Pressure of a gas

Gases exert pressure on any surface with which they come in contact, because gas molecules are constantly in motion. We humans have adapted so well physiologically to the pressure of the air around us that we are usually unaware of it, perhaps as fish are not conscious of the water s pressure on them. 

It is easy to demonstrate atmospheric pressure. One eveiyday example is the ability to drink a liquid through a straw. Sucking air out of the straw reduces the pressure inside the straw. The greater atmospheric pressure on the liquid pushes it up into the straw to replace the air that has been sucked out. 

Pressure is one of the most readily measurable properties of a gas. To understand how we measure the pressure of a gas, it is helpful to know how the units of measurement are derived. We begin with velocity and acceleration. 

Velocity is defined as the change in distance with elapsed time that is. 

The SI unit for velocity is m/s, although we also use cm/s. Acceleration is the change in velocity with time, or 

H2 (molecular hydrogen) HF (hydrogen fluoride) A gas is a substance that is normally in the 

N2 (molecular nitrogen) HCl (hydrogen chloride) gaseous state at ordnary temperatures and pressures a vapor is the gaseous form 

O2 (molecular oxygen) HBr (hydrogen bromide) of any substance that is a liqiid or a solid at normal temperatures and pressures. Thus, at 25 C arxl 1 atm pressure, we 

F2 (molecular fluorine) CO (carbon monoxide) speak of water vapor and oxygen gas. 

Of the gases listed in Table 5.1, only Oj is essential for our survival. Hydrogen sulfide (H2S) and hydrogen cyanide (HCN) are deadly poisons. Several others, such as CO, NO2, O3, and SO2, are somewhat less toxic. The gases He, Ne, and Ar are chemically inert that is, they do not react with any other substance. Most gases are colorless. Exceptions are F2, CI2, and NO2. The dark-brown color of NO2 is sometimes visible in polluted air. All gases have the following physical characteristics  

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When fluid flow in the reservoir is considered, it is necessary to estimate the viscosity of the fluid, since viscosity represents an internal resistance force to flow given a pressure drop across the fluid. Unlike liquids, when the temperature and pressure of a gas is increased the viscosity increases as the molecules move closer together and collide more frequently. 

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... 

Increasing or decreasing the partial pressure of a gas is the same as increasing or decreasing its concentration. The effect on a reaction s equilibrium position can be analyzed as described in the preceding example for aqueous solutes. Since the concentration of a gas depends on its partial pressure, and not on the total pressure of the system, adding or removing an inert gas has no effect on the equilibrium position of a gas-phase reaction. 

ED q, narcotic potency, is expressed as the partial pressure of a gas in breathing mixtures requited to produce a certain degree of anesthesia in 50% of the test animals. 

Static pre.s.sure is the pressure of the moving fluid. The static pressure of a gas is the same in all directions and is a scalar point function. It can be measured by drilling a hole in the pipe and keeping a probe flush with the pipe wall. 

This remarkably simple relationship is depicted in Figure 14. It was apparent from his results that the volume fraction of the solvent determined the probability of interaction with the solute in much the same way that the partial pressure of a gas determines the probability of collision. It also indicated that the influence of each stationary phase component was independent and unaffected by presence of the other. 

Dalton s law of partial pressure States that die total pressure of a gas mixture IS equal to the sum of the pressures which each component gas would exert if it occupied the same space alone. 

Knowledge of the temperature and pressure of a gas stream at the wellhead is important for determining whether hydrate formation can be expected when the gas is expanded into the flow lines. The temperature at the wellhead can change as the reservoir conditions or production rate changes over the producing life of the well. Thus, wells that initially flowed at conditions at which hydrate formation in downstream equipment was not expected may eventually require hydrate prevention, or vice versa. 

Next to sales contract specifications, coiTosion protection ranks highest among the reasons for the removal of acid gases. The partial pressure ol the acid gases may be used as a measure to determine whether treatment IS required. The partial pressure of a gas is defined as the total pressure of the system times the mole % of the ga,seous component. Where ( 02 is present with free water, a partial pres.sure ot. hi psia or greater would indicate that CO2 corrosion should be expected. If CO2 is not removed, inhibition and special metallurgy may be required. Below 15 psia, COt corrosion is not normally a problem, although inhibition may be required. 

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. 

According to Boyle s law, pressure of a gas is inversely proportional to the volume, if the temperature is held constant. For example, 2 ft at 4 psi would exert only 1 psi if allowed to expand 8 ft. ... 

In other words, the partial pressure of a gas in a mixture is equal to its mole fraction multiplied by die total pressure. This relation is commonly used to calculate partial pressures of gases in a mixture when the total pressure and the composition of the mixture are known (Example 5.9). 

Dalton, John, 25,27,266 Dalton s atomic theory, 25 Dalton s law A relation stating that the total pressure of a gas mixture is the sum of the partial pressures of its components, 115,117... 

Consider the motion of a billiard ball. After it is struck by the cue, it moves until it strikes a cushion, front which it bounces, apparently with undiminished velocity. It rolls along in a new direction until it strikes another cushion, changing its direction again. It may continue to roll until it has hit the cushions six or seven times. The billiard ball seems almost tireless as it rebounds time and again from the walls of the billiard table. Could there be a connection between the untiring motion of a billiard ball and the untiring pressure of a gas in a balloon ... 

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. 

FIGURE4.14 talThe pressure of a gas o arises from the impact of its molecules on o the walls of the container, (b) When the volume of the sample is decreased, there are more molecules in a given volume "j and so there are more collisions with the wi same area of the wall in a given time g... 

Dalton s law is consistent with our picture of a gas and adds a little more information. The total pressure of a gas arises, as we have seen, from the battering... 

Our task is to find the relation between the partial pressure of a gas and its mole fraction. 

To find the relation between the partial pressure of a gas in a mixture and its mole fraction, we first express the partial pressure, Pa, of a gas A in terms of the amount of A molecules present, wA, the volume, V, occupied by the mixture, and the temperature, T ... 

The relation that we have derived for the partial pressure of a gas A is... 

The partial pressure of a gas is the pressure that it would exert if it were alone in the container the total pressure of a mixture of gases is tire sunt of the partial pressures of the components the partial pressure of a gas is related to the total pressure by the mole fraction PA = xAP. 

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. 

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