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 Grahams Law of Effusion

Graham’s law states that the rates of effusion of two gases are inversely proportional to the square roots of their molar masses at the same temperature and pressure:

but if time is used the equation changes

Graham's Law deals with the effusion of gases.  This is not to be confused with diffusion which declares that molecules will move from a place of higher concentration to a place of lower concentration.  The principle of effusion depends upon a movement or diffusion of gases but it relates to the rate of travel of a gas through a predefined pathway and how the rate depends upon the molecular mass of the gas.  Specifically, the law states that the relative rates of effusion of two gases through a tube or pathway of equal size is inversely proportional to the square root of the molecular masses of the gases.

Effusion is the term used to describe the passage of a gas through a tiny orifice into an evacuated chamber, as shown in the figure below.

The rate of effusion measures the speed at which the gas travels through the tiny hole into a vacuum. Another term to remember for the test is diffusion. Diffusion is the term used to describe the spread of a gas throughout a space or throughout a second substance.

 Sample Questions Highlight to reveal other answers 1. If equal amounts of helium and argon are placed in a porous container and allowed to escape, which gas will escape faster and how much faster? 1. Set rate1 = He = x and rate2 = Ar = 1. The weight of He = 4.00 and Ar = 39.95. By Graham's Law, x / 1 = square root (39.95 / 4.00) = 3.16 times as fast. 2. What is the molecular weight of a gas which diffuses 1/50 as fast as hydrogen? 2. Set rate1 = other gas = 1 and rate2 = H2 = 50. The weight of H2 = 2.02 and the other gas = x. By Graham's Law, 1 / 50 = square root (2.02 / x) = molecular weight of 5050. 3. Two porous containers are filled with hydrogen and neon respectively. Under identical conditions, 2/3 of the hydrogen escapes in 6 hours. How long will it take for half the neon to escape? 3. Set rate1 = H2 = x and rate2 = Ne = 1. The weight of H2 = 2.02 and Ne = 20.18. By Graham's Law, x / 1 = square root (20.18 / 2.02) = 3.16 times as fast. 0.67 / 3.16 = 0.211 = amount of Ne leaving in 6 hours. Therefore 0.211 / 6 = 0.50 / x. x = 14.2 hours 4. If the density of hydrogen is 0.090 g/L and its rate of diffusion is 6 times that of chlorine, what is the density of chlorine? 4. Set rate1 = H2 = 6 and rate2 = Cl2 = 1. The weight of H2 = 2.02 and Ne = x. By Graham's Law, 6 / 1 = square root (x / 2.02) = 72.72 (molec. wt. of Cl2) 72.72 g / 22.414 L = 3.24 g/L. (22.414 is molar volume.) 5. How much faster does hydrogen escape through a porous container than sulfur dioxide? 5. Set rate1 = H2 = x and rate2 = SO2 = 1. The weight of H2 = 2.02 and SO2 = 64.06. By Graham's Law, x / 1 = square root (64.06 / 2.02) = 5.63 times as fast