Physical chemistry equations for gases

Table 5.27 Compressibility of Water Table 5.28 Mass of Water Vapor In Saturated Air Table 5.29 Van der Waals Constants for Gases Table 5.30 Triple Points of Various M aterlals 5.9.1 Some Physical Chemistry Equations for Gases...

Equations of state (EOS) offer many rich enhancements to the simple pV = nRT ideal gas law. Obviously, EOS were developed to better calculate p, V, and T, values for real gases. The point here is such equations are excellent vehicles with which to introduce the fact that gases cannot be really treated as point spheres without mutual interactions. Perhaps the best demonstration of the existence of intermolecular forces that can also be quantified is the Joule-Thomson experiment. Too often this experiment is not discussed in the physical chemistry course. It should be. The effect could not exist if intermolecular forces were not real. The practical realization of the effect is the liquefaction of gases, nitrogen and oxygen, especially. 

It has always seemed appropriate to this writer that the elbow in the adsorption isotherms of nitrogen on finely divided materials at liquid air temperatures should have been called Point B, because it was the outcome of a brilliant series of experimental measurements of such isotherms by the man we honor today. It was correctly identified as the approximate position of the completion of a mono-layer of adsorption on the surface of the material and the beginning of multilayer adsorption. It is now common knowledge to students of even elementary physical chemistry that, in 1938, a theory of adsorption of gases in multimolecular layers was published. Point B was merged into the BET equation. The Washington Section of the American Chemical Society made him the Hillebrand prize winner in 1945 for this work. 

In equation (6-1) the increment of work, dW, refers to all of the work (i.e., electrical, mechanical, pressure-volume, chemical, etc.) performed by the system (the sample) on its surroundings. The development of thermodynamics given in most physical chemistry texts is confined to gases where d W becomes simply pressure-volume work, PdV, where P is the external environment. In the case of an elastomer deformed by an amount dL in tension and exerting a restoring force f the mechanical work performed on the system to accomplish the deformation, namely fdL, must also be included in dW. Thus, for an elastomer strained uni axially in tension,... 

In a complicated physical chemistry problem you might have to derive your own mathematical formula or find some approximation scheme. The method must be developed for each problem. The following simple example requires algebraic manipulation as well as numerical calculation Under ordinary conditions, gases nearly obey the ideal gas equation which is... 

A general reference often consulted today for the physical and chemical properties of common chemicals is Lange s Handbook of Chemistry (Dean 1999), which lists many chemical compounds and their most important properties. It is organized into separate chapters of Physical constants of organic molecules with 4300 compounds and Physical constants of inorganic molecules, and lists each compound alphabetically by name. Some of these properties are very sensitive to temperature, but less sensitive to pressure, and they are listed as tables, or more compactly as equations of the form /(T) for example, liquid heats of evaporation, heat capacities of multi-atom gases, vapor pressures over liquids, liquid and solid solubilities in liquids, and liquid viscosities. Some of these properties are sensitive both to temperature and pressure. 

In your study of chemistry so far, you ve learned how to name compounds, balance equations, and calculate reaction yields. You ve seen how heat is related to chemical and physical change, how electron configuration influences atomic properties, how elements bond to form compounds, and how the arrangement of bonding and lone pairs accounts for molecular shapes. You ve learned modern theories of bonding and, most recently, seen how atomic and molecular properties give rise to the macroscopic properties of gases, liquids, solids, and solutions. 

In Chapter 2.5.3, the phenomena of atmospheric water are described from a meteorological and hydrological point of view. Here, the physicochemical properties of droplets that are important for an understanding of cloud physics and chemistry will briefly be described. Atmospheric droplets are always solutions of gases and salts and partly suspended particles. Key properties such as the size and salinity of droplets are dominantly determined by the CCN (Chapter 4.3.5). Although droplets can normally be considered diluted solutions, during nucleation and evaporation processes highly concentrated solutions occur and instead of concentrations in thermodynamic equations (if they are still valid) activities have to be used. 

Equation (3.52) can be rearranged to isolate b. The approximation is better than not if p and AT are kept as small as possible in the experiment. Table 3.3 lists van der Waals a and b for several gases, as compiled in the Handbook of Chemistry and Physics [1]. It is interesting to correlate a and b with the complexity and size of a given atom or molecule. 

If a hypothesis successfully passes many tests, it becomes known as a theory. A theory is a tested explanation of basic natural phenomena. An example is the molecnlar theory of gases— the theory that all gases are composed of very small particles called molecules. This theory has withstood many tests and has been fruit-fnl in snggesting many experiments. Note that we cannot prove a theory absolutely. It is always possible that further experiments will show the theory to be limited or that someone will develop a better theory. For example, the physics of the motion of objects devised by Isaac Newton withstood experimental tests for more than two centnries, nntil physicists discovered that the equations do not hold for objects moving near the speed of light. Later physicists showed that very small objects also do not follow Newton s eqnations. Both discoveries resulted in revolutionary developments in physics. The first led to the theory of relativity the second, to quantum mechanics, which has had an immense impact on chemistry. 

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