Real gases standard state

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. 

Why do we not choose as the standard state for a real gas the state where/ —> P —> 0. (Hint What would be the values of the chemical potentials that we would tabulate at the 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).

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. 

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). 

Later, we will make equilibrium calculations that involve activities, and we will see why it is convenient to choose the ideal gas as a part of the standard state condition, even though it is a hypothetical state/ With this choice of standard state, equations (6.94) and (6.95) allow us to use pressures, corrected for non-ideality, for activities as we make equilibrium calculations for real gases.s... 

The real energy of ion solvation, af, defined by Eq. (2), expresses the change in ion energy upon its transfer from a gas phase into a solution. Unlike the chemical energy of solvation, psi, the value of the real energy of solvation, also in the standard state, can be calculated from experimental data using the formula, e.g., for the hydration of the cation ... 

The standard state for a real gas is thus a hypothetical state in which the gas is at a pressure of p° = 1 bar and behaving ideally. 

In mixtures of real gases the ideal gas law does not hold. The chemical potential of A of a mixture of real gases is defined in terms of the fugacity of the gas, fA. The fugacity is, as discussed in Chapter 2, the thermodynamic term used to relate the chemical potential of the real gas to that of the (hypothetical) standard state of the gas at 1 bar where the gas is ideal ... 

The standard state (and thus any standard thermodynamic property) of a pure solid refers to the pure substance in the solid phase under the pressure p of 1 bar (0.1 MPa). The standard state of a pure liquid refers to the pure substance in the liquid phase at p = 1 bar. When the substance is a pure gas, its standard state is that of an ideal gas at p = 1 bar (or, which is equivalent, that of a real gas at P = o). 

Should we regard 407.1 2.0 kJ mol-1 as the final value for the enthalpy of reaction 2.13 under the experimental conditions Recall that the starting assumption was p = 1 bar and the standard state conditions refer to the ideal gases at that pressure or to the real gases at zero pressure. The ideal gas model (or the ideal gas equation) describes very well the behavior of most gases at 1 bar, so it is... 

That is, as the pressure approaches zero, the fugacity approaches the pressure. Figure 10.5 indicates the relationship between P and/for ideal and real gases. The standard state for a real gas is chosen as the state at which the fugacity is equal to 0.1 MPa, 1 bar, along a line extrapolated from values off at low pressure, as indicated in Figure 10.5. The standard state for a real gas is then a hypothetical 0.1 MPa standard state. 

In addition to the correction for the new standard state, it is necessary to correct for the transformation from the real gas at standard pressure to the ideal gas at standard pressure, which is defined as the standard state. ... 

MPa). Also, a pressure, usually near 1 bar, will exist at which the real gas has a fugacity of unity. bar also real gas at zero pressure. (See Exercise 1, this chapter.) (0.1 MPa). Also, a pressure of the real gas will exist, not zero and not that of unit fugacity, with an entropy equal to that in the standard state. (0.1 Mpa). V =(RT/P°). 

Show that, on this basis, the enthalpy of the gas in the standard state must be equal to that at zero pressure. Hint If the gas were ideal, /= P at aU pressures. For the real gas, f = k = 0.1 MPa. Proceed by analogy with the discussion in Section 10.2.)... 

The first term on the right-hand side is the idea gas limit, and the remaining -logarithmic terms express the successive virial corrections for the real gas behavior. It is evidently most convenient for this problem to choose the standard state pressure as P° = 0, where all gases are ideal. With this choice, we can write the relationship between fugacity and pressure as... 

In general, activity is merely an alternative way to express chemical potential. The general objective is to express fil in a form that emulates the ideal gas expression (6.55), but with the actual vapor pressure PL of component i (rather than that assumed from Dalton s law). The trick will be to choose a standard-state divisor in (6.55) that makes this expression valid for the components of a real solution. 

Gas (g). 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. 

The standard state defined in terms of the ideal gas presents no difficulty. In order to go from the ideal gas to the real gas at the same temperature,... 

The standard state means that for each state a reference state of the aggregate exists. For gases, the thermodynamic standard reference state is taken to the ideal gaseous state at one atmosphere pressure at each temperature. The ideal gaseous state is the case of isolated molecules which gives no interactions and which obey the equation of state of a perfect gas. The standard reference state for pure liquids and solids at a given temperature is the real state of the liquid or solid substance at a pressure of 1 atmosphere. 

Standard-State conventions for chemical elements and dissolved solutes are summarized in Table si. 1. Note that the Standard states for gases and for solutes are hypothetical, ideal states and not actual states. For gases, this choice of Standard State is useful because the ideal gas represents a good limiting approximation to the real behavior of gases and possesses equations of state that are mathematically tractable in applications. For solutes, the choice of a hypothetical Standard State is of value because the alternative choice, consisting simply of the pure solute at unit mole fraction, is not very relevant to a solution component whose concentration must always remain small. Moreover, by... 

It has already been mentioned that the state of an ideal gas at the temperature of the system and the pressure of 1 atmosphere is most frequently chosen as the standard state of gases. The idea of such an ideal gas can be explained by the imagination of a real gas which is first expanded to zero pressure and then by means of isothermal compression compressed to 1 atm. into the region of the ideal gas. As with an ideal gas pressure equals fugacity, we can substitute in equation (V-8a) p° = f° — 1, whereby the following equation is obtained ... 

With respect to composition, the standard states used in this chapter are states of the pure species. For gases, the physical state is the ideal-gas state and for liquids and solids, the real state at the reference pressure and system temperature. 

This step is necessary because, by convention, the standard state of a real gas is actually the hypothetical state of the ideal gas at one bar. Allowance must be made for the difference between these two states in exact determinations. Since the enthalpy of an ideal gas is independent of pressure, the difference between its value and that of the real gas may be determined by integrating Eq. (1.13.17) between pressure 0 and pressure P. In general this value tends to be very small compared to the contribution from all other steps. 

A standard-state pressure of 1 stairdardatirrosphere (101.325 kPa) was irr use for nrairy years, aird older data tabulatioirs are for this pressure. The stairdard is irow 1 bar (10 Pa), but for purposes of this chapter, the differeirce is of iregligible coirsequeirce. With respect to compositioir, the standard states used hr this chapter are states of the pure species. For gases, the physical state is the ideal-gas state aird for liquids aird solids, the real state at the stairdard-state pressure aird at the system temperature. In summary, the standard states used in this chapterare ... 

Property values in the standard state are denoted by the degree symbol. For example, Cp is the standard-state heat capacity. Since the standard state for gases is the ideal-gas state, Cp for gases is identical with Cp , and the data of Table C.l apply to the standard state for gases. All conditions for a standard state are fixed except temperature, which is always the temperature of the system. Standard-state properties are therefore functions of temperature only. The standard state chosenfor gases is a hypothetical one, for at 1 bar actual gases are not ideal. However, they seldom deviate much from ideality, and in most instances enthalpies for the real-gas state at 1 bar and the ideal-gas state are little different. 

Our table refers to the real fluid existing at the standard-state pressure of 1 bar. Since this pressure is below the critical pressure of water [p = 217.6 bar at T = 647.14 K ( ) ], there is a first order transition at the normal boiling point. Therefore, this is a two-phase (liquid-real gas) table for the real fluid at p=l bar. 

STANDARD STATE, REFERS ONLY TO LIQUID-PHASE PROPERTIES AND NOT TO GAS-PHASE PROPERTIES WHICH ARE FOR THE REAL GAS AT P = 1 BAR. 

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