Critical constants of gases

Used by permission of Flexware, Inc., http //www.flexwareinc/ gasprop.htm. Critical constants of gases may also be found in Landolt-Bomstein, Physikalisch-chemische Tabellen, 6th ed., II. Band, 1. Teil,... 

As the parameters of each of the two-parameter semi-empirical equations can be evaluated in terms of the critical constants of the gases of interest, we provide in Table 5.3 a set of values of the critical constants for some gases of interest. 

Reasonable choices of a and b can often predict the critical constants of real gases to within 10 or 20% of their observed values. 

Critical Constants of a Gas The most characteristic property of gases is that their molecules lie far apart from one another and are in continuous rapid motion. Each molecule, therefore, leads almost an independent existence. This is particularly so when temperature is high and pressure is low. 

The critical constants of some common gases are given in the following table. We see that although Zc is less than 0.375, the disprepancy is rather small. 

In the original equation of van Laar, the effective molar volume was assumed to be independent of composition this assumption implies zero volume-change of mixing at constant temperature and pressure. While this assumption is a good one for solutions of ordinary liquids at low pressures, it is poor for high-pressure solutions of gases in liquids which expand (dilate) sharply as the critical composition is approached. The dilated van Laar model therefore assumes that... 

We have seen that the value of an equilibrium constant tells us whether we can expect a high or low concentration of product at equilibrium. The constant also allows us to predict the spontaneous direction of reaction in a reaction mixture of any composition. In the following three sections, we see how to express the equilibrium constant in terms of molar concentrations of gases as well as partial pressures and how to predict the equilibrium composition of a reaction mixture, given the value of the equilibrium constant for the reaction. Such information is critical to the success of many industrial processes and is fundamental to the discussion of acids and bases in the following chapters. 

Arrhenius recognized that for molecules to react they must attain a certain critical energy, E. On the basis of collision theory, the rate of reaction is equal to the number of collisions per unit time (the frequency factor) multiplied by the fraction of collisions that results in a reaction. This relationship was first developed from the kinetic theory of gases . For a bimolecular reaction, the bimolecular rate constant, k, can be expressed as... 

The macroscopic properties of the three states of matter can be modeled as ensembles of molecules, and their interactions are described by intermolecular potentials or force fields. These theories lead to the understanding of properties such as the thermodynamic and transport properties, vapor pressure, and critical constants. The ideal gas is characterized by a group of molecules that are hard spheres far apart, and they exert forces on each other only during brief periods of collisions. The real gases experience intermolecular forces, such as the van der Waals forces, so that molecules exert forces on each other even when they are not in collision. The liquids and solids are characterized by molecules that are constantly in contact and exerting forces on each other. 

Table 2.4 displays critical constants Tc, Pc, Vc and critical compressibility factor Zc for a number of common gases. (Accurate determination of the critical point is experimentally challenging, and quoted values are generally uncertain in the final decimal.) One can see from the table that many common gases (including N2, 02, and CH4) are actually supercritical fluids ( permanent gases ) under ambient temperature conditions, incapable of liquefaction by any applied pressure whatsoever. (Aspects of cryogenic gas-liquefaction techniques are discussed in Section 3.6.3.)... 

For a gas, the effect of pressure on the viscosity depends on the region of P and T of interest relative to the critical point. Near the critical state, the change in viscosity with T at constant pressure can be very large. The correlation of Uyehara and Watson [15] is presented for the reduced viscosity estimated from the corresponding-states method. The critical viscosities of a few gases and liquids are available [15]. These are necessary to calculate the... 

A distinction must be made between Ihe coniacl potentials in air and the so-called "intrinsic contact potentials in a vacuum with all adsorbed gases removed According to Millikan, the intrinsic potential difference between two metals A and B is expressed by VAfl = (i(v4 - vg /e. in which It is Planck s constant. t, i and ug are the critical frequencies of phutoeleclric emission for the two metals (see Photoelectric Effect), and e is the electronic charge. In any ease, if (he electronic work funclions of the metals are )>,t and ps- the contact potential difference is V. sa = [p./, - pn)/e. The work funclions. and hence V, . are in general dependent upon the medium surrounding the metals. Accurate measurements of these potentials are. unlorlunnlely, very difficult. 

A power plant operating on heat recovered from the exhaust gases of internal-combustion < uses isobutane as the working medium in a modified Rankine cycle in which the upper pressure I is above the critical pressure of isobutane. Thus the isobutane does not undergo a change of p" as it absorbs heat prior to its entry into the turbine. Isobutane vapor is heated at 4,800 kPa to 2 and enters the turbine as a supercritical fluid at these conditions. Isentropic expansion in the turh produces superheated vapor at 450 kPa, which is cooled and condensed at constant pressure, resulting saturated liquid enters the pump for return to the heater. If the power output of the modi Rankine cycle is 1,000 kW, what is the isobutane flow rate, the heat-transfer rates in the heater condenser, and the thermal efficiency of the cycle ... 

The physical properties of supercritical fluids tend to lie between those of gases and liquids. The increased density relative to a gas, and the decreased viscosity relative to a liquid, allow supercritical fluids to be used as excellent solvents in many laboratory and industrial applications (19-25). Also, some notable solvation peculiarities of supercritical fluids have been discovered. For example, supercritical water can dissolve nonpolar oils because the dielectric constant of supercritical water decreases drastically near the critical point (26). 

A critical characteristic of energetic materials is the Chapman-Jouguet (CJ) state. This describes the chemical equilibrium of the products at the end of the reaction zone of the detonation wave before the isentropic expansion. In the classical ZePdovich-Neumann-Doring (ZND) detonation model, the detonation wave propagates at constant velocity. This velocity is the same as at the CJ point which characterizes the state of reaction products in which the local speed of sound decreases to the detonation velocity as the product gases expand. 

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