Gases imperfection

Vanderzee, C. E. and W. W. Rodenburg, 1970, Gas Imperfections and Thermodynamic Excess Properties of Gaseous Hydrogen Fluoride, Journal of Chemical Thermodynamics, Vol. 2, pp. 461-478,. 

Note that there is no net change in the number of moles of gas in this equilibrium. Therefore, by Le Chatelier s principle, this reaction will be independent of external pressure (ignoring second-order effects due to gas imperfections). Under these conditions the N of the expl will... 

Gas thermometers that employ equation (1.10) can be constructed to measure either pressure while holding the volume constant (the most common procedure) or volume while holding the pressure constant. The (pV) product can be extrapolated to zero p. but this is an involved procedure. More often, an equation of state or experimental gas imperfection data are used to correct to ideal behavior. Helium is the usual choice of gas for a gas thermometer, since gas imperfection is small, although other gases such as hydrogen have also been used. In any event, measurement of absolute temperature with a gas thermometer is a difficult procedure. Instead, temperatures are usually referred to a secondary scale known as the International Temperature Scale or ITS-90. 

When the 4He CVGT is used between 3.0 and 4.2 K (or the 3He CVGT between 3.0 and 24.5561 K), gas imperfection must be taken into account and equation (A2.2) becomes... 

The standard enthalpy of formation of monomeric HF is a hypothetical state that must be related to that of the real associated liquid, gas, or aqueous solution met in calorimetiy. Considerable difficulty has been encountered in allowing for the heat of association, which varies with temperature and pressure. For example, the presence of traces of water can affect the polymerization by entering into the hydrogen bonding (30) the treatment of results will depend on the association model adopted. The magnitude of corrections for gas imperfections has... 

The correction for gas imperfection may seem small. However, we should keep in mind that an error of — 0.4 J moF affects the free energy by about 125 J mol near room ternperamre because AS would be multiplied by T. An error of 125 J mol would change an equilibrium constant of 1.00 to 1.05, which is a difference of 5%. 

Note 2. The term P(<9V/dE)p, where P is pressure of gas V - its volume and E specific energy, might be considered as a measure of gas imperfection of the detonation products, since for an ideal gas (E= RT), this term would be unity... 

Corner s Equation of State. At the high temps pressures encountered in explosives technology, the perfect gas law is not applicable. The calculation of pressures developed by expls therefore requires the adoption of a suitable equation of state. Furthermore, in calculating the explosion products it is necessary to correct the ideal thermodynamic equilibria of the relevant chem reactions for the effect of the gas imperfection. This correction also depends on the equation of state adopted. Most equations of state, whether empirical or theoretical, are not suitable for application at the high temps pressures developed by expls. Comer has recently discussed a theoretical equation of state applicable to propellent expls (Ref 3)... 

This example is presented because it illustrates most of the thermodynamic methods without the necessity of taking into account the complications arising from gas imperfection of the detonation products... 

Finally, if we allow for gas imperfections by including the second virial term, we can... 

What property of helium makes it particularly suitable for gas thermometry over the temperature range covered by this experiment Is the correction for gas imperfection in this experiment of significant magnitude in relation to the experimental uncertainty If not by how much must the precision of the pressure measurements be improved before gas imperfection corrections become significant How does this depend on the choice of gas to be used ... 

Let us now consider the question of gas imperfections, i.e., the behavior of Zas a function of temperature for the saturated vapor. It is difficult to carry out p-V-Tmeasurements on gases close to condensation and such data are scarce, but data are available for water and theoretical extrapolations have been made for the vapor of normal liquids based on data obtained at higher temperatures. Figure 1 shows the variation of the compressibility factor Z for a saturated vapor as a function of temperature in the... 

The size of the kelvin, the SI temperature unit with symbol K, is defined by the statement that the triple point of pure water is exactly 273.16 K. The practical usefulness of the thermodynamic scale suffers from the lack of convenient instruments with which to measure absolute temperatures routinely to high precision. Absolute temperatures can be measured over a wide range with the helium-gas thermometer (appropriate corrections being made for gas imperfections), but the apparatus is much too complex and the procedure much too cumbersome to be practical for routine use. 

CIlearly the equilibrium constant for a dissociation reaction can be obtained directly from the pressure of a given mass of gas, provided the effect of gas imperfection is known, and provided it is certain that the molecule concerned and its primary dissociation products are the only species present. The first condition is fulfilled in almost all work at pressures near to or less than atmospheric, and only for work of the highest accuracy is it necessary to take gas imperfections into account. The second can be checked by the internal consistency of the results, if the equilibrium constant is determined over a range of temperature. 

A fine example of tliis type of work is the determination of Z)q(I2) from vapour density measurements at high temperatures by Perlman and Rollefson 8 8 These workers were interested in obtaining very accurate values of the equilibrium constant to see whether they exhibited any trend which would indicate the presence of 13 and incidentally in obtaining an accurate value of Dq(12) for comparison with the spectroscopically derived result. They introduced highly purified iodine into a silica bulb of known volume contained in a furnace controlled at temperatures between 723° K and 1,274° K, measured the pressure, and then removed the iodine and weighed it. Gas imperfection for molecular iodine was taken into account, but atomic iodine was assumed to be a perfect gas. 

Palacios by taking account of gas imperfection by a characteristic equation, obtained a good value for the chemical constant of hydrogen (Ih2= 1-105) from the vapour pressure equation. 

We are, then, led in the harmonic approximation under the assumption of a cell model and the neglect of gas phase nonclassical rotation, molar volume, and gas imperfection corrections to Equation 2. We choose to call this the complete equation. ... 

G. F. Curtiss and J. O. Hirschfelder. J. Chem. Phys. 10, 491-6 (1942). Vapor pressure AH vaporization, gas imperfections, water, alcohols, amines. 

Added to this value should be tO.2 kcal mol" (estimated correction for gas imperfection) and -2.8 kcal mol" (calculated enthalpy difference for the ideal gas between 25 C and 164.4 C, the approximate normal boiling point). 

Table 8.1 contains values of the standard entropies of a number of important chemical compounds. These are the molar entropies of the real substances, corrected in the case of gases for gas imperfections, at a pressure of 1 atm. and temperature of 25 °C. 

This equation gives the effect of gas imperfection on the equilibrium constant we notice that as p -> 0, K reduces to... 

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