Diffusion, Effusion, and Diffusion, Effusion, and Graham’s Law of Graham’s Law of

DiffusionDiffusion

What is diffusion?What is diffusion? The The movementmovement of particles from of particles from

regions of regions of higherhigher concentrations to concentrations to regions of regions of lowerlower concentration. concentration.

Eventually, the particles will disperse Eventually, the particles will disperse evenlyevenly throughout the space. throughout the space.

High

Low

What is effusion?What is effusion?

The The passagepassage of a gas under pressure of a gas under pressure through a tiny through a tiny openingopening..

Graham’s law of diffusionGraham’s law of diffusion

Thomas Thomas GrahamGraham studied effusion in studied effusion in detail and determined that the detail and determined that the raterate of of effusion is effusion is indirectlyindirectly proportional to the proportional to the squaresquare root of the molar root of the molar massmass of the of the gas, if pressure and temperature are gas, if pressure and temperature are kept constant.kept constant.

In other words:In other words:

vA

vB

=Molar MassB

Molar MassA

How does that work?How does that work?

Let’s go back to the Let’s go back to the KineticKinetic Molecular Theory Molecular Theory We saw that the We saw that the movementmovement of particles is of particles is

proportionalproportional to the amount of to the amount of kinetickinetic energy. energy. KE= ½ m KE= ½ m v v 22

So, if the KE is So, if the KE is constantconstant, ½ m, ½ mAA vvAA2 2 = ½ m= ½ mBB vvBB

2 2

With a little algebra, we get:With a little algebra, we get:

vA

vB

=Molar MassB

Molar MassA

Example ProblemsExample Problems

At the same temperature, which At the same temperature, which molecule travels faster, Omolecule travels faster, O22 or N or N22? ? How much faster?How much faster?

At room temperature, Xe atoms have At room temperature, Xe atoms have an average speed of 240 m/s. At the an average speed of 240 m/s. At the same temperature, what is the speed same temperature, what is the speed of Hof H22 molecules? molecules?

What is the molar mass of a gas if it What is the molar mass of a gas if it diffuses 0.907 times the speed of diffuses 0.907 times the speed of argon gas?argon gas?

AnswersAnswers

1) N1) N22 (lower molar mass) (lower molar mass) (32/28) = 1.07 times faster(32/28) = 1.07 times faster

2) x/240 = 2) x/240 = (131.3/2) (131.3/2) x/240 = 8.10x/240 = 8.10x = 1944 m/sx = 1944 m/s

3) 1/0.907 = 3) 1/0.907 = (x/39.9)(x/39.9)(1/0.907)(1/0.907)22 = ( = ((x/39.9))(x/39.9))22

1.216 = x/39.91.216 = x/39.9x = 48.5 g/molx = 48.5 g/mol