I The Ideal Gas

I The ideal gas law relates the amount of a gas present to its pressure, temperature, and volume. 

I The ideal gas law can be used to find molar mass If the mass of the gas is known, or the density of the gas if its molar mass Is known,... 

Figure 5.8 I The ideal gas model breaks down at high pressures and low temperatures.

Laboratory experiments show that for a wide range of conditions the pressure (p), volume (V) and temperature (7) of all gases follow closely the same relationship, which is called the ideal gas equation. In SI units (see Appendix I), the ideal gas equation can be written in the following forms. For mass m (in kilograms) of a gas... 

C of the mixture in the ideal gas state Cpgp = Cp of the component i in the ideal gas state = weight fraction of component /... 

U p = internal molar energy of component i at 25°C and in the ideal gas state... 

It suffices to carry out one such experiment, such as the expansion or compression of a gas, to establish that there are states inaccessible by adiabatic reversible paths, indeed even by any adiabatic irreversible path. For example, if one takes one mole of N2 gas in a volume of 24 litres at a pressure of 1.00 atm (i.e. at 25 °C), there is no combination of adiabatic reversible paths that can bring the system to a final state with the same volume and a different temperature. A higher temperature (on the ideal-gas scale Oj ) can be reached by an adiabatic irreversible path, e.g. by doing electrical work on the system, but a state with the same volume and a lower temperature Oj is inaccessible by any adiabatic path. 

Other conventions for treating equiUbrium exist and, in fact, a rigorous thermodynamic treatment differs in important ways. Eor reactions in the gas phase, partial pressures of components are related to molar concentrations, and an equilibrium constant i, expressed directiy in terms of pressures, is convenient. If the ideal gas law appHes, the partial pressure is related to the molar concentration by a factor of RT, the gas constant times temperature, raised to the power of the reaction coefficients. 

The origin of the fugacity concept resides in Eq. (4-72), an equation vahd only for pure species i in the ideal gas state. For a real fluid, an analogous equation is written ... 

The definition of fugacity is completed by setting the ideal-gas-state fugacity of pure species i equal to its pressure ... 

The definition of the fugacity of a species in solution is parallel to the definition of the pure-species fugacity. An equation analogous to the ideal gas expression, Eq. (4-73), is written for species i in a flmd mixture ... 

A simplified estimate can be made by first converting the flow at actual conditions to the flow at standard conditions (i.e., at 70 F and 1 atm). The calculation basis for the linear velocity assumes a roughness coefficient of 0.0005 and a kinematic viscosity for air of 1.62 x lO fF/sec. From the ideal gas law, the following expression is developed ... 

Since non-ideal gases do not obey the ideal gas law (i.e., PV = nRT), corrections for nonideality must be made using an equation of state such as the Van der Waals or Redlich-Kwong equations. This process involves complex analytical expressions. Another method for a nonideal gas situation is the use of the compressibility factor Z, where Z equals PV/nRT. Of the analytical methods available for calculation of Z, the most compact one is obtained from the Redlich-Kwong equation of state. The working equations are listed below ... 

The total energy of condensation from the ideal gas to the liquid state (the reverse process of vaporization) as a consequence of 1-1 contacts (i.e., intermolecular interactions of component 1 with like molecules) is the product of the energy of condensation per unit volume, the volume of liquid, and the volume fraction of component 1 in the liquid, or... 

V = V . In such a case, V can be obtained directly from the ideal gas law, without recourse to measurement, and hence, the volumetric composition can be readily computed. On the other hand, in non-ideal (i.e., real) mixtures and solutions,... 

If each component gas as well as the mixture obeys the ideal gas law, it follows that the pure-component volume of component i is... 

Kautz, C. H., Lovrude, M. E., Herron, R R. L., McDermott, L. C. (1999). Research on student understanding of the ideal gas law. Proceedings, 2nd International Conference of the European Science Education Research Association (ESERA), Kiel, Germany, I, 83-85. 

We can use the ideal gas equation to calculate the molar mass. Then we can use the molar mass to identify the correct molecular formula among a group of possible candidates, knowing that the products must contain the same elements as the reactants. The problem involves a chemical reaction, so we must make a connection between the gas measurements and the chemistry that takes place. Because the reactants and one product are known, we can write a partial equation that describes the chemical reaction CaC2(. ) +H2 0(/) Gas -I- OH" ((2 q) In any chemical reaction, atoms must be conserved, so the gas molecules can contain only H, O, C, and/or Ca atoms. To determine the chemical formula of the gas, we must find the combination of these elements that gives the observed molar mass. 

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