The Pressure of a Gas

According to Dalton s laM of partial pressures, observed experimentally at sufficiently low pressures, the pressure of a gas mixture m a given volume V is the sum of the pressures that each gas would exert alone in the same volume at the same temperature. Expressed in tenns of moles n. 

Just as increasing the pressure of a gas or a gas mixture introduces non-ideal corrections, so does increasing the concentration. As before, one can introduce an activity a- and an activity coefficient y and write a- = cr-[. and... 

A compressor is a machine that is used to increase the pressure of a gas or vapor. They can be grouped into two major classifications centrifugal and positive displacement. This section provides a general discussion of these types of compressors. 

Boylefelaw Relation stating that at constant T and n, the pressure of a gas is inversely proportional to its volume, 105-106... 

The pressure of a gas sample can be measured in a device similar to a barometer, called a manometer. Figures 4-2B and 4-2C show two types. Figure 4-2 B shows a closed-end manometer. Here the downward pressure exerted by the column of mercury is balanced by the pressure of the gas sample placed in the flask. The gas pressure is, in the example shown, 105 mm. As in the barometer, only mercury vapor is present in the right-hand tube. 

If gases are heated or cooled at constant volume, the pressure changes, also at the rate of 7-5 of its value at 0°C. Then the pressure of a gas... 

In the discussion so far, the fluid has been considered to be a continuum, and distances on the molecular scale have, in effect, been regarded as small compared with the dimensions of the containing vessel, and thus only a small proportion of the molecules collides directly with the walls. As the pressure of a gas is reduced, however, the mean free path may increase to such an extent that it becomes comparable with the dimensions of the vessel, and a significant proportion of the molecules may then collide direcdy with the walls rather than with other molecules. Similarly, if the linear dimensions of the system are reduced, as for instance when diffusion is occurring in the small pores of a catalyst particle (Section 10.7), the effects of collision with the walls of the pores may be important even at moderate pressures. Where the main resistance to diffusion arises from collisions of molecules with the walls, the process is referred to Knudsen diffusion, with a Knudsen diffusivily which is proportional to the product where I is a linear dimension of the containing vessel. 

FIGURE 4.3 The pressure of a gas arises from the collisions that its molecules make with the walls of the container. The storm of collisions, shown in the inset, exerts an almost steady force on the walls. 

We have shown that the pressure of a gas can be related to the height of a column of liquid and its density by... 

The pressure of a gas, the force that it exerts divided by the area subjected to the force, arises from the impacts of its molecules. 

FIGURE 4.8 Boyle s law summarizes the effect of pressure on the volume of a fixed amount of gas at constant temperature. As the pressure of a gas sample is increased, the volume of the gas decreases. 

It follows that doubling the absolute temperature doubles the pressure of a gas, provided the amount and volume are constant. 

In Section 4.4, we used a molecular model of a gas to explain qualitatively why the pressure of a gas rises as the temperature is increased as a gas is heated, its molecules move faster and strike the walls of their container more often. The kinetic model of a gas allows us to derive the quantitative relation between pressure and the speeds of the molecules. 

The following calculation of the pressure of a gas based on the kinetic model may seem complicated at first, but it breaks down into many small steps. 

Almost all aquatic organisms rely on the presence of dissolved oxygen for respiration. Although oxygen is nonpolar, it is very slightly soluble in water and the extent to which it dissolves depends on its pressure. We have already seen (in Section 4.2) that the pressure of a gas arises from the impacts of its molecules. When a gas is introduced into the same container as a liquid, the gas molecules can burrow into the liquid like meteorites plunging into the ocean. Because the number of impacts increases as the pressure of a gas increases, we should expect the solubility of the gas—its molar concentration when the dissolved gas is in dynamic equilibrium with the free gas—to increase as its pressure increases. If the gas above the liquid is a mixture (like air), then the solubility of each component depends on that component s partial pressure (Fig. 8.21). 

We use the seven-step approach in compact form. The problem asks for the pressure of a gas after a change in conditions. A simple diagram helps us organize the information ... 

Molecular speed affects pressure in two ways that are illustrated in Figure 5-12. First, faster-moving molecules hit the walls more often than slower-moving molecules. The number of collisions each molecule makes with the wall is proportional to the molecule s speed. Second, the force exerted when a molecule strikes the wall depends on the molecule s speed. A fast-moving molecule exerts a larger force than the same molecule moving slower. Force per collision increases with speed, and number of collisions increase with speed, so the total effect of a single molecule on the pressure of a gas is proportional to the square of its speed. 

Robert Boyle (1627-1691) studied the effect of changing the pressure of a gas on its volume at constant temperature. He measured the volume of a given quantity of gas at a given pressure, changed its pressure, and measured the volume again. He obtained data similar to the data shown in Table 11-1. After repeating the process many times with several different gases, he concluded that... 

According to the ideal gas law, the pressure of a gas is directly proportional to the absolute temperature, that is, P = (nRJV)T. This linear relationship can be represented by P = mT + b, where m is the slope, equal to (nR/V), and b is the intercept of the line, which is zero in the absence of any imprecision in the data. The slope and intercept may thus be determined by linear regression of the four datapoints versus the model equation P = mT + b. 

The pressure of a gas is a macroscopic manifestation of the microscopic gas particles colliding with the internal walls of the container. 

Before we start describing the gas law relationships, we will need to describe the concept of pressure. When we use the word pressure with respect to gases, we may be referring to the pressure of a gas inside a container or we might be referring to atmospheric pressure, the pressure due to the weight of the atmosphere above us. The pressure at sea level is 1 atmosphere (atm). Commonly, the unit torr is used for pressure, where 1 torr = 1 mm Hg (millimeters of mercury), so that atmospheric pressure at sea level equals 760 torr. The SI unit of pressure is the pascal (Pa), so that latm = 760 mm Hg = 760 torr = 1.01325 X 10s Pa (or 101.325 kPa). 

When we use the word pressure, we may be referring to the pressure of a gas inside a container or to atmospheric pressure, the pressure due to the weight of the atmosphere above us. These two different types of pressure are measured in slightly different ways. Atmospheric pressure is measured using a barometer (Figure 8.1). 

Boyle s law describes the relationship between the volume and the pressure of a gas when the temperature and amount are constant. If you have a container like the one shown in Figure 8.3 and you decrease the volume of the container, the pressure of the gas increases because the number of collisions of gas particles with the container s inside walls increases. 

Gay-Lussac s law describes the relationship between the pressure of a gas and its Kelvin temperature if the volume and amount are held constant. Figure 8.5 represents the process of heating a given amount of gas at a constant volume. 

A common consideration is the presence of water vapor, H20(g). Water generates a vapor pressure, which varies with the temperature. Daltons law is used in these cases to adjust the pressure of a gas sample for the presence of water vapor. The total pressure (normally atmospheric pressure) is the pressure of the gas or gases being collected and the water vapor. When the pressure of an individual gas is needed, the vapor pressure of water is subtracted from the total pressure. Finding the vapor pressure of water requires measuring the temperature and using a table showing vapor pressure of water versus temperature. 

Boyle s experiments with the vacuum pump ceased in 1662, when Hooke moved to London to become curator of the Royal Society. However, by this time, Boyle and Hooke had performed a number of additional experiments that are described in the second edition of Spring of the Air, published in 1669. Included in the second edition was a statement of what is now known as Boyle s law the pressure of a gas is inversely proportional to its volume. In other words, if the pressure is doubled, the gas is compressed to one-half of its former volume and if the pressure is halved, the volume doubles. 

Example If the pressure of a gas essentially consisting of pump fluid molecules is measured with an ionization vacuum gauge, then the pressure reading (applying to air or Nj), as shown in Table 3.2, is too high by a factor of about 10. 

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