Graham's law

thumb|Thomas Graham

Graham's law of effusion (also called Graham's law of diffusion) was formulated by Scottish physical chemist Thomas Graham in 1848. Graham found experimentally that the rate of effusion of a gas is inversely proportional to the square root of the molar mass of its particles.

Graham's law is most accurate for molecular effusion which involves the movement of one gas at a time through a hole. It is only approximate for diffusion of one gas in another or in air, as these processes involve the movement of more than one gas.

Around the time Graham did his work, the concept of molecular weight was being established largely through the measurements of gases. Daniel Bernoulli suggested in 1738 in his book Hydrodynamica that heat increases in proportion to the velocity, and thus kinetic energy, of gas particles. Italian physicist Amedeo Avogadro also 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. Graham's law for diffusion could thus be understood as a consequence of the molecular kinetic energies being equal at the same temperature.

The rationale of the above can be summed up as follows:

Kinetic energy of each type of particle (in this example, Hydrogen and Oxygen, as above) within the system is equal, as defined by thermodynamic temperature:

:<math> \frac{1}{2}m_{\rm H_{2v^{2}_{\rm H_{2=\frac{1}{2}m_{\rm O_{2v^{2}_{\rm O_{2 </math>

Which can be simplified and rearranged to:

:<math> \frac{v^{2}_{\rm H_{2}{v^{2}_{\rm O_{2} = \frac{m_{\rm O_{2}{m_{\rm H_{2} </math>

or:

:<math> \frac{v_{\mathrm H_{2}{v_{\mathrm O_{2} = \sqrt{\frac{m_{\mathrm O_{2}{m_{\mathrm H_{2 </math>

Ergo, when constraining the system to the passage of particles through an area, Graham's law appears as written at the start of this article.

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