Average speed of molecules

We have seen that effusion reveals that the average speed of molecules in a gas is inversely proportional to the square root of their molar mass. In effusion experiments at different temperatures, we find that the rate of effusion increases as the temperature is raised. Specifically, for a given gas, the rate of effusion increases as the square root of the temperature ... 

That is, the higher the temperature and the lower the molar mass, the higher is the average speed of molecules in a gas. 

Temperature is a measure of the average speed of molecules. If heat is added, then the average speed increases. Even though gas molecules are very far apart relative to their size, because they move so very fast, they collide a lot with each other. Those collisions are what cause gas pressure. Gas pressure is the force of all of the molecules colliding with the sides of a container. When there are fewer molecules bouncing around and hitting the sides, the pressure is lower. More molecules hitting the sides increases the pressure. 

Average speed of molecules at T2 Average speed of molecules at T,... 

Where the diffusion coefficient, known as the Knudsen diffusivity DAk, is proportional to the product of the average speed of molecules and an appropriate mean step size Xk, the following holds true ... 

Oxygen molecules have an average speed of about 480 m/s at room temperature. At the same temperature, what is the average speed of molecules of sulfur hexafluoride, SFe ... 

Use the Maxwell-Boltzmann distribution of molecular speeds to calculate root-mean-square, most probable, and average speeds of molecules in a gas (Section 9.5, Problems 41-44). 

Average speed of molecules is directly proportional to the square root of the temperature and inversely proportional to the square root of the molar mass. 

Further, statistical mechanics and thermodynamics serve to relate the microscopic to the macroscopic. These theories are probabilistic, but they have no exceptions because of the immensity of the number of molecules—10 in a sip of water—and the rapidity of molecular motion at ambient temperatures. Thus, the average speed of molecules "scales up" to temperature, their puny interactions with light waves into color, the resistance of their crystals to being squeezed to hardness, their multitudinous and frequent collisions into a reaction that is over in a second or a millennium (Atkins, 1984, 1987, 1991 Joesten et al., 1991 Hoffmann, 1995). 

Temperature Average speed of molecules Average translational kinetic energy of molecules Intermolecular freedom of motion... 

Average distance between molecules Density in a sealed container Average speed of molecules Average translational kinetic energy of molecules Collisions with container walls per second Collisions per unit area of wall per second Pressure (P)... 

The average speed of molecules in a gas also increases with the temperature of the gas, but the spread of speeds is greater at higher temperatures. 

There are comparable ways to estimate the average speed of molecules, of which root-mean-square speed is one. 

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