Ideal gas standard state

Ideal gas, standard state, 936 Ilkovic equation, 1246 Ilkovic, D., polarography, 1424 Image dipole, 896... 

Of particular interest is the solvation process that takes place between the standard states of the solute in the ideal gas and in the solution. At a given temperature Tthe ideal gas standard state is specified by the standard pressure, P° = 0.1 MPa (formerly 0.101 325 MPa = 1 atmosphere was generally sped-... 

Thus, it is customary to express activities of gaseous species in terms of the pressure symbol P. It has to be remembered that Pt in the formulation of K is in fact P/P° and hence has the same numerical value as the pressure in atm unit of the species i only if the latm ideal gas standard state is chosen for species... 

We define the standard state of a real gas so that Eq. (51) is general (i.e., so that it also applies to ideal gases). For ideal gases, the standard state is at 1.0 bar pressure. For real gases, we also use a 1.0-bar ideal gas as the standard state. We find the standard state by the two-step process shown in Fig. 6. First we extrapolate the real gas to very low pressure, where / —> P and the gas becomes ideal (Step I). We then convert the ideal gas to 1.0 bar (step II). The convenience of an ideal gas standard state is that it allows temperature conversions to be made with ideal gas heat capacities (which are pressure independent). Conversion to the real gas state is then made at the temperature of interest. 

Although equilibrium constants for gas-phase reactions are evaluated by (15.14) with data for ideal-gas standard states, they are related by Eq. (15.1... 

The ideal-gas standard state heat of reaction is -42.1 kcal/mol of vinyl acetate for ri and -316 kcal/mol of ethylene for r,. These values are calculated from ideal-gas heats of formation from the DIPPR database. Thus the reactions are quite exothermic, particularly the combustion reaction to carbon dioxide, which also is more sensitive to temperature because of the higher activation energy. 

Thermodynamic data are taken from refs. 44 and 100. AS°, entropy of the recombination reaction. Values of 5° are based on the 1 atm, ideal gas, standard state. A(recombination) =. 4(decomposition) X itr/10as°/4.575 where A (decomposition) is the preferred value. 

The ideal-gas standard-state G° can be looked up from standard references for a large number of substances. 

For nonisothermal processes, the change of energy functions contains a change of standard state. The standard-state values need to be known. The ideal-gas standard-state values are given in standard tables. These have to be looked up or, alternatively, heat capacity data are employed instead of the standard-state values. Consider the change of enthalpy the difference is found by integrating the heat capcity. 

Fugacity is freed from the ideal-gas standard state g°. It is completely determined by the properties of the fluid at the temperature of interest. 

Standard Absolute Ionic Entropies at 25" C (Mol Fraction and Ideal Gas Standard State)" ... 

Literature sources. For ideal-gas standard states, properties of formation can be extracted from spectroscopic experiments via statistical mechanics [7]. In these cases, the final values obtained for the formation properties are usually accurate. However, for condensed-phase standard states, properties of formation are usually obtained by combining values from other kinds of reactions for example, for organics, properties of formation may be obtained by combining property changes during combustion reactions. In these cases, the values for properties of formation may be less accurate than those obtained for ideal gases. 

In these expressions, T is absolute temperature in kelvins and p is the partial pressure of a component in psia. We also calculated the heat of reaction in the ideal gas standard state (25°C, 1 atm) by using available heats of formation of the components. The standard state heat of reaction is -42.1 kcal /mol of vinyl acetate for Rl and -316 kcal /mol of ethylene for R2. The reactions are thus quite exothermic, which we also observed in the laboratory. 

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... 

Entropy of Formation The ideal gas standard entropy of formation (AS°298) of a chemical compound is the increment of entropy associated with the reaction of forming that compound in the ideal gas state from the constituent elements in their standard state definea as the existing phase at a temperature of 298.15 K and one atmosphere (101.325 kPa). Thus ... 

Some workers, while retaining the one-molar ideal solution standard state for the solution phase, use a one-atmosphere standard state in the gas... 

The standard free-energy change AF is the difference between the free energies of the products and reactants when each is in a chosen standard state. These standard states are chosen so as to make evaluation of the free energy as simple as possible. For example, for gases the standard state is normally that corresponding to unit fugacity at the temperature of the reaction. If the gas is ideal, this standard state reduces to 1 atm pressure. 

Standard Partial Molal Ionic Entropies in Water-Methanol Solutions at 25°C (Mol Fraction and Ideal Ionic Gas Standard States)... 

Solution The problem really asks for the calculation of the difference in the free energy of formation between two standard states. The gas standard state is in the hypothetical ideal-gas state at T°, P°, and the liquid is in the pure liquid state at the same temperature and pressure. We construd the following path from the hypothetical ideal-gas state at P°, T° (g), to the saturated vapor at T, to the saturated liquid at T°, to the pure liquid at T, P°. To obtain G°(Z) we add corresponding changes to G°(g) ... 

For the ideal gaseous standard state, is evidently the molar enthalpy of an ideal gas. For standard states based on Henry s law, where y 1 as X ot m 0,lTi is the partial molar enthalpy of the solute in the hypothetical pure substance having yg = 1 or the hypothetical ideal one molal solution respectively. Substances in these strange states have partial molar enthalpies (and volumes) equal to that at infinite dilution, hence providing a method of measurement. This can be seen by considering Equations (8.38) and (8.39), which show that 71° becomes equal to // when y is 1.0. Therefore for Henryan standard states where y, -> 1 as X or m 0, must be the partial molar enthalpy of i at infinite dilution, and for Raoultian standard states where y, 1 as Xj -> 1, //° must be the partial molar enthalpy (the molar enthalpy) of pure i (confirming what we stated by simple inspection, above). 

Figure 7.6 Chemical potential as a function of pressure at constant temperature, for a real gas (solid eurve) and the same gas behaving ideally (dashed curve). Point A is the gas standard state. Point B is a state of the real gas at pressure p. The fugacity / p ) of the real gas at pressure p is equal to the pressure of the ideal gas having the same chemical potential as the real gas (point C).

Finally, it is perfectly possible to choose a standard state for the surface phase. De Boer [14] makes a plea for taking that value of such that the average distance apart of the molecules is the same as in the gas phase at STP. This is a hypothetical standard state in that for an ideal two-dimensional gas with this molecular separation would be 0.338 dyn/cm at 0°C. The standard molecular area is then 4.08 x 10 T. The main advantage of this choice is that it simplifies the relationship between translational entropies of the two- and the three-dimensional standard states. 

As noted earlier, the standard state of a gas is the hypothetical ideal gas at 1 atmosphere and the specified temperature T. 

The values of the thermodynamic properties of the pure substances given in these tables are, for the substances in their standard states, defined as follows For a pure solid or liquid, the standard state is the substance in the condensed phase under a pressure of 1 atm (101 325 Pa). For a gas, the standard state is the hypothetical ideal gas at unit fugacity, in which state the enthalpy is that of the real gas at the same temperature and at zero pressure. 

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). 

For species present as gases ia the actual reactive system, the standard state is the pure ideal gas at pressure F°. For Hquids and soHds, it is usually the state of pure real Hquid or soHd at F°. The standard-state pressure F° is fixed at 100 kPa. Note that the standard states may represent different physical states for different species any or all of the species may be gases, Hquids, or soHds. 

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). 

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