Ideal-gas state

Next the properties of each component must be determined at the temperature being considered in the ideal gas state and, if possible, in the saturated liquid state. 

Generally the properties of mixtures in the ideal gas state and saturated liquids are calculated by weighting the properties of components at the same temperature and in the same state. Weighting in these cases is most often linear with respect to composition ( ), ... 

Properties of mixtures as a real gas or as a liquid under pressure are determined starting from the properties of mixtures in the ideal gas state or saturated liquid after applying a pressure correction determined as a function of a property or a variable depending on pressure )... 

The other method is to employ the principle of corresponding states and calculate the Cp/ of the mixture in the liquid phase starting from the mixture in the ideal gas state and applying an appropriate correction ... 

The enthalpy of pure hydrocarbons In the ideal gas state has been fitted to a fifth order polynomial equation of temperature. The corresponding is a polynomial of the fourth order ... 

Hgp = enthalpie of the component i in the ideal gas state Xw = weight fraction of the component i... 

It is necessary to determine first the properties of each component in the ideal gas state, next to weight these values in order to obtain the property of the mixture in the ideal gas state. 

The conductivity of a pure hydrocarbon in the ideal gas state is expressed as a function of reduced temperature according to the equation of Misic and Thodos (1961) ... 

The conductivity of a gas mixture in the ideal gas state can be calculated by the Lindsay and Bromley method (1950) ... 

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

With all components in the ideal gas state, the standard enthalpy of the process is exothermic by —165 kJ (—39.4 kcal) per mole of methane formed. Biomass can serve as the original source of hydrogen, which then effectively acts as an energy carrier from the biomass to carbon dioxide, to produce substitute (or synthetic) natural gas (SNG) (see Euels, synthetic). 

Property changes are readily determined for fluids in the ideal gas state, and these in combination with residual properties are used to compute property changes of real fluids. The computational scheme is suggested in Figure 5, and is based on the following identity ... 

Equation 153 is vaUd only for pure species / in the ideal gas state. For a real fluid, an analogous equation is as follows ... 

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

Hea.t Ca.pa.cities. The heat capacities of real gases are functions of temperature and pressure, and this functionaHty must be known to calculate other thermodynamic properties such as internal energy and enthalpy. The heat capacity in the ideal-gas state is different for each gas. Constant pressure heat capacities, (U, for the ideal-gas state are independent of pressure and depend only on temperature. An accurate temperature correlation is often an empirical equation of the form ... 

For the ideal-gas state there is an exact relation between the constant pressure heat capacity and the constant volume heat capacity, C, via the ideal-gas constant, R. 

From this equation, the temperature dependence of is known, and vice versa (21). The ideal-gas state at a pressure of 101.3 kPa (1 atm) is often regarded as a standard state, for which the heat capacities are denoted by CP and Real gases rarely depart significantly from ideaHty at near-ambient pressures (3) therefore, and usually represent good estimates of the heat capacities of real gases at low to moderate, eg, up to several hundred kPa, pressures. Otherwise thermodynamic excess functions are used to correct for deviations from ideal behavior when such situations occur (3). 

TABLE 2-198 Heat Capacities of Inorganic and Organic Compounds in the Ideal Gas State... 

A substance is in the ideal gas state when the volume of its molecules is a zero fraction of the total volume taken up by the substance and when the individual molecules are far enough apart from each other so that there is no interaction between them. Although this only occurs at infinite volume and zero pressure, in practice, ideal gas properties can be used for gases up to a pressure of two atmospheres with little loss of accuracy. Thermal properties of ideal gas mixtures may be obtained by mole-fraction averaging the pure component values. 

Enthalpy of Formation The ideal gas standard enthalpy (heat) of formation (AHJoqs) of chemical compound is the increment of enthalpy associated with the reaction of forming that compound in the ideal gas state from the constituent elements in their standard states, defined as the existing phase at a temperature of 298.15 K and one atmosphere (101.3 kPa). Sources for data are Refs. 15, 23, 24, 104, 115, and 116. The most accurate, but again complicated, estimation method is that of Benson et al. " A compromise between complexity and accuracy is based on the additive atomic group-contribution scheme of Joback his original units of kcal/mol have been converted to kj/mol by the conversion 1 kcal/mol = 4.1868 kJ/moL... 

---