MOLECULAR EFFUSION AND DIFFUSION

The ideal-gas equation can be derived from the frve statements given in the text for the kinetic-molecular theory. 

Rather than perform the derivation, however, let s consider in qualitative terms how the ideal-gas equation might follow from these statements. The total force of the molecular collisions on the walls and hence the pressure (force per unit area. Section 10.2) produced by these collisions depend both on how strongly the molecules strike the walls (impulse imparted per collision) and on the rate at which the collisions occur  

For a molecule traveling at the rms speed, the impulse imparted by a collision with a wall depends on the momentum of the molecule that is, it depends on the product of the molecule s mass and speed /nUrms- The coUision rate is proportional to the number of molecules per unit volume, nj V, and to their speed, which is be- 

If we put in a proportionality constant, calling it R, the gas constant, you can see that we obtain the ideal-gas equation  

Check Ina conceptual exercise of this kind, there is no numerical answer to check. All we can check in such cases is our reasoning in the course of solving the problem. 

Consider two gas cylinders of the same volmne and temperature, one containing 1.0 mol of propane, C3H8, and the other 2.0 mol of methane, CH4. Which of the following statements is true (a) The C3H8 and CH4 molecules have the same (J ) The C3H8 and CH4 molecules have the same average kinetic energy, (c) The rate at which the molecules collide with the cylinder walls is the same for both cylinders, (d) The gas pressure is the same in both cylinders. 

How is the rms speed of N2 molecules in a gas sample changed by (a) an increase in temperature, (b) an increase in volume, (c) mixing with a sample of Ar at the same temperature  

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MOLECULAR EFFUSION AND DIFFUSION We observe that the kinetic-molecular theory helps account for such gas properties as effusion and diffusion. 

MOLECULAR EFFUSION AND DIFFUSION (SECTION 10.8) It Mows from kinetic-molecular theory that the rate at which a gas undergoes effusion (escapes through a tiny hole) is inversely proportional to the square root of its molar mass (Graham s law). The diffusion of one gas through the space occupied by a second gas is another phenomenon related to the speeds at which molecules move. Because moving molecules undergo frequent collisions with one another, the mean free path—the mean distance traveled between collisions—is short. Collisions between molecules limit the rate at which a gas molecule can diffuse. 

Rates of molecular motion are directly proportional to molecular speeds, so Equation predicts that for any gas, rates of effusion and diffusion increase with the square root of the temperature in kelvins. Also, at any particular temperature, effusion and diffusion are faster for molecules with small molar masses. 

Effusion and diffusion are substantially the same process. Diffusion is movement of a substance from an area of higher concentration to an area of lower concentration. Effusion is the movement of a gas through a small opening. Graham s Law of Effusion states the rate of effusion is inversely proportional to the square root of the molecular mass. 

Understand the kinetic-molecular theory and how it explains the gas laws, average molecular speed and kinetic energy, and the processes of effusion and diffusion ( 5.6) (SP 5.13) (EPs 5.53-5.65)... 

KINETIC-MOLECULAR THEORY OF GASES EFFUSION AND DIFFUSION (sections 10.7 and 10.8)... 

Graham s law effusion rate A effusion rate B 1 molecular mass of B V molecular mass of A Effusion and diffusion... 

Effusion and diffusion rates are inversely proportional to the square root of the molar mass (Graham s law) because they are directly proportional to molecular speed. 

How the Kinetic-Molecular Theory Explains the Gas Laws 170 Effusion and Diffusion 175... 

Since the masses of the molecules are proportional to their molecular weights and the average velocity of the molecules is a measure of the rate of effusion or diffusion, all we have to do to this equation to get Graham s law is to take its square root. (The square root of v2 is not quite equal to the average velocity, but is a quantity called the root mean square velocity. See Problem 12.18.)... 

We shall consider in detail the predictions of the hard-sphere model for the viscosity, thermal conductivity, and diffusion of gases indeed, the kinetic theory treatment of these three transport properties is very similar. But first let us consider the simpler problem of molecular effusion. 

Thomas Graham determined that the rates of diffusion and effusion of gases are inversely proportional to the square roots of their molecular or atomic weights. This is Graham s Law. In general, it says that the lighter the gas, the faster it will effuse (or diffuse). Mathematically, Graham s Law looks like this ... 

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