Daltons Law of Partial Pressure

To what temperature must 5.00 L of oiygen at 50.°C and 600. torr be heated in order to have a volume of 10.0 L and a pressure of 800. torr  

If gases behave according to the kinetic-molecular theory, there should be no difference in the pressure-volume-temperature relationships whether the gas molecules are all the same or different. This similarity in the behavior of gases is the basis for an understanding of Dalton s law of partial pressures  

The total pressure of a mixture of gases is the sum of the partial pressures exerted by each of the gases in the mixture. 

Each gas in the mixture exerts a pressure that is independent of the other gases present. These pressures are called partial pressures. Thus, if we have a mixture of three gases, A, B, and C, exerting partial pressures of 50. torr, 150. torr, and 400. torr, respectively, the total pressure will be 600. torr  

To determine the amount of O2 or any other gas collected over water, we subtract the pressure of the water vapor (vapor pressure) from the total pressure of the gases  

Thus far we have concentrated on the behavior of pure gaseous substanees, but experimental studies very often involve mixtures of gases. For example, for a study of air pollution, we may be interested in the pressure-volume-temperature relationship of a 

Consider a case in which two gases, A and B, are in a container of volume V. The pressme exerted by gas A, according to the ideal gas equation, is 

In a mixture of gases A and B, the total pressure Fj is the result of the collisions of both types of molecules, A and B, with the walls of the container. Thus, according to Dalton s law, 

As mentioned earlier, gas pressure results from the impact of gas molecules agamst the walk of the container. 

Pa and Pb are the partial pressures of gases A and B, respectively. For a mixture of gases, then, Pj depends only on the total number of moles of gas present, not on the nature of the gas molecules. 

AIM To understand the relationship between the partiai and totai pressures of a gas mixture, and to use this reiationship in caicuiations. 

Studies of gaseous mixtures show that each component behaves independently of the others. In other words, a given amount of oxygen exerts the same pressure in a 1.0-L vessel whether it is alone or in the presence of nitrogen (as in the air) or helium. 

Among the first scientists to study mixtures of gases was John Dalton. In 1803 Dalton summarized his observations in this statement For a mixture of gases in a container, the total pressure exerted is the sum of the partial pressures of the gases present. The parti pressure of a gas is the pressure that the gas would exert if it were alone in the container. This statement, known as Dalton s law of partial pressures, can be expressed as follows for a mixture containing three gases  

Assuming that each gas behaves ideally, we can calculate the partial pressure of each gas from the ideal gas law  

When two gases are present, the total pressure Is the sum of the partial pressures of the gases. 

When two or more gases are mixed, they each occupy the entire volume of the container. They each have the same temperature as the other(s). However, each gas exerts its own pressure, independent of the other gases. Moreover, according to Dalton s law of partial pressures, their pressures must add up to the total pressure of the gas mixture. 

00 atm into a rigid 1.00-L container at 300 K, will they fit (b) If so, what will be their total volume and total pressure  

(a) The gases will fit gases expand or contract to fill their containers, (b) The total volume is the volume of the container—1.00 L. The temperature is 300 K, given in the problem. The total pressure is the sum of the two partial pressures. Partial pressure is the pressure of each gas (as if the other were not present). The oxygen pressure is 

00 atm. The oxygen has been moved from a 1.00-L container at 300 K to another 1.00-L container at 300 K, and so its pressure does not change. The nitrogen pressure is 1.00 atm for the same reason. The total pressure is 

EXAMPLE 12.22. If the N2 of the last example were added to the O2 in the container originally containing the O2, how would the problem be affected  

Unless otherwise noted, all art on this page is 0 Cengage Learning 2014. 

This important observation indicates some fundamental characteristics of an ideal gas. The fact that the pressure exerted by an ideal gas is not affected by the identity (composition) of the gas particles reveals two things about ideal gases (1) the volume of the individual gas particle must not be important, and (2) the forces among the particles must not be important. If these factors were important, the pressure exerted by the gas would depend on the nature of the individual particles. These observations will strongly influence the model that we will eventually construct to explain ideal gas behavior. 

Mixtures of helium and oxygen can be used in scuba diving tanks to help prevent the bends. For a particular dive, 46 L He at 25°C and 1.0 atm and 12 L O2 at 25°C and 1.0 atm were pumped into a tank with a volume of 5.0 L. Calculate the partial pressure of each gas and the total pressure in the tank at 25°C. 

Thus far we have concentrated on the behavior of pure gaseous substances, but experimental studies very often involve mixtures of gases. For example, for a study of air pollution, we may be interested in the pressure-volume-temperature relationship of a sample of air, which contains several gases, hi this case, and all cases involving mixtures of gases, the total gas pressure is related to partial pressures, that is, the pressures of individual gas components in the mixture. In 1801 Dalton formulated a law. 

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The Driving Force for Mass Transfer. The rate of mass transfer increases as die driving force, C g — CL, is increased. C+ can lie enhanced as follows. From Daltons law of partial pressures... 

Step 2 Our variables fit the following form of Daltons Law of Partial Pressures. 

Now we have to look at air as a mixture of gases. Indeed, there is nitrogen, oxygen, argon, water vapor, and other gases and vapors in the air. Each of these is a part, a fraction of the total. How big a fraction If all of the air were just O2 then the fraction of O2 would be 100%/100% = 1. But you know it is less than that you are given the numbers which tell you what is the fraction of O2 in the air. Check a textbook and find the Dalton law of partial pressures. It says that the total pressure is a sum of partial pressures ... 

For a mixture of ideal gases we have the Dalton law of partial pressures, according to which the pressure exerted by each component of the mixture is... 

In order to determine the composition of the vapor (in mole fraction), we can use Daltons law of partial pressures to set up the following ... 

Dalton s law of partial pressures The total pressure (P) exerted by a mixture of gases is equal to the sum of the partial pressures (p) of the components of the gas mixture. The partial pressure is defined as the pressure the gas would exert if it was contained in the same volume as that occupied by the mixture. 

Steam Distillation. Distillation of a Pair of Immiscible Liquids. Steam distillation is a method for the isolation and purification of substances. It is applicable to liquids which are usually regarded as completely immiscible or to liquids which are miscible to only a very limited extent. In the following discussion it will be assumed that the liquids are completely immiscible. The saturated vapours of such completely immiscible liquids follow Dalton s law of partial pressures (1801), which may be stated when two or more gases or vapoms which do not react chemically with one another are mixed at constant temperature each gas exerts the same pressure as if it alone were present and that... 

When kc and K g values are reported in units (SI) of kmoL/[(s m") (kPa)], one must be careful in converting them to a mole-fracdion basis to multiply by the total pressure actually employed in the original experiments and not by the total pressure or the system to Be designed. This conversion is valid for systems in which Dalton s law of partial pressures p = ypr) is valid. 

Dalton S Law of Partial Pressures. The total pressure (P) of a gaseous mixture equals the sum of the partial pressures of its components. By definition, the partial pressure of any component gas is the hypothetical pressure it would exert by occupying the entire volume (V) of the mixture at the same temperature (T). That is,... 

If the vapor phase behaves as an ideal gas mixture, then by Dalton s law of partial pressures,... 

Dalton s Law of partial pressures considers a mixture of two or more gases, and states that the total pressure of the mixture is equal to the sum of the individual pressures, if each gas separately occupied the space. 

This is nothing else than the well-known Law of Mixed Gases, or Law of Partial Pressures, discovered experimentally by John Dalton in 1801, and expressed by him in the somewhat vague... 

Using Dalton s law of partial pressures to express p, in terms of p gives... 

If we assume that Dalton s law of partial pressure holds in the vapor phase, it is easy to show that >2 is related to the total pressure, p, by the equation... 

Dalton s law of partial pressure 264, 406 Davies, C. A. 449, 456, 507 Debye heat capacity equation for solids 572-80, 651-4... 

Dalton summarized his observations in terms of the partial pressure of each gas, the pressure that the gas would exert if it occupied the container alone. In our example, the partial pressures of oxygen and nitrogen in the mixture are 0.60 atm and 0.40 atm, respectively, because those are the pressures that the gases exert when each one is in the container alone. Dalton then described the behavior of gaseous mixtures by his law of partial pressures ... 

This is Dalton s law of partial pressures. To obtain a total pressure, simply add the contributions from all gases present Ptotal Pi + P2 + P3 +------------ Pi... 

Gaseous solutions are easy to prepare and easy to describe. The atoms or molecules of a gas move about freely. When additional gases are added to a gaseous solvent, each component behaves independently of the others. Unless a chemical reaction occurs, the ideal gas equation and Dalton s law of partial pressures describe the behavior of gaseous solutions at and below atmospheric pressure (see Chapter 5). 

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