Gases, density molecular masses

The molecular weight (mean relative molecular mass) was obtained by determination of density but, in order to determine that the gas was monatomic and its atomic and molecular weights identical, it was necessary to measure the velocity of sound in the gas and to derive from this the ratio of its specific heats kinetic theory predicts that Cp/C = 1.67 for a monatomic and 1.40 for a diatomic gas. 

The ideal gas equation and the molecular view of gases lead to several useful applications. We have already described how to cany out calculations involving P-V-n-T relationships. In this section, we examine the use of the gas equation to determine molar masses, gas density, and rates of gas movement. 

The density of a vapour or gas at constant pressure is proportional to its relative molecular mass and inversely proportional to temperature. Since most gases and vapours have relative molecular masses greater than air (exceptions include hydrogen, methane and ammonia), the vapours slump and spread or accumulate at low levels. The greater the vapour density, the greater the tendency for this to occur. Gases or vapours which are less dense than air can, however, spread at low level when cold (e.g. release of ammonia refrigerant). Table 6.1 includes vapour density values. 

Substituting for number density in terms of pressure and expressing mean speed in terms of absolute temperature and molecular mass m then gives the desired final result for total intensity, or number of molecules in an equilibrium gas striking a surface of unit surface area per unit time,... 

Choices A, B, C, and D involve the strength of intermolecular forces. Because the two compounds differ in structure, there would be intermolecular differences between the two compounds. However, because both isomers have the same molecular mass, they would have the same gas density. 

Many students would choose answer choice (E). The reason molecular mass is the wrong answer is the question did not state the conditions when comparing one gas to another. For example, 1 mole of hydrogen gas at 50 K in a 1.0-liter container might have a higher density than 0.01 mole of uranium hexafluoride (UF6 at 200 K in a 20-liter container, even though the UF6 has a greater molecular mass. 

Of a special astronomical interest is the absorption due to pairs of H2 molecules which is an important opacity source in the atmospheres of various types of cool stars, such as late stars, low-mass stars, brown dwarfs, certain white dwarfs, population III stars, etc., and in the atmospheres of the outer planets. In short absorption of infrared or visible radiation by molecular complexes is important in dense, essentially neutral atmospheres composed of non-polar gases such as hydrogen. For a treatment of such atmospheres, the absorption of pairs like H-He, H2-He, H2-H2, etc., must be known. Furthermore, it has been pointed out that for technical applications, for example in gas-core nuclear rockets, a knowledge of induced spectra is required for estimates of heat transfer [307, 308]. The transport properties of gases at high temperatures depend on collisional induction. Collision-induced absorption may be an important loss mechanism in gas lasers. Non-linear interactions of a supermolecular nature become important at high laser powers, especially at high gas densities. 

Two principal mechanisms that may be responsible for mass loss from red giants are considered shock wave-driven winds and radiatively (dust)-dr iven winds. Effect of the periodic shocks accompanying nonlinear oscillations of red giants is most prominent in the outer layers of the stellar atmosphere where shocks are able not only to expel gas but also increase gas density so that some molecular components become supersaturated. In 0-rich stars the most abundant condensible species are silicon monoxide and iron, whereas in C-rich stars these are carbon, silicon carbide and iron. 

This detector was invented by Martin and James (1) and is a universal detector. The design was simplified and subsequently made available by the Gow-Mac Instrument Company. Use of two of these detectors in a dual column mode is the basis for the direct determination of molecular weight (the mass chromatograph). The hydrodynamics of the gas density detector as they apply to the mass chromatograph have been studied (36). 

Mass chromatography is a new form of gas chromatography that uses two gas density detectors operated in parallel and provides (a) mass of components within 1-2% relative without determination of response factors, (b) molecular weight of components within 0.25-1% in the mass range 2—400, and (c) a powerful identification tool by the combined use of retention time and molecular weight data. The theoretical basis of the technique and its scope as a molecular weight analyzer, a qualitative identification tool, and a quantitative analyzer in the polymer field are discussed. 

With the Chromalytics Model MC-2 mass chromatograph, a sample is introduced into the unit, split into two portions, collected onto traps, and then analyzed simultaneously with two gas density detectors as shown in Figure 1. The peak height or area ratios from each detector are measured and the molecular weights calculated from Equation 3. 

Molar masses, and therefore molecular masses, can also be calculated using the ideal gas law. Imagine, for instance, that an unknown gas bubbling up in a swamp is collected, placed in a sample bulb, and found to have a density of 0.714 g/L at STP. What is the molecular mass of the gas ... 

Helium is recommended as carrier and makeup gas Response and sensitivity is based on difference between relative molecular mass of analyte and that of the carrier gas approximate calibration can be done on the basis of relative density The sensing elements (hot wires) never touch sample, thus making GADE suitable for the analysis of corrosive analytes such as acid gases gold-sheathed tungsten wires are most common Best used with SFe as a carrier gas, switched with nitrogen when analyses are required Detector can be sensitive to vibrations and should be isolated on a cushioned base Ultimate sensitivity depends on the number of C-H bonds on analyte... 

It appears as though this compound, CxOy, is carbon monoxide (C + O = 12 + 16 = 28 g/mol). By using this technique, we are able to determine atomic mass, especially for the lighter elements. Even crude gas density experiments may be used along with chemical composition data and known atomic masses to establish molecular mass, which leads us to the molecular formula of a gas. 

EXAMPLE 2 A hydride of silicon that has the empirical formula SiH3 (approximately 31 g/empirical formula) was found to have an approximate gas density at S.T.P. of 2.9 g/L. By comparison with oxygen, whose molecular mass and density are known, the molecular mass of the hydride is... 

The approximate molar mass, calculated from the gas density data, is 89 g/mol. The empirical formula, calculated from the percentage composition data, is C2H3O with the empirical formula unit mass of 43.0. The exact molar mass must be (2)(43) = 86.0 g/mol since this is the only multiple of 43.0 (whole-number multiple) reasonably close to the approximate molecular formula of 89 g/mol. The molecule must be the equivalent of 2 empirical formulas CqHgO. 

Using the kinetic molecular theory, explain why the density of a gas is less than that of a liquid. (Density is mass per unit of volume.)... 

You have learned that the volume of a gas at a certain temperature and pressure is the same as the volume of any other gas at the same temperature and pressure. For example, all gases have the approximate volume of 22.4 L at STP. The molecular masses of different gases, however, are all different. This means that each gas has a different density, or mass per unit of volume. (Look back at Figure 12.7 to see three examples.)... 

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