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

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. 

Tables often indude formation properties of a species in more than one standard state. Develop a relationship between the Gibbs free energy of formation in the liquid and in the gas standard state.

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) ... 

Numerical example For water, the saturation pressure at 7 = 298.15 K is = 0.03169 bar. Using eq. (id.26). the deference between the free energies of formation in the liquid and gas standard states is... 

Comments In this problem we chose the standard states to be in the gas phase. This choice is made arbitrarily and independently of whether the reaction actually takes place in the liquid or in the gas phase. We could have chosen other standard states, for example, liquid for water and/or ethanol and gas or aqueous for ethylene. The first consideration is whether the formation values for the state of choice are available or not (in this problem, for example, liquid and gas state values for ethanol and water can be found in the appendix, but for ethylene the only values listed are for the gas standard state). Once the standard state is fixed, then the activities to be used in the equilibrium constant must match the standard states. In principle, the final answer must be the same regardless of the choice of the standard state, except for possible inaccuracies in the tabulated values. 

Solution We determined that only two of the four reactions are independent. We may choose any two independent reactions to describe the system, namely, any two of the four in R1-R6, or any linear combination of these, such as reactions R5 and R6 in Example m.iq. We choose reactions Ri and R2 and build the stoichiometric table shown below using the gas standard state for all components. 

Problem 14.6 The standard enthalpy of formation of water in the gas standard state is... 

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. 

For the standard chemical potential of a gas, this book will usually use the notation /i°(g) to emphasize the choice of a gas standard state. 

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. 

Standard Hydrogen Electrode The standard hydrogen electrode (SHE) is rarely used for routine analytical work, but is important because it is the reference electrode used to establish standard-state potentials for other half-reactions. The SHE consists of a Pt electrode immersed in a solution in which the hydrogen ion activity is 1.00 and in which H2 gas is bubbled at a pressure of 1 atm (Figure 11.7). A conventional salt bridge connects the SHE to the indicator half-cell. The shorthand notation for the standard hydrogen electrode is... 

Whereas there is no universally accepted specification for marketed natural gas, standards addressed in the United States are Hsted in Table 6 (8). In addition to these specifications, the combustion behavior of natural gases is frequently characteri2ed by several parameters that aid in assessing the influence of compositional variations on the performance of a gas burner or burner configuration. The parameters of flash-back and blow-off limits help to define the operational limits of a burner with respect to flow rates. The yeUow-tip index helps to define the conditions under which components of the natural gas do not undergo complete combustion, and the characteristic blue flame of natural gas burners begins to show yellow at the flame tip. These... 

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