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'''Graham's law''', known as '''Graham's law of [[effusion]]''', was formulated by Scottish physical chemist [[Thomas Graham (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 mass of its particles.<ref name=LM>[[Keith J. Laidler]] and John M. Meiser, ''Physical Chemistry'' (Benjamin/Cummings 1982), pp.18-19</ref>  This formula can be written as:
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:<math>{\mbox{Rate}_1 \over \mbox{Rate}_2}=\sqrt{M_2 \over M_1}</math>
 
where:
:''Rate<sub>1</sub>'' is the rate of effusion of the first gas (volume or number of moles per unit time).
:''Rate<sub>2</sub>'' is the rate of effusion for the second gas.
:''M<sub>1</sub>'' is the [[molar mass]] of gas 1
:''M<sub>2</sub>'' is the molar mass of gas 2.
 
Graham's law states that the rate of effusion of a gas is inversely proportional to the square root of its molecular weight. Thus, if the molecular weight of one gas is four times that of another, it would diffuse through a porous plug or escape through a small pinhole in a vessel at half the rate of the other (heavier gases diffuse more slowly). A complete theoretical explanation of Graham's law was provided years later by the [[kinetic theory|kinetic theory of gases]]. Graham's law provides a basis for separating [[isotopes]] by diffusion &mdash; a method that came to play a crucial role in the development of the atomic bomb.
 
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.
 
==History==
Graham's research on the diffusion of gases was triggered by his reading about the observation of [[Germany|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 [[suspension (chemistry)|suspensions]] of particles too large to pass through a parchment filter. He termed these materials [[colloid]]s, 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 [[Amedeo 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.
 
==Example==
Let gas 1 be H<sub>2</sub> and gas 2 be O<sub>2</sub>.
 
:<math>{\mbox{Rate H}_2 \over \mbox{Rate O}_2}={\sqrt{32} \over \sqrt{2}}={\sqrt{16} \over \sqrt{1}}= \frac{4}{ 1}</math>
 
Therefore, hydrogen molecules effuse four times faster than those of oxygen.<ref name=LM/>
 
Graham's Law can also be used to find the approximate molecular weight of a gas if one gas is a known species, and if there is a specific ratio between the rates of two gases (such as in the previous example). The equation can be solved for either one of the molecular weights provided the subscripts are consistent.
 
:<math>{M_2}={M_1 \mbox{Rate}_1^2 \over \mbox{Rate}_2^2}</math>
 
Graham's law was the [[Gaseous diffusion|basis]] for separating <sup>235</sup>U from <sup>238</sup>U found in natural [[uraninite]] (uranium ore) during the [[Manhattan project]] to build the first atomic bomb. The United States government built a gaseous diffusion plant at the then phenomenal cost of $100 million in Clinton, Tennessee. In this plant, [[uranium]] from uranium ore was first converted to [[uranium hexafluoride]] and then forced repeatedly to diffuse through porous barriers, each time becoming a little more enriched in the slightly lighter <sup>235</sup>U isotope.
 
==See also==
* [[Gas laws]]
* [[Scientific laws named after people]]
* [[Viscosity]]
* [[Drag (physics)]]
 
==References==
{{Reflist}}
 
{{DEFAULTSORT:Graham's Law}}
[[Category:Gas laws]]

Latest revision as of 23:24, 8 January 2015

If your computer is running slow, you have possibly gone by the different stages of rage plus frustration. Having such a superb tool like a computer can seem like a curse plus a blessing at the same time whenever this happens. It is perfect whenever it is very running quickly and smooth, however, then when it begins acting weird plus slows technique down, frustration sets inside. How may anything because fabulous as a computer make a person so mad?

So 1 day my computer suddenly started being weird. I was so frustrated, because my files were missing, and I cannot open the files which I needed, and then, suddenly, everything stopped working!

Your PC would have a fragmented hard drive or the windows registry would have been corrupted. It would additionally be as a result of the dust plus dirt which needs to be cleaned. Whatever the problem, we can constantly find a answer. Here are certain tricks on how to make your PC run quicker.

Review the files plus clean it up regularly. Destroy all of the unnecessary and unused files considering they only jam the computer program. It might surely boost the speed of your computer plus be thoughtful which a computer do not infected by a virus. Remember usually to update your antivirus software every time. If you never utilize the computer rather usually, we can take a free antivirus.

Google Chrome crashes on Windows 7 when the registry entries are improperly modified. Missing registry keys or registry keys with improper values could lead to runtime errors and thereby the issue occurs. You are recommended to scan the entire system registry plus review the outcome. Attempt the registry repair process using third-party registry cleaner software software.

You could moreover see with it that it is especially easy to download plus install. You could avoid those treatments that usually require you a fairly complicated set of instructions. Furthermore, you need to no longer want any different program requirements.

Google Chrome is my lifeline and for this day happily. My all settings plus research related bookmarks were saved inside Chrome plus stupidly I didn't synchronize them with the Gmail to store them online. I may not afford to install new variation and sacrifice all my work settings. There was no method to retrieve the aged settings. The just way left for me was to miraculously fix it browser in a way that all data plus settings stored in it are recovered.

If you wish To have a computer with fast running speed, you'd better install a good registry cleaner to wash the useless files for we. As long as you take care of the computer, it may keep inside advantageous condition.

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