atkins_echem_ch01

# atkins_echem_ch01 - TEOC01 5:08 PM Page 12 Chapter 1 The...

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TEOC01 11/4/04 5:08 PM Page 12± Equations of state 1.1 The perfect gas equation of state 1.2 Using the perfect gas law Box 1.1 The gas laws and the weather 1.3 Mixtures of gases: partial pressures The kinetic model of gases 1.4 The pressure of a gas according to the kinetic model 1.5 The average speed of gas molecules 1.6 The Maxwell distribution of speeds 1.7 Diffusion and effusion 1.8 Molecular collisions Real gases Box 1.2 The Sun as a ball of perfect gas 1.9 Molecular interactions 1.10 The critical temperature 1.11 The compression factor 1.12 The virial equation of state 1.13 The van der Waals equation of state 1.14 The liquefaction of gases CHECKLIST OF KEY IDEAS FURTHER INFORMATION 1.1 DISCUSSION QUESTIONS EXERCISES Chapter 1 The properties of gases Although gases are simple, both to describe and in terms of their internal structure, they are of immense importance. We spend our whole lives surrounded by gas in the form of air, and the local variation in its properties is what we call the ‘weather’. To understand the atmospheres of this and other planets we need to understand gases. As we breathe, we pump gas in and out of our lungs, where it changes composition and temperature. Many industrial processes involve gases, and both the outcome of the reaction and the design of the reaction vessels depend on a knowledge of their properties. Equations of state We can specify the state of any sample of substance by giving the values of the following properties (all of which are defined in the Introduction ): V , the volume of the sample p , the pressure of the sample T , the temperature of the sample n , the amount of substance in the sample However, an astonishing experimental fact is that these four quantities are not independent of one another . For instance, we cannot arbitrarily choose to have a sample of 0.555 mol H 2 O in a volume of 100 cm 3 at 100 kPa and 500 K: it is found experi­ mentally that the state simply does not exist. If we select the amount, the volume, and the temperature, then we find that we have to accept a particular pressure (in this case, close to 230 kPa). The same is true of all substances, but the pressure in general will be di C erent for each one. This experimental

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TEOC01 11/4/04 5:08 PM Page 13± generalization is summarized by saying the substance obeys an equation of state , an equation of the form p = f ( n , V , T ) (1.1) This expression tells us that the pressure is some function of amount, volume, and temperature and that if we know those three variables, then the pressure can have only one value. The equations of state of most substances are not known, so in general we cannot write down an explicit expression for the pressure in terms of the other variables. However, certain equations of state are known. In particular, the equation of state of a low-pressure gas is known, and proves to be very simple and very useful. This equation is used to describe the behaviour of gases taking part in reac­ tions, the behaviour of the atmosphere, as a starting point for problems in chemical engineering, and even in the description of the structures of stars.
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