Gas Law Relationships

Before we start describing the gas law relationships, we will need to describe the concept of pressure. When we use the word pressure with respect to gases, we may be referring to the pressure of a gas inside a container or we might be referring to atmospheric pressure, the pressure due to the weight of the atmosphere above us. The pressure at sea level is 1 atmosphere (atm). Commonly, the unit torr is used for pressure, where 1 torr = 1 mm Hg (millimeters of mercury), so that atmospheric pressure at sea level equals 760 torr. The SI unit of pressure is the pascal (Pa), so that latm = 760 mm Hg = 760 torr = 1.01325 X 10s Pa (or 101.325 kPa). 

We can use the gas law relationships, especially the ideal gas law and the combined gas law, in reaction stoichiometry problems. For example, suppose you have 2.50 g of an impure sample of KC103 and you want to determine how many grams of pure KC103 are present. You heat the mixture and the KC103 decomposes according to the equation ... 

Before we leave the Kinetic Molecular Theory (KMT) and start examining the gas law relationships, let s quantify a couple of the postulates of the KMT. Postulate 3 qualitatively describes the motion of the gas particles. The average velocity of the gas particles is called the root mean square speed and is given the symbol rms. This is a special type of average speed. 

The gas laws relate the physical properties of volume, pressure, temperature, and moles (amount) to each other. First we will examine the individual gas law relationships. You will need to know these relations for the AP exam, but the use of the individual equation is not required. Then we will combine the relationships in to a single equation that you will need to be able to apply. But first, we need to describe a few things concerning pressure. 

The gas law relationships can be used in reaction stoichiometry problems. For example, suppose you have a mixture of KC103 and NaCl, and you want to determine how many... 

Ideal Gas Law relationship describing the behavior of an ideal gas, PV = nRT where P is the pressure, V is volume, n is number... 

Volumetric flow rates of different gases are often compared to equivalent volumes of air at standard atmospheric temperature and pressure. The ideal gas law works well when used to size fans or compressors. Unfortunately, the gas law relationship, PV/T = constant, is frequently applied to choked gas streams flowing at sonic velocity. A typical misapplication could then be the conversion to standard cubic feet per minute in sizing SRVs. Whether the flow is sonic or subsonic depends mainly on the backpressure on the SRV outlet. In the API calculations, this is taken into account by the backpressure correction factor. 

Following Henry s gas law relationship, as the pressure of the gas increases, the solubility increases in direct ratio. Doubling the pressure of C02 doubles the solubility. Charts such as the ABCB Gas Volume Test Charts indicate the gas volumes of C02 dissolved in water at different pressures and temperatures. The charts are based on the solubility of C02 in water and the absence of other gases. Using these charts for sparkling wine and not correcting for the presence of other gases can lead to substantial error. 

Skill 15.8 Setting up and solving problems involving gas law relationships. See Skill 15.6. 

During this type of measurement, the volume of gas adsorbed by a unit mass of solid denoted by VyW depends on the equilibrium pressure, the absolute temperature, the solid, and the gas. The adsorbable gas will be below it s critical temperature and the pressure inside the equipment as measured by the manometer shown is expressed as a fraction of the saturation vapour pressure P. The resulting ratio P/P is called relative pressure. The amount of gas adsorbed can be calculated using the gas law relationships, the measured pressures, and known volumes of the equipment. 

Density is the most commonly measured property of a gas, and is obtained experimentally by measuring the specific gravity of the gas (density of the gas relative to air = 1). As pressure increases, so does gas density, but the relationship is non-linear since the dimensionless gas compressibility (z-factor) also varies with pressure. The gas density (pg) can be calculated at any pressure and temperature using the real gas law ... 

Charles and Gay-Lussac, working independently, found that gas pressure varied with the absolute temperature. If the volume was maintained constant, the pressure would vary in proportion to the absolute temperature [I j. Using a proportionality constant R, the relationships can be combined to form the equation of state for a perfect gas, otherwi.se known as the perfect gas law. 

Many process components do not conform to the ideal gas laws for pressure, volume and temperature relationships. Therefore, when ideal concepts are applied by calculation, erroneous results are obtained—some not serious when the deviation from ideal is not significant, but some can be quite serious. Therefore, when data are available to confirm the ideality or non-ideality of a system, then the choice of approach is much more straightforward and can proceed with a high degree of confidence. 

The solution of the work compression part of the compressor selection problem is quite accurate and easy when a pressure-enthalpy or Mollier diagram of the gas is available (see Figures 12-24A-H). These charts present the actual relationship of the gas properties under all conditions of the diagram and recognize the deviation from the ideal gas laws. In the range in which compressibility of the gas becomes significant, the use of the charts is most helpful and convenient. Because this information is not available for many gas mixtures, it is limited to those rather common or perhaps extremely important gases (or mixtures) where this information has been prepared in chart form. The procedure is as follows ... 

The ideal gas law is readily applied to problems of this type. A relationship between the variables involved is derived from this law. In this case, pressure and temperature change, while n and V remain constant. 

The law of combining volumes, like so many relationships involving gases, is readily explained by the ideal gas law. At constant temperature and pressure, volume is directly proportional to number of moles (V = kin). It follows that for gaseous species involved in reactions, the volume ratio must be the same as the mole ratio given by the coefficients of the balanced equation. 

Using the ideal gas law and the relationship (n — 1) oc p between refractive index n and density p leads us to the refractive index structure function. 

Finally, the Ideal Gas Law can be used to describe the relationship between air density and pressure ... 

According to the ideal gas law, the pressure of a gas is directly proportional to the absolute temperature, that is, P = (nRJV)T. This linear relationship can be represented by P = mT + b, where m is the slope, equal to (nR/V), and b is the intercept of the line, which is zero in the absence of any imprecision in the data. The slope and intercept may thus be determined by linear regression of the four datapoints versus the model equation P = mT + b. 

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. 

We obtain n, the symbol used for the moles of gas, by dividing the mass of the gas by the molecular weight. In effect, n = mass/molecular weight (n = m/MW). Substituting this relationship into the ideal gas law gives... 

Substituting this relationship into the ideal gas law gives... 

In the combined gas equation, we held just the amount constant. If, however, we hold two quantities constant and look at the relationship between the other two we can derive the other common gas laws shown below in Table 5-1. 

It is possible to combine Avogadro s law and the combined gas law to produce the ideal gas equation, which incorporates the pressure, volume, temperature, and amount relationships of a gas. The ideal gas equation has the form of... 

While studying gases in this chapter you will consider four main physical properties—volume, pressure, temperature, and amount—and their interrelationships. These relationships, commonly called gas laws, show up quite often on the AP exam, so you will spend quite a bit of time working problems in this chapter. But before we start looking at the gas laws, let s look at the Kinetic Molecular Theory of Gases, the extremely useful model that scientists use to represent the gaseous state. 

We could work this into the combined gas law, but more commonly the amount of gas is related to the other physical properties through another relationship that Avogadro developed ... 

Most gas law experiments use either the combined gas law or the ideal gas equation. Moles of gas are a major factor in many of these experiments. The combined gas law can generate the moles of a gas by adjusting the volume to STP and using Avogadro s relationship of 22.4 L/mol at STE The ideal gas equation gives moles from the relationship n = PV/RT. 

The pressure dependence, as before, is derived not only from the perfect gas law for p, but from the density-pressure relationship in Z as well. Also, the effect of the stoichiometry of a reacting gas mixture would be in Z. But the mole fraction terms would be in the logarithm, and therefore have only a mild effect on the induction time. For hydrocarbon-air mixtures, the overall order is approximately 2, so Eq. (7.46) becomes... 

Liquid densities can be assumed constant in many systems unless large changes in composition and temperature occur. Vapor densities usually caimot be considered invariant and some sort of FVr relationship is almost always required. The simplest and most often used is the perfect-gas law ... 

This relationship for Newtonian viscosity is valid normally for temperatures higher than 50 °C or more above the Tg. The utility of the Arrhenius correlation can be limited to a relatively small temperature range for accurate predictions. The viscosity is usually described in this exponential function form in terms of an activation energy, Af, absolute temperature T in Kelvin, the reference temperature in Kelvin, the viscosity at the reference T, and the gas law constant Rg. As the temperature approaches Tg for PS (Tg = 100°C), which could be as high as 150°C, the viscosity becomes more temperature sensitive and is often described by the WLF equation [10] ... 

Gas-liquid relationships, in the geochemical sense, should be considered liquid-solid-gas interactions in the subsurface. The subsurface gas phase is composed of a mixture of gases with various properties, usually found in the free pore spaces of the solid phase. Processes involved in the gas-liquid and gas-solid interface interactions are controlled by factors such as vapor pressure-volatilization, adsorption, solubility, pressure, and temperature. The solubility of a pure gas in a closed system containing water reaches an equilibrium concentration at a constant pressure and temperature. A gas-liquid equilibrium may be described by a partition coefficient, relative volatilization and Henry s law. 

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