Temperature molecular speeds

As temperature increases, the speed of the molecules increases. The distribution curve for molecular speeds (Figure 5.9) shifts to the right and becomes broader. The chance of a molecule having a very high speed is much greater at 1000°C than at 25°C. Note, for example,... 

Distribution of molecular speeds of oxygen molecules at 25°C and 1000°C. At the higher temperature the fraction of molecules moving at very high speeds is greater. 

The graph below shows the distribution of molecular speeds for helium and carbon dioxide at the same temperature. 

The distribution of molecular speeds in gas can be determined experimentally. To du so, the gas is heated to the required temperature in an oven. The molecules then stream out of the oven through a small hole into an evacuated region. To ensure that the molecules form a narrow Iteam, they may also pass through a senes of slits, and the pressure must Ik kept very low so that collisions within the beam do not cause spreading. 

This important result is used to find the root mean square speeds of the gas-phase molecules at any temperature (Fig. 4.25). We can rewrite this equation to emphasize that, for a gas, the temperature is a measure of mean molecular speed. From... 

J I I Describe the effect of molar mass and temperature on the Maxwell distribution of molecular speeds (Section 4.11). 

Maxwell distribution of molecular speeds The formula for calculating the percentage of molecules that move at any given speed in a gas at a specified temperature. 

To complete our analysis, we must determine the effect of a change in temperature. According to Equation, kinetic energy is proportional to temperature, and according to Equation, kinetic energy is proportional to the square of the molecular speed. Thus, the square of the molecular speed is proportional to temperature. 

Schematic view of the effect of increasing the temperature of a gas. Molecular speeds increase, resulting in more wall collisions and more force per collision, so the pressure increases.

Pressure is proportional to the square of molecular speed, which in turn is proportional to temperature. For an ideal gas, then, the pressure is directly proportional to temperature, and a plot of P vs. T yields a straight line. Again, this agrees with the ideal gas equation. 

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. 

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. 

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. 

FIGURE 4.27 The range of molecular speeds for several gases, as given by the Maxwell distribution. All the curves correspond to the same temperature. The greater the molar mass, the lower the average speed and the narrower the spread of speeds. 

The average kinetic energy per gas molecule, ( mu2)avg, is independent of the nature of the gas and is directly proportional to the temperature. In this case, the kinetic energy is defined by the standard physical formula in terms of molecule mass, m, and the molecular speed, u. This statement may be taken as a more exact definition of temperature than the qualitative one given in Chapter 1. A list of some common energy units is given in Table 6-1. 

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. 

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