Molecular speeds average

C05-0105. At an altitude of 40 km above the Earth s surface, the temperature is about-25 °C, and the pressure is about 3.0 torr. Calculate the average molecular speed of ozone (O3) at this altitude. 

C05-0115. Consider two gas bulbs of equal volume, one filled with H2 gas at 0 °C and 2 atm, the other containing O2 gas at 25 °C and 1 atm. Which bulb has (a) more molecules (b) more mass (c) higher average kinetic energy of molecules and (d) higher average molecular speed ... 

We see that the average molecular speed is directly proportional to the square root of the absolute temperature. 

In Eq. (PP), N is the gas concentration (molecules cm 3), um is the average molecular speed in the gas phase, R is the gas constant (J K 1 mol ), T the temperature (K), and M is the molecular weight (kg) of the gas. The normalized rates, i.e., divided by the rate of gas-surface collisions in Eq. (PP), will be referred to as conductances, T, for reasons that will become apparent shortly. However, the reader should keep in mind that these conductances just reflect the speeds of the individual processes. 

Another quantity which is closely related to the average molecular speed is the speed of sound, which we will write as 5SOund- As noted in Chapter 3, sound waves are actually waves of gas pressure (Figure 3.6)—the density of gas molecules is alternately slightly higher or lower than the equilibrium value. This disturbance travels at a characteristic speed which is clearly not very different from the average molecular speed, but getting the precise numerical value requires a fairly sophisticated treatment. The answer turns out to be... 

Intermolecular collisions do not cause large deviations from the ideal gas law at STP for molecules such as N2 or He, which are well above their boiling points, but they do dramatically decrease the average distance molecules travel to a number which is far less than would be predicted from the average molecular speed. Collisions randomize the velocity vector many times in the nominal round trip time, leading to diffusional effects as discussed in Chapter 4. If all of the molecules start at time t = 0 at the position x = 0, the concentration distribution C(x,t) at later times is a Gaussian ... 

The velocity distribution functions allow us to evaluate the average value of any function of r, or c by integrating over the appropriate distribution. For example, the average molecular speed, (c), is, using Eqs. (55) and (57),... 

M Calculate the fraction of molecules that have speeds greater than twice the average molecular speed. 

C. A decrease in volume (V) occurs at constant temperature (7). Average molecular speed is determined only by temperature and will be constant. V and P are inversely related, so pressure will increase. With less wall area and at higher pressure, more collisions occur per second. 

The average molecular speed (Problem 4.20.6) is obtained by evaluating... 

In gases the diffusion rates are clearly dependent on the molecular speed, and consequently we should expect a dependence of the diffusion coefficient on temperature since the temperature indicates the average molecular speed. 

First of all, should be proportional to the area A, because doubling the area will double the number of collisions with the wall. Second, Z should be proportional to the average molecular speed, M, because molecules moving twice as fast will collide twice as often with a given wall area. Finally, the wall collision rate should be proportional to the number density, N/T because twice as many molecules in a given volume will have twice as many collisions with the wall. All of these arguments are consistent with the kinetic theory of gases and are confirmed by the full mathematical analysis. We conclude that... 

Rates of molecule-wall and molecule-molecule collisions from the kinetic theory of gases depend on the average molecular speed u. 

Which of the following comparisons of the average kinetic energies and the average molecular speeds of H2 and N2 gases at 300 K is correct ... 

In the TC processing the average molecular speed and the flow rate vary with z because of changing temperature. The retention time and the coordinate for any temperature profile of the column are related by the equations ... 

FYom this formula it is seen that to calculate /i we need to determine the mean molecular speed ( ci )m- For real systems the average molecular speed is difficult to determine. Assuming that the system is sufficiently close to equilibrium the velocity distribution may be taken to be Maxwellian. For molecules in the absolute Maxwellian state the peculiar velocity equals the microscopic molecular velocity, i.e., Ci = ci, because the macroscopic velocity... 

How fast does a molecule move, on the average, at any temperature 77 One way to estimate molecular speed is to calculate the root-mean-square (rms) speed (u, which is an average molecular speed. One of the results of the kinetic theory of gases is that the total kinetic energy of a mole of any gas equals 7 T Earlier we saw that the average kinetic energy of one molecule is mu and so we can write... 

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)... 

The deviation ofthe work performed in areal expansion of a gas from that of reversible expansion can be shown to be of order dlKu). Here (u) is the average molecular speed and the is the speed of the piston. What piston speed is required f or a 10 % deviation from the reversible work formula ... 

Knowledge Required (1) The understanding of Avogadro s Principle. 2) The relationships of average molecular speed and kinetic energy to temperature and pressure conditions. 

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