The Simple Gas Laws

PRACTICE EXAMPLE B We want to increase the pressure exerted by the 1.000 kg red cylinder in Example 6-3 to 100.0 mbar by placing a weight on top of it. What must be the mass of this weight Must the added weight have the same cross-sectional area as tire cylinder Explain. 

In this section, we consider relationships involving the pressure, volume, temperature, and amoimt of a gas. Specifically, we will see how one variable depends on another, as the remaining two are held fixed. Collectively, these relationships are referred to as the simple gas laws. You can use these laws in problem solving, but you will probably prefer the equation developed in the next section— the ideal gas equation. You may find that the greatest use of the simple gas laws is in solidifying your qualitative imderstanding of the behavior of gases. 

In 1662, working wifh air, Robert Boyle discovered the first of fhe simple gas laws, now known as Boyle s law. 

For a fixed amount of gas at a constant temperature, the gas volume is inversely proportional to the gas pressure. 

The equation PV = a can be used to derive another equation that is useful for situations in which a gas undergoes a change at constant temperature. If we write equation (6.5) for the initial state (i) and for the final state (f), we get 

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We look at the simple gas laws to explore the behaviour of systems with no interactions, to understand the way macroscopic variables relate to microscopic, molecular properties. Finally, we introduce the statistical nature underlying much of the physical chemistry in this book when we look at the Maxwell-Boltzmann relationship. 

Supercompressibility of Natural Cos All gases deviate from the simple gas laws to a varying extent. This deviation is called super-compressibility and must be taken into account in gas measurement, particularly at high line pressure. For example, since natural gas is more compressible under high pressure at ordinary temperatures than is called for by Boyles law, gas purchased at an elevated pressure gives a greater volume when the pressure is reduced than it would if the gas were ideal. 

A perfect" gas is one which closely conforms id the simple gas laws" of expansion and contraction, such as Boyle s Law, formulated in England by The Hon Robert Boyle (1627-169D (Ref 1, p 141-R) and called in France Mariotte s Law, because it was formulated independently from Boyle by Edme Mariotte (1629-1684) (Ref 1, p 515-L). This law, called in Germany and Russia... 

Problem 11 (a) Show in what aspects vander Waals equation is an improvement over the simple gas laws ... 

There is much in favor of the assumption that in the ideal case the molecules of a solute behave in an inert solvent as if they were gas molecules. This is the simplest and most useful assumption. It receives support from the well established principles of physical chemistry according to which osmotic pressure, vapor pressure, and related phenomena in dilute solutions are calculated by means of the simple gas laws. 

Structure of adsorbed films on dilute solutions. Gibbs s equations (7.1 to 7.7) permit the calculations of the area per molecule, if the surface tension is determined over a range of concentration of the solutions. The area per molecule is proportional to the slope of the curve relating the lowering of surface tension to the activity /2c2 (the vapour pressure of component 2 if the vapour obeys the simple gas laws). This assumes... 

The phrase van der Waals radius arises as a distinction from intemudear distance radii. Thus, from the van der Waals equation for the P-Vrelation in gases (an improvement on the simple gas law PV=nRT), a quantity b can be found which refers to the space taken up out of the whole gas volume V by the molecules themselves. 

The table shows that the theoretical deduction k = (p. 92) is only realised for the monatomic permanent gases, and also for mercury vapour, which is likewise monatomic. This also holds for certain metallic vapours not cited in the table. For all other gases k<% and the difference % — k is greater the more complicated the molecule and the more the gas in question deviates from the simple gas laws. Yet even where the laws of Boyle and Charles are followed with great exactness, as for... 

Hence L and P must both be proportional to the temperature, and hence also to one another. When, therefore, the temperature of a gas which obeys the simple gas laws is raised, the kinetic energy of the molecules increases in the same ratio as their internal energy, so that we have... 

The increase of h depends on the deviations from the simple gas laws. According to Van der Waals theory, h must be a maximum when the product fv is a minimum. This relationship is confirmed quahtatively by Koch s experiments. 

For real gases the simple gas laws no longer hold strictly, and the equations deduced in the last paragraph are no longer Ann. de Physik, 27, 311 (1908). 

We can simphfy equations (6) and (7) very materially, by considering evaporation at so low a temperature that we may assume the vahdity of the simple gas laws at least approxi-... 

The free ions of weak electrolytes, even in relatively concentrated solutions, are present in such small quantities that they still conform to the simple laws. It is possible that the free electric charges on the ions exert appreciable forces on one another in concentrated solutions. This would cause deviations from the simple laws analogous to the deviations from the simple gas laws which are accounted for by van der Waals theory. 

This problem is analogous to describing the behavior of a gas using Newton s laws of motion for the individual molecules and keeping track of all their trajectories (i.e., a microscopic approach). It can be conceptualized, but in practice it is impossible. It is much more fruitful to characterize such a system in terms of the simple gas laws of thermodynamics (i.e., a macroscopic approach). The key issue is selection of an appropriate representation for the system. 

The simple gas laws that we discussed in Section 10.3, such as Boyle s law, are special cases of the ideal-gas equation. For example, when the quantity of gas and fhe femperafure are held constant, n and T have fixed values. Therefore, the product nRT is the product of three constants and must itself be a constant. 

The ideal gas law contains within it the simple gas laws tiiat we have learned. For example, recall that Boyle s law states that V oc 1/P when the amoimt of gas (n) and the temperature of the gas (T) are kept constant. To derive Boyle s law, we can rearrange the ideal gas law as follows ... 

As the temperature of a fixed amoxmt of gas in a fixed volume increases, the pressure increases. In an aerosol can, this pressure increase can cause the can to explode, which is why aerosol cans should not be heated or incinerated. Table 11.2 summarizes the relationships between all of the simple gas laws and the ideal gas law. 

Simple Gas Laws The simple gas laws show how one of the properties of a gas varies with another. They are Volume (V) and Pressure V) 1 V oc — (Boyle s law) Volume (V) and Temperature (T) V oc T (Charles s law) Volume (V) and Moles (n) V oc n (Avogadro s law) Simple Gas Laws Each of the simple gas laws allows us to see how two properties of a gas are interrelated. They are also useful in calculating how one of the properties of a gas changes when another does. Boyle s law, for example, can be used to calculate how the volume of a gas will change in response to a change in pressure, or vice versa. 

Calculations involving the simple gas laws usually consist of finding one of the initial or final conditions given the other initial and final conditions. In this case, use Boyle s law to find V2 given Pj, Vi, and V2. 

Insoluble liquids steam distillation The mutual solubility of some liquids is so small that they can be considered substantially insoluble points K and M (Fig. 9.8) are then for all practical purposes on the vertical axes of these diagrams. This is the case for a mixture such as a hydrocarbon and water, for example. If the liquids are completely insoluble, the vapor pressure of either component cannot be influenced by the presence of the other and each exerts its true vapor pressure at the prevailing temperature. When the sum of the separate vapor pressures equals the total pressure, the mixture boils, and the vapor composition is readily computed, assuming the applicability of the simple gas law,... 

We have learned about pressure and its characteristics. We now broaden our discussion to include the four basic properties of a gas sample pressure (P), volume (V), temperature (T), and amount in moles (n). These properties are interrelated— when one changes, it affects the others. The simple gas laws describe the relationships between pairs of these... 

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