Kinetic Theory of Gases: Graham's Law of Diffusion

Submitted by ChemPRIME Staff on Thu, 12/16/2010 - 13:27
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  • Faster-moving molecules can escape more readily through small holes or pores in containers. Such an escape is called effusionThe escape of a gas through an orifice.. They can also mix more rapidly with other gases by diffusionThe spreading of one substance into another (usually involves gases or liquids).. Such processes are usually carried out at constant temperatureA physical property that indicates whether one object can transfer thermal energy to another object., and so the relative rates of diffusion or effusion of two gases A and B depend only on the molar masses MA and MB:

    \text{(}u_{\text{A}}\text{)}_{\text{rms}}=\sqrt{\frac{\text{3}RT}{M_{\text{A}}}}\text{           (}u_{\text{B}}\text{)}_{\text{rms}}=\sqrt{\frac{\text{3}RT}{M_{\text{B}}}}

    The rates of effusion or diffusion are proportional to the rms velocities, and so

    \frac{\text{Rate of diffusion of A}}{\text{Rate of diffusion of B}}=\frac{\text{(}u_{\text{A}}\text{)}_{\text{rms}}}{\text{(}u_{\text{B}}\text{)}_{\text{rms}}}=\frac{\sqrt{\frac{\text{3}RT}{M_{\text{A}}}}}{\sqrt{\frac{\text{3}RT}{M_{\text{B}}}}}=\sqrt{\frac{\text{3}RT}{M_{\text{A}}}\text{ }\times \text{ }\frac{M_{\text{B}}}{\text{3}RT}}=\sqrt{\frac{M_{\text{B}}}{M_{\text{A}}}}\text{     (1)}

    This result is known as Graham’s law of diffusion after Thomas Graham (1805 to 1869), a Scottish chemist, who discovered it by observing effusion of gases through a thin plug of plaster of paris.

    EXAMPLE 1 Calculate the relative rates of effusion of He(g) and O2(g) .

    SolutionA mixture of one or more substances dissolved in a solvent to give a homogeneous mixture. From Eq. (1)

    \frac{\text{Rate of diffusion of He}}{\text{Rate of diffusion of O}_{\text{2}}}=\frac{\sqrt{M_{\text{O}_{\text{2}}}}}{\sqrt{M_{\text{He}}}}=\sqrt{\frac{\text{32}\text{.00 g mol}^{-\text{1}}}{\text{4}\text{.003 g mol}^{-\text{1}}}}=\text{2}\text{.83}

    In other words we would expect He to escape from a balloon nearly 3 times as fast as O2.