Graham's Law

Graham's Law

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In chemistry and in physics, the movement of particles becomes very important. One way in which particles move is through effusion. The formula for the rate of effusion of gas molecules was developed by a chemist by the name of Thomas Graham in the 19th century.



December 21, 1805�September 16, 1869.



Thomas Graham was born in December of 1805 in Glasgow, Scotland. His father was a workman who desired that his son enter the Church of Scotland. However, Graham became a student at the University of Glasgow in 1819, where he became interested in the field of chemistry. He left the university in 1826 and went off to be a professor of chemistry at several universities, two of which were the Royal College of Science and Technology and the University of London.



In 1841, he founded the Chemical Society of London, of which he was the first president. His study in the field of colloids (a type of homogenous mixture) led to the discovery of dialysis and his earning of the name �the father of colloid chemistry.�



Another of Graham�s accomplishments was in his study of diffusion and effusion of gases. His formula for the effusion of gases even carries his name; it is called Graham�s Law.




Graham�s Law

�Physics. The flow of a gas through a small orifice at such a density that the mean distance between the molecules is large compared with the diameter of the orifice� (�effusion�).

In other words, effusion is the flow of individual gas molecules through a hole that is smaller than the mean free path, which is �the average distance [a] particle travels between collisions with other particles� (�Mean free path�). This means that in effusing through the hole the gas molecules do not collide with one another.
ef�fu�sion �noun

One of the postulates of the Kinetic Molecular Theory states that average kinetic energy of gas particles depends solely on the temperature of the gas. Since this is the case, the kinetic energy of two gas molecules, hydrogen and oxygen for example, may be written as the following.











When simplified the equation becomes this.









Rearranging yields this equation.











And taking the square root of both sides gives us the following.













This formula is a simplified version of Graham�s Law which states �that the rate of effusion of a gas is inversely proportional to the square root of the mass of its particles� (�Graham�s Law�).

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In chemistry textbooks the formula is commonly written as













where r indicates the rate of effusion of a gas and M indicates the molar mass of that gas.













�The derivation of Graham�s law from kinetic theory was considered a triumph of the theory and greatly strengthened confidence in its validity�

(Ebbing 210).




A Practical Application

The principle of effusion is used in the refining of fuel rods to be used in nuclear fission reactors. The fuel rods are primarily composed of uranium-238, which is not reactive. Only about .72% of the fuel rod is uranium-235, the isotope needed for fission. To concentrate U-235, uranium hexafluoride is allowed to gasify and effuse through porous membranes where the uranium hexafluoride contain U-235 moves faster (approximately 4% faster) than the molecules containing U-238, thereby providing the necessary concentration for fission to occur.



Works Cited



Ebbing, Darrel D. General Chemistry. Fifth Edition. Ed. Mark S. Wrighton. Boston: ����������� Houghton Mifflin Company, 1996.



"effusion." Dictionary.com Unabridged (v 1.1).� 2007. http://dictionary.reference.com/

������ ����������� browse/effusion (13 Nov. 2007).



�Effusion.� Wikipedia. http://en.wikipedia.org/wiki/Effusion (13 Nov. 2007).



�Graham, Thomas.� Encyclopedia Britannica. 2007. http://www.britannica.com/eb/

���������������� article-9037612/Thomas-Graham (13 Nov. 2007).



�Graham�s Law.� Wikipedia. http://en.wikipedia.org/wiki/Graham%27s_Law_of_

���������������� Effusion (13 Nov. 2007).



�Mean free path.� Wikipedia. http://en.wikipedia.org/wiki/Mean_free_path (13 Nov.

���������������� 2007).



The Kinetic Molecular Theory. http://chemed.chem.purdue.edu/genchem/topicreview/

���������������� bp/ch4/kinetic4.html (9 Oct. 2007).



�Thomas Graham (chemist).� Wikipedia. http://en.wikipedia.org/wiki/Thomas_Graham_

���������������� (chemist) (9 Oct. 2007).
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