Standard state Raoultian

In the following, the Raoultian and Henrian standard states will be presented. These two are the far most frequent standard states applied in solution thermodynamics. Before discussing these standard states we need to consider Raoult s and Henry s laws, on which the Raoultian and Henrian standard states are based, in some detail. 

Figure 3.7 The activity of Ni of molten Fe-Ni at 1850 K using both a Raoultian and a Henrian standard state. Data are taken from reference [3].

If an arbitrary standard state is marked with, a formal definition of a Raoultian standard state for component A of a solution is... 

Here Raoultian standard states are used for both the pure metal and the impurity. The slope dxB/dr of the phase boundaries can now be derived by differentiation with respect to temperature. Let/(xB) denote the left-hand side of eq. (4.35) or (4.36) then (see Lupis, Further reading)... 

The activity of a component in a solution is essentially a relative quantity. From the definition of activity it follows that the numerical value of the activity of a particular component is dependent on the choice of the standard state. There is no fundamental reason for preferring one standard state over another. Convenience dictates the choice of the standard state. Up to now, we have chosen the pure state as the standard state. That is, a pure component in its stable state of existence at the specified temperature and latm pressure is chosen as the standard state. This particular choice is known as the Raoultian standard state. 

The Raoultian standard state is quite satisfactory in dealing with many solution systems. But there are some inconvenience and limitations associated with this standard state ... 

With the Raoultian standard state, it is found not infrequently that the activity of a solute in a dilute solution is very small. 

The numerical value of the activity of j at the Henrian standard state is 1 on the Henrian activity scale, but y° on the Raoultian activity scale. 

This equation relates the activity on the Henrian scale to the activity on the Raoultian scale. The Henrian standard state is sometimes called the infinitely dilute solution standard state because it is mostly used for dilute solutions. 

In thermodynamic considerations of A-B binary solution, if the standard state of B is clanged from the Raoultian standard state to the Henrian standard state, the standard molar free energy changes accordingly. 

In a similar way we may find the free energy change associated with the change in the standard state from the Raoultian to the 1 wt% standard state. 

The standard free energy change at temperature T for the reaction is AG° when Raoultian standard states, i.e., pure liquid A, gaseous B and pure solid M at latm are used. 

It is sometimes more convenient to use alternative standard states for the species involved in the reaction. When die standard state of liquid A is changed from Raoultian to Henrian standard state, the free energy change of the reaction... 

The activity of silicon in a binary Fe-Si liquid alloy containing Nsl = 0.02 is 0.000022 at 1,600°C relative to the Raoultian standard state. The Henrian activity coefficient y% is experimentally determined to be 0.0011. 

Calculate the change of the standard molar free energy of silicon for the change of the standard state from Raoultian to Henrian. 

In the treatment of thermodynamic properties of mixed systems of molten salts or slags used as standard state pure components (Raoultian standard states), the use of single ion activity is to be avoided, as it leads to contradictions. 

Fig. 11.11. Raoultian activities of H2O and CO2 in the binary solution at 600°Cand 2 kb. Data from Bowers and Helgeson (1983). The curved lines are fit to the data with Margules equations, discussed in Chapter 15. The inset refers to a discussion of standard states in Chapter 12.

Changing ideal to mean Raoultian ideality, the ideal one molal standard state would give... 

But we do have a choice as to what kind of activity coefficient we want to use, Raoultian or Henryan. You might think that if the standard state consists of pure i, normally a pure solid or liquid, it might be difficult to use a dilute solution (Henryan) standard state. However, using hypothetical states makes it quite simple, and quite instmctive. But first we consider the Raoultian standard state. 

For water vapor, a gas, the /° = 1 bar standard state is used, but for hquid water, /° is the fugacity of pure water (often approximately equal to the vapor pressure of pure water). This results in / = /° and a = 1 for pure water, the Raoultian standard state. 

We can use a Raoultian standard state (pure water) for the solvent, but its deviation from ideal behavior, whether based on a mole fraction or a molality scale, is often converted to the osmotic coefficient , which does not actually have a standard state. It is an absolute system property. 

Figure 8.7 Henryan activity of sucrose, Raoultian activity of water, and osmotic coefficients in sucrose solutions at 25°C. The inset is an enlargement of the region up to 1 molal, and the circle shows the ideal one molal standard state.

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). 

Vanadium melts at 1720°C (1993 K). The Raoultian activity coefficient of vanadium at infinite dilution in liquid iron at 1620°C (1893 K) is 0.068. Calculate the free energy change accompanying the transfer of the standard state from pure solid vanadium to the infinitely dilute, weight percent solution of vanadium in pure iron at 1620°C. 

---