{"id":307,"date":"2016-01-11T19:59:56","date_gmt":"2016-01-11T19:59:56","guid":{"rendered":"https:\/\/opentextbc.ca\/introductorychemistryclone\/chapter\/molecular-effusion-and-diffusion-2\/"},"modified":"2020-07-22T17:12:26","modified_gmt":"2020-07-22T17:12:26","slug":"molecular-effusion-and-diffusion","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introductorychemistryclone\/chapter\/molecular-effusion-and-diffusion\/","title":{"raw":"Molecular Effusion and Diffusion","rendered":"Molecular Effusion and Diffusion"},"content":{"raw":"[latexpage]\r\n
\r\n

Learning Objectives<\/p>\r\n\r\n<\/header>\r\n

\r\n
    \r\n \t
  1. Explore the nature of gas movement: molecular effusion and diffusion.<\/li>\r\n \t
  2. Examine and apply Graham's law of effusion.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

    Effusion<\/h1>\r\nThe movement of gas molecules can be divided into a few different types. [pb_glossary id=\"1630\"]Effusion[\/pb_glossary] is the movement of gas molecules from one container to another via a tiny hole. Typically the container to\u00a0which\u00a0the gas is moving is kept under lower pressure.\r\n\r\n[caption id=\"attachment_302\" align=\"aligncenter\" width=\"286\"]\"5<\/a> Figure 6.10 \"Molecular Effusion.\"[\/caption]\r\n\r\nIn 1846, the Scottish chemist Thomas Graham found that the rate of effusion of a gas (the amount of gas transferred between containers in a certain amount of time) is\u00a0inversely proportional to the square root of its\u00a0molar mass. This means that gases with a lighter molecular weight have higher effusion rates.\r\n\r\n[caption id=\"attachment_303\" align=\"aligncenter\" width=\"318\"]\"Portrait<\/a> Figure 6.11 \"Thomas Graham.\" Graham proposed his law of effusion in 1846.[\/caption]\r\n\r\nThis finding is summarized in [pb_glossary id=\"1632\"]Graham\u2019s law of effusion[\/pb_glossary]:\r\n\r\n\\[\\dfrac{\\text{Rate of Effusion (Gas 1)}}{\\text{Rate of Effusion (Gas 2)}}=\\sqrt{\\dfrac{M_2}{M_1}}\\]\r\n\r\nThis finding can be rationalized by thinking through the process of effusion on the molecular level. For a gas molecule to successfully move from one container to another, it must hit and pass through the tiny hole present in the container. Gases with higher rms speed are more likely to hit and pass through the hole so effusion is dependent on rms speed:\r\n\r\n\\[\\dfrac{\\text{Rate of Effusion (Gas 1)}}{\\text{Rate of Effusion (Gas 2)}}=\\dfrac{\\sqrt{\\dfrac{3RT}{M_1}}}{\\sqrt{\\dfrac{3RT}{M_2}}}=\\sqrt{\\dfrac{M_2}{M_1}}\\]\r\n
    \r\n

    Example 6.20<\/p>\r\n\r\n<\/header>\r\n

    \r\n

    Problem<\/h1>\r\nAn unknown halogen (diatomic) gas effuses at a rate that is approximately 1.89 times the rate of I2<\/sub> gas at the same temperature. Determine the molar mass and identity of this unknown gas.\r\n

    Solution<\/h2>\r\n

    \\(\\begin{array}{rrl}\r\n\\dfrac{\\text{Rate of Effusion (Gas 1)}}{\\text{Rate of Effusion (Gas 2)}}&=&\\sqrt{\\dfrac{M_2}{M_1}} \\\\ \\\\\r\n\\dfrac{\\text{Rate of Effusion (Gas \\ce{I2})}}{\\text{Rate of Effusion (Gas 2)}}&=&\\sqrt{\\dfrac{M_2}{M\\ce{I2}}}}=\\dfrac{1}{1.89}=\\sqrt{\\dfrac{M_2}{253.80\\text{ g\/mol}}} \\\\ \\\\\r\n0.279&=&\\dfrac{M_2}{253.80\\text{ g\/mol}} \\\\ \\\\\r\nM_2&=&71.1\\text{ g\/mol}\r\n\\end{array}\\)<\/p>\r\nTherefore, the unknown gas is Cl2<\/sub>.\r\n\r\n<\/div>\r\n<\/div>\r\n

    Diffusion<\/h1>\r\nAnother type of gas movement is called [pb_glossary id=\"1633\"]diffusion[\/pb_glossary]; it is the movement of gas molecules through one or more additional types of gas via random molecular motion. Similar to effusion, gases with lower molecular weights (which have a higher rms speed)\u00a0diffuse faster than gases with\u00a0higher molecular weights. However, in diffusion, movement is much more complicated as collisions occur between molecules that change the direction and speed of the molecules. As a result of these collisions, the path a molecule travels in diffusion is made up of numerous straight, short segments. The term [pb_glossary id=\"1635\"]mean free path[\/pb_glossary] is used to describe the average distance travelled by a molecule between collisions.\r\n\r\n[caption id=\"attachment_304\" align=\"aligncenter\" width=\"282\"]\"One<\/a> Figure 6.12 \"Molecular Diffusion.\"[\/caption]\r\n\r\n[caption id=\"attachment_305\" align=\"aligncenter\" width=\"299\"]\"Particle<\/a> Figure 6.13 \"Particle Mean Free Path.\" Stylized depiction of the path travelled by a gas particle during diffusion. Other particles have been omitted for clarity.[\/caption]\r\n\r\nView this video on diffusion<\/a> by Dr. Jessie A. Key for more information.\r\n
    \r\n

    Key Takeaways<\/p>\r\n\r\n<\/header>\r\n

    \r\n