Graham's Law - History

History

Graham's research on the diffusion of gases was triggered by his reading about the observation of German chemist Johann Döbereiner that hydrogen gas diffused out of a small crack in a glass bottle faster than the surrounding air diffused in to replace it. Graham measured the rate of diffusion of gases through plaster plugs, through very fine tubes, and through small orifices. In this way he slowed down the process so that it could be studied quantitatively. He first stated the law as we know it today in 1831. Graham went on to study the diffusion of substances in solution and in the process made the discovery that some apparent solutions actually are suspensions of particles too large to pass through a parchment filter. He termed these materials colloids, a term that has come to denote an important class of finely divided materials.

At the time Graham did his work the concept of molecular weight was being established, in large part through measurements of gases. Italian physicist Amadeo Avogadro had suggested in 1811 that equal volumes of different gases contain equal numbers of molecules. Thus, the relative molecular weights of two gases are equal to the ratio of weights of equal volumes of the gases. Avogadro's insight together with other studies of gas behaviour provided a basis for later theoretical work by Scottish physicist James Clerk Maxwell to explain the properties of gases as collections of small particles moving through largely empty space.

Perhaps the greatest success of the kinetic theory of gases, as it came to be called, was the discovery that for gases, the temperature as measured on the Kelvin (absolute) temperature scale is directly proportional to the average kinetic energy of the gas molecules. The kinetic energy of any object is equal to one-half its mass times the square of its velocity. Thus, to have equal kinetic energies, the velocities of two different molecules would have to be in inverse proportion to the square roots of their masses. The rate of effusion is determined by the number of molecules entering an aperture per unit time, and hence by the average molecular velocity. Graham's law for diffusion could thus be understood as a consequence of the molecular kinetic energies being equal at the same temperature.