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Chemistry: The Central Science | 13th Edition | ISBN: 9780321910417 | Authors: Theodore E. Brown; H. Eugene LeMay; Bruce E. Bursten; Catherine Murphy; Patrick Woodward; Matthew E. Stoltzfus
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Kinetic-Molecular Theory of Gases: Effusion and

Chapter , Problem 86E

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QUESTION:

Problem  86e

Kinetic-Molecular Theory of Gases: Effusion and Diffusion (Sections)

At constant pressure, the mean free path (A) of a gas molecule is directly proportional to temperature. At constant temperature, A is inversely proportional to pressure. If you compare two different gas molecules at the same temperature and pressure, A is inversely proportional to the square of the diameter of the gas molecules. Put these facts together to create a formula for the mean free path of a gas molecule with a proportionality constant (call it Pmfp. Ike the ideal-gas constant) and define units for Pmfp.

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QUESTION:

Problem  86e

Kinetic-Molecular Theory of Gases: Effusion and Diffusion (Sections)

At constant pressure, the mean free path (A) of a gas molecule is directly proportional to temperature. At constant temperature, A is inversely proportional to pressure. If you compare two different gas molecules at the same temperature and pressure, A is inversely proportional to the square of the diameter of the gas molecules. Put these facts together to create a formula for the mean free path of a gas molecule with a proportionality constant (call it Pmfp. Ike the ideal-gas constant) and define units for Pmfp.

ANSWER:

Step 1 of 3

From the given, the pressure is constant, the mean free path  of a gas molecule is proportional to the temperature.

This can be represented as follows:

                                                           ..........................(1)

When the temperature is constant, the mean free path $(\lambda)$ for the same gas molecule is inversely proportional to pressure.

This gives the following relation:

                                                           ..............................(2)

From relations (1) and (2) the possible relation between , and  is given below:

                                                          ..................(3)

 

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