THE PROPERTIES OF GASES

Gases differ remarkably from liquids and solids in that the volume of a sample of gas depends in a striking way on the temperature of the gas and the applied pressure. The volume of a sample of liquid water, say 1 kg of water, remains essentially the same when the temperature and pressure are changed somewhat. Increasing the pressure from 1 atm to 2 atm causes the volume of a sample of liquid water to decrease by less than 0.01% and increasing the temperature from 0 C to 100° C causes the volume to increase by only 2%. On the other hand, the volume of a sample of air is cut in half when the pressure is increased from 1 atm to 2 atm, and it increases by 36.6% when the temperature is changed from 0° C to 100° C. 

We can understand why these interesting phenomena attracted the attention of scientists during the early years of development of modern chemistry through the application of quantitative experimental methods of investigation of nature, and why many physicists and chemists during the past century have devoted themselves to the problem of developing a sound theory to explain the behavior of gases. 

In addition to.our desire to understand this part of the physical world, there is another reason, a practical one, for studying the gas laws. This reason is concerned with the measurement of gases. The most convenient way to determine the amount of material in a sample of a solid is to weigh it on a balance. This can also be done conveniently for liquids or we may measure the volume of a sample of a liquid, and, if we want to know its freight, multiply the volume by its density, as foilnd by a previous experiment. The method of weighing is usually not conveniently used for gases, because their densities are 

It has been found by experiment that all ordinary gases behave in nearly the same way. The nature of this behavior is described by the perfect-gas laws (often referred to briefly as the gas laws). 

It is found experimentally that, to within the reliability of the gas laws (better than 1% under ordinary conditions) the volume of a sample of any gas is determined by only three quantities the pressure of the gas, the temperature of the gas, and the number of molecules in the sample of the gas. The law describing the dependence of the volume of the gas on the pressure is called Boyle s law that describing the dependence of the volume on the temperature is called the law of Charles and Gay-Lussac and that describing the dependence of the volume on the number of molecules in the sample of gas is called Avogadro s law. 

Most gases behave similarly at low pressure and high temperature. 

The height (h) of the liquid column is a measure of the atmospheric pressure (P) expressed as the length of the column for a particular liquid. 

Common pressure units mmHg, cmHg, cmH20 

U-shaped tube filled with liquid, and connected to an experimental system - Open-tube pressure of system = atmospheric pressure when levels are equal 

1 Torr = 1 mmHg (Not exact, but correct to better than 2 x 10 Torr) 

3 (a) The difference in column height will be equal to the difference in 

31 Beeausc P, V and T are state functions, the intermediate conditions are irrelevant to the final states. We can simply use the ideal gas law in the form 

41 Density is proportional to the molar mass of the gas as seen from the ideal gas law  

Because we want the pressure to be the same, we c3n set these two equal to each other. Because volume, mass of the gases, and the gas constant R are the same on both sides of the equation, they will cancel. 

Gas molecules are widely spaced and gases are highly compressible. Gas molecules are in ceaseless chaotic motion. 

Atomic and molecular gases move rapidly and respond quickly to changes in 

A glass tube, sealed at one end, filled with liquid mercury, and inverted into a beaker also containing liquid mercury (Torricelli) 

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R. C. Reid, J. M. Prausnitz, B.E. Polling, The Properties of Gases and Liquids, 4th edition, McGraw-Hill, New York, 1988. 

B. D. Smith and R. Srivastava, Thermodynamic Data for Pure Compounds, Part A, Elsevier Science Pubhshers, Amsterdam, The Netherlands, 1986 DIPPR, Project 801, Data Compilation (July 1990) R. C. Reid, J. M. Prausnitz, and B. E. Poling, The Properties of Gases and Eiquids, 4th ed.,... 

Reid, R. C. and Sherwood, T. K, The Properties of Gases and Liquids, Second Edition, New York McGraw-Hill Book Company, 1966, p. 314. 

Robert Boyle, an Irish chemist noted for his pioneering experiments on the properties of gases, discovered methanol (CH3OH) in 1661. For many years methanol, known as wood alcohol, was produced by heating hardwoods such as maple, birch, and hickory to high temperatures m the absence of air. The most popular modern method of producing methanol, which IS also the least costly, is from natural gas (methane) by the direct combination of carbon monoxide gas and hydrogen in the presence of a catalyst. Methanol also can be produced more expensively from oil, coal, and biomass. 

These two possibilities are attractive because they are simple—one factor alone is held responsible for the weight difference. We must be prepared, however, for disappointment. There is the third possibility that neither of these proposals, A or B, accounts for the properties of gases. After all, neither A nor B applies to the beans and marbles example. The bag probably wouldn t contain the same number of beans as marbles (as in B) but, in addition, beans and marbles don t weigh the same (as in A). We need more information to decide if either proposal A or B applies to gases. More information is obtained by observing how some gases behave when mixed. 

These simple, integer volume ratios confirm the usefulness of the interpretation that equal volumes contain equal numbers of molecules. This proposal was first made in 1811 by an Italian scientist, Amadeo Avogadro hence it is called Avogadro s Hypothesis. It has been used successfully in explaining the properties of gases for a century and a half. 

Thus we see that the properties of gases provide a substantial basis for developing the atomic theory. The gaseous state is, in many ways, the simplest state of matter for us to understand. The regularities we discover are susceptible to detailed mathematical interpretation. We shall examine these regularities in this chapter. We shall find that their interpretation, called the kinetic theory, provides an understanding of the meaning of temperature on the molecular level. 

The first characteristic equation to be proposed which gave an adequate representation of the properties of gases was the equation of van der Waals, which resulted from a revision of the deduction of the equation (1) from the kinetic theory, and the introduction of corrections in the fundamental assumptions that ... 

In this chapter, we follow a typical scientific path. First, we collect experimental observations on the properties of gases and summarize these observations mathematically. We then formulate a simple qualitative molecular model of a gas suggested by these observations and go on to express it quantitatively. Finally, we use more detailed experimental observations to refine the model so that it accounts for the properties of real gases. 

Summaries of the properties of gases, particularly the variation of pressure with volume and temperature, are known as the gas laws. The first reliable measurements of the properties of gases were made by the Anglo-Irish scientist Robert Boyle in 1662 when he examined the effect of pressure on volume. A century and a half later, a new pastime, hot-air ballooning, motivated two French scientists, Jacques Charles and Joseph-Louis Gay-Lussac, to formulate additional gas laws. Charles and... 

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