Standard states hypothetical

Standard states—hypothetical solutions containing unit mole fraction of hydrocarbon data from Wetlaufer et al., 1964. 

Standard states—hypothetical unit mole fraction at 298 K. c Calculated using solubility data reported by Kretschmer and Wiebbe, 1951. d Calculated using data reported by Lannung and Gjaldbaek, 1960. 

Appendix C-2 gives constants for the zero-pressure, pure-liquid, standard-state fugacity equation for condensable components and constants for the hypothetical liquid standard-state fugacity equation for noncondensable components... 

PURE calculates pure liquid standard-state fugacities at zero pressure, pure-component saturated liquid molar volume (cm /mole), and pure-component liquid standard-state fugacities at system pressure. Pure-component hypothetical liquid reference fugacities are calculated for noncondensable components. Liquid molar volumes for noncondensable components are taken as zero. 

FO(I) Vector (length 20) of pure-component liquid standard-state fugacities at zero pressure or hypothetical liquid standard-... 

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 standard state of an electrolyte is the hypothetical ideally dilute solution (Henry s law) at a molarity of 1 mol kg (Actually, as will be seen, electrolyte data are conventionally reported as for the fonnation of mdividual ions.) Standard states for non-electrolytes in dilute solution are rarely invoked. 

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. 

Solutions in water are designated as aqueous, and the concentration of the solution is expressed in terms of the number of moles of solvent associated with 1 mol of the solute. If no concentration is indicated, the solution is assumed to be dilute. The standard state for a solute in aqueous solution is taken as the hypothetical ideal solution of unit molality (indicated as std. state or ss). In this state... 

This procedure can now be repeated with a base D that is slightly weaker than C, using C as the reference. In this stepwise manner, a series of p determinations can be made over the acidity range from dilute aqueous solution to highly concentrated mineral acids. Table 8-18 gives pS bh+ values determined in this way for nitroaniline bases in sulfuric and perchloric acid solutions. This technique of determining weak base acidity constants is called the overlap method, and the series of p kBH+ values is said to be anchored to the first member of the series, which means that all of the members of the series possess the same standard state, namely, the hypothetical ideal 1 M solution in water. 

There are many ways to express the energy of a molecule. Most common to organic chemists is as a heat of formation, AHf. This is the heat of a hypothetical chemical reaction that creates a molecule from so-called standard states of each of its constituent elements. For example, AHf for methane would be the energy required to create CH4 from graphite and H2, the standard states of carbon and hydrogen, respectively. 

The difficulties engendered by a hypothetical liquid standard state can be eliminated by the use of unsymmetrically normalized activity coefficients. These have been used for many years in other areas of solution thermodynamics (e.g., for solutions of electrolytes or polymers in liquid solvents) but they have only recently been employed in high-pressure vapor-liquid equilibria (P7). 

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... 

Standard States of Solutes in Solution For a solute, particularly in situations where only dilute solutions can or will be considered, the usual procedure is to define the standard state in terms of a hypothetical solution that follows Henry s law at either a concentration of. y2 =1 or mi = 1. These standard states are known as Henry s law standard states. The standard state solutions are said to be hypothetical because real solutions at these high concentrations do not follow Henry s law. 

This behavior suggests as a convenient standard state, a hypothetical solution that obeys equation (6.112) when m = 1. In this standard state... 

The standard state is chosen as a hypothetical 1 molar equation that obeys equation (6.135), in which case... 

For a Raoulf s law standard state, H° = Hf and L, = //, — Hf. These are the differences described in Chapter 5. For a Henry s law standard state, H° is the enthalpy in a hypothetical m = 1 (or X2 — 1 or c = 1) solution that obeys Henry s law. To help in understanding the nature of these standard state enthalpies, we will show that... 

The standard state is the hypothetical m — 1 solution that obeys Henry s Law. The values are relative to those for H+ being equal to zero. 

The standard state entropy change refers to the hypothetical process so conducted as to convert pure 1 and 2 to a uniquely specified array of 1, 2 pairs e.g., to the pure 1, 2 compound.In short, the standard state entropy change is just that portion of A/Siir other than AiS jf. ... 

The choice of the standard state is largely arbitrary and is based primarily on experimental convenience and reproducibility. The temperature of the standard state is the same as that of the system under investigation. In some cases, the standard state may represent a hypothetical condition that cannot be achieved experimentally, but that is susceptible to calculations giving reproducible results. Although different standard states may be chosen for various species, throughout any set of calculations it is important that the standard state of a component be kept the same so as to minimize possibilities for error. 

The effect of pressure on AG° and AH0 depends on the choice of standard states employed. When the standard state of each component of the reaction system is taken at 1 atm pressure, whether the species in question is a gas, liquid, or solid, the values of AG° and AH0 refer to a process that starts and ends at 1 atm. For this choice of standard states, the values of AG° and AH0 are independent of the system pressure at which the reaction is actually carried out. It is important to note in this connection that we are calculating the enthalpy change for a hypothetical process, not for the actual process as it occurs in nature. This choice of standard states at 1 atm pressure is the convention that is customarily adopted in the analysis of chemical reaction equilibria. 

Equation 29 implies that is the chemical potential of a hypothetical solution in which XA = 1, but the vapor pressure over the solution still obeys Henry s law as extrapolated from infinite dilution. Thus the standard state is a hypothetical Henry s law solution of unit mole fraction. 

If we take the standard state as the hypothetical 1 molar Henry s law solution (sometimes shortened to hypothetical ideal 1 molar solution, where the ideality referred to is Henry s law ideality in molarity units, that is, the proportionality of partial pressure and molarity, not Raoult s law ideality) we get... 

We are now in a position to consider the difference in chemical potential between a solute in its (hypothetical) standard state in a liquid solution and that same chemical species in its gas-phase standard state. This difference is... 

In our quantum mechanical solvation modeling,12 27 we take the standard state of the vapor to be a 1 molar ideal gas at 298° K and the standard state of the solute to be a hypothetical 1 molar Henry s law solute at the same... 

The mole fraction X in the previous equation is replaced with a new unitless variable at, the species activity. The standard potentials pt° are defined at a new standard state a hypothetical one-molal solution of the species in which activity and molality are equal, and in which the species properties have been extrapolated to infinite dilution. 

Table 5 lists equilibrium data for a new hypothetical gas-phase cyclisation series, for which the required thermodynamic quantities are available from either direct calorimetric measurements or statistical mechanical calculations. Compounds whose tabulated data were obtained by means of methods involving group contributions were not considered. Calculations were carried out by using S%g8 values based on a 1 M standard state. These were obtained by subtracting 6.35 e.u. from tabulated S g-values, which are based on a 1 Atm standard state. Equilibrium constants and thermodynamic parameters for these hypothetical reactions are not meaningful as such. More significant are the EM-values, and the corresponding contributions from the enthalpy and entropy terms. 

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 case of liquid solutions is more complicated because the conventions vary. These are always stated in introductory chapters of the thermochemical databases and deserve a careful reading. In most tables and in the present book, it is agreed that the standard state for the solvent is the pure solvent under the pressure of 1 bar (which corresponds to unit activity). For the solute, the standard state may refer to the substance in a hypothetical ideal solution at unit molality (the amount of substance of solute per kilogram of solvent) or at mole fraction x = 1. 

The experiments are usually carried out at atmospheric pressure and the initial goal is the determination of the enthalpy change associated with the calorimetric process under isothermal conditions, AT/icp, usually at the reference temperature of 298.15 K. This involves (1) the determination of the corresponding adiabatic temperature change, ATad, from the temperature-time curve just mentioned, by using one of the methods discussed in section 7.1 (2) the determination of the energy equivalent of the calorimeter in a separate experiment. The obtained AT/icp value in conjunction with tabulated data or auxiliary calorimetric results is then used to calculate the enthalpy of an hypothetical reaction with all reactants and products in their standard states, Ar77°, at the chosen reference temperature. This is the equivalent of the Washburn corrections in combustion calorimetry... 

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