles. This is analogous to the diminution in density of the atmosphere, but on account of the small weight of the gaseous molecules a height of some hundreds of miles is necessary to get the same gradation in density as is evident in less than a millimetre with the comparatively massive gamboge particles. The gamboge particles and gaseous molecules are equally supported against the action of gravity by their kinetic energies. By counting the numbers of particles

Fig: Gamboge emulsion

Perrin's experiment with gamboge emulsion.

it was possible to find the law of distribution at different heights.

If n and n' are the numbers of gamboge particles per cm³ at two heights h cm. apart, then if the "solution" obeys the gas laws the osmotic pressures, p and p', are in the ratio of n to n'. The ratio p/p', however is connected with the height h by the well-known logarithmic barometric pressure formula. The distance h, required to produce a given fall of pressure is inversely proportional to the density, or molar weight, of the gas. To halve the density (or pressure) in an oxygen atmosphere, a vertical ascent of 5 kilometres as required; in hydrogen, with lighter molecules, the ascent is 5 x 16 = 80 km., whilst with carbon dioxide, with heavier molecules, it is only 5 x 16 / 22 = 3.64 km. The "molecular weight" of the gamboge particles could thus be calculated from the height in which the number per cm³ is halved. The weight of each particle was found by counting the number per cm³, and finding the total weight per cm³. The number of particles required to make up the molecular weight could thus be found: it was N₀ = 6.8 x 10²³, which is nearly the same as the value of Avogadro's constant for a gas. By examining the Brownian movement of the suspended particles in tobacco-smoke, de Broglie found N₀ = 6.43 x 10²³.

The suspended particles in a gamboge emulsion obey the gas laws. It seems very probable that particles in true solutions, more closely similar to those of gases, should also obey the gas laws and that osmotic pressure is caused by molecular bombardment. A partition allowing only water molecules to pass through, and arresting gamboge particles, would be subjected to a feeble bombardment by the latter and experience a small osmotic pressure. In the case of true solutions, the number of solute molecules in a given space is much larger and the pressure is correspondingly greater.

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Molecular Weight Of Substances In Solutions
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