Mixtures of Gases and Partial Pressures

Many gas samples are not pure, but are mixtures of gases. Dry air, for example, is a mixture containing nitrogen, oxygen, argon, carbon dioxide, and a few other gases in trace amounts (Table 5.3). 

Because the molecules in an ideal gas do not interact (as we will discuss further in Section 5.8), each of the components in an ideal gas mixture acts independently of the others. For example, the nitrogen molecules in air exert a certain pressure— 78% of the total pressure— that is independent of the other gases in the mixmre. Likewise, the oxygen molecules in air exert a certain pressure—21% of the total pressure—that is also independent of the other gases in the mixture. The pressure due to any individual component in a gas mixture is its partial pressure (P ). We can calculate partial pressure from the ideal gas law by assuming that each gas component acts independently. 

For a multicomponent gas mixture, we calculate the partial pressure of each component from the ideal gas law and the number of moles of that component (nj as follows  

The sum of the partial pressures of the components in a gas mixture equals the total pressure  

The total number of moles in the mixture, when substituted into the ideal gas law, indicates the total pressure of the sample. 

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Given all but one of the following properties for a mixture of gases, calculate the one not given total pressure of the mixture of gases and partial pressure of each gas. 

Thermod5mamic equilibrium relations are used to define the partitioning of gases between the vapor and hquid phases. The amormt of gas in the vapor phase is most often expressed as pressure (in units of atmospheres, bars or Pascals). One atmosphere is equal to 1013.25 millibars pressure (mbar) and 101.325 kilopascals (kPa 1 bar = 10 Pa). In a mixture of gases the partial pressure, Pi, of an individual gas, i, is its fraction of the total gas pressure. The total pressure of gases in the atmosphere, Patm. is equal to the sum of the partial pressures of the individual gases... 

In a mixture of gases, the partial pressure of any one gas is the pressure that gas alone would exert if the other gases were removed (and volume and temperature were kept constant). Chemists had already noticed that the volume of liquids is not additive. For example, if 100 mL of one liquid is mixed with 100 mL of another liquid, the total volume is not exactly 200 mL—the total usually is a little less or a little more than 200 mL. Therefore, it was not clear that the pressure of two gases in a mixture should be additive. It was Dalton who argued that they are. 

Dalton s Law Relationship between Partial Pressures P in Mixture of Gases and Total Pressure (Ptotai) (5.6)... 

The total fixed volume of a mixture of gases and vapors at a giv en condition is the same as the olume of any one component (gas laws), and its pressure is composed of the sum of the individual partial pressures of each component. 

Suppose, in the first place, that an excess of mercury is maintained in the system the partial pressure p, of the mercury vapor in the gaseous mixture will be equal, by the law of the mixture of gases and vapors whose truth is oneof our fundamental hypoth-... 

From the ideal gas equation it can be seen that, at constant temperature and volume, the pressure exerted by any gas is proportional to the number of molecules (or atoms, if the gas is monatomic, such as helium and argon). This is because pressure is a consequence of molecules colliding with the container walls, so the more molecules, the more collisions. For a mixture of gases, the total pressure is related to the total number of molecules present. To put this another way, the total pressure of the mixture is equal to the sum of the pressures that each gas would exert if it alone occupied the container. This is Dalton s Law of partial pressures. So atmospheric pressure is approximately given by ... 

The "partial" pressure of an individual gas in a mixture of gases represents the pressure the gas would exert in the same container at the same temperature if it were the only gas present. The total pressure in a mixture of gases is the sum of the individual partial pressures of the gases present in the mixture. The fact that the partial pressures of the gases in a mixture are additive suggests that the total pressure in a container is a function of the number of molecules present, and not of the identity of the molecules or of any other property (such as the molecules inherent atomic size). 

Rearrangements of the ideal gas law are used to calculate the rtvrlar mass of a gas, the density of a gas, the partial pressure of each gas in a mixture of gases, and the amounts of gaseous reactants or products in a reaction. 

If air and water are present together in a confined space, a balance condition will he reached where the air has become saturated with water vapour. If the temperature of the mixture is known, then the pressure of the water vapour will be the pressure of steam at this temperature (see also Section 1.3) (Table 23.1). Dalton s Taw of partial pressures (see also Section 1.5) states that the total pressure of a mixture of gases is equal to the sum of the individual pressures of the constituent gases, taken at the same temperature and occupying the same volume. Since the water saturation vapour pressure will remain constant, depending on temperature and not on volume, this pressure can be obtained from steam tables as below. The partial pressure exerted by the dry air must therefore be the remainder. 

The total pressure can be regarded as a sum of the parts furnished by the individual pressures exerted by each of the components of the gas mixtures. The pressure exerted by each of the gases in a gas mixture is called the partial pressure of that gas. The partial pressure is the pressure that the gas would exert if it were alone in the container. In the example of Figure 4-3, the total pressure in the third bulb is 113 mm. The partial pressure of water vapor in this bulb is 20 mm and the partial pressure of air is 93 mm. 

FIGURE 4.19 A representation of the experiment that Dalton performed on a gas mixture. According to Dalton s law, the total pressure, P, of a mixture of gases is the sum of the partial pressures PA and PB of gases A and B. Each partial pressure is the pressure that one of the gases would exert if it were the sole gas in the container (at the same temperature). 

Departures from ideality have been studied extensively for gases and gas mixtures. For most conditions of interest in the Earth s atmosphere, the assumption of ideal behavior is a reasonable approximation. The two most prevalent gases (N2 and O2) are non-polar and have critical temperatures (126 K and 154 K) far below most temperatures of environmental interest. These gases behave fairly ideally even though their pressures are high. For other gases, the partial pressures common in the atmosphere are so low that ideal behavior is a good approximation. 

There are several ways to describe the chemical composition of a mixture of gases. The simplest method is merely to list each component with its partial pressure or number of moles. Two other descriptions, mole fractions and parts per million, also are used frequently. 

The total pressure of a mixture of gases is 1.20atm. The mixture contains O.lOmol of N, and 0.20mol of 02. What is the partial pressure of O, ... 

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