Standard state Henrian

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].

The activity of Ni in molten Fe-Ni at 1850 K using the Henrian standard state is also given in the figure (ordinate given on the right-hand y-axis). 

Correspondingly, a formal definition of a Henrian standard state for component B of a solution is... 

To resolve these problems, we now define a new standard state called the Henrian standard state which originates from Henry s law. 

The Henrian standard state is a hypothetical, non-physical state for component j. suppose that we are interest in the composition marked x in the following figure ... 

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. 

Note that both the Henrian standard state and lwt% standard state are based on Henry s law. The difference is that the former is at Nj = 1 on the Henry s law line whereas the latter is at wt% j = 1. Note also that in dilute solutions in which j obeys Henry s law the value of aj(wM) numerically the seme as (wt% j). 

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. 

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... 

Calculate the activity of silicon in the same alloy, but relative to the Henrian standard state. 

Much of the discussion thus far has been concerned with binary solutions. Most practical systems, however, are more complex and consist of several components. It is now in order to examine the thermodynamics of solutions which contain several dilute solutes. The activity of B in dilute solution with respect to the Henrian standard state is given by... 

When defining a Henrian standard state, it is imperative to consider those species actually existing in the infinitely dilute solution, or behavior according to Henry s law will not be observed. In the case of electrolytes, this means that the individual ions must be selected as the species of interest. The standard state of each ionic species is chosen so that the ratio of its activity to its concentration becomes one at infinite dilution, at 101.325 kPa pressure, and the actual temperature. 

Replacing the activities of S and V by their surface excesses and defining a Henrian standard state for S yields... 

As both the Henrian and 1 wt% standard states are based on Henry s law, for dilute solutions,... 

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. 

Single ion activities should be used for components where the activities are expressed in terms of the ideal dilute solution as the standard state (Henrian activities). 

This standard state is so defined that the Henrian activity approaches the atom fraction at infinite dilution, i.e. 

Assuming that the solution obeys Henry s law up to 1 wt % of A, then h is unity at this concentration, and thus the standard state is the 1 wt% solution. Deviations from this equality of activity and weight percent are measured in terms of Henrian activity coefficient relative to the infinitely dilute, weight percent standard state, i.e. 

Though in both the equations (6.27) and (6.30) h and f have been used for denoting the Henrian activity and activity coefficient of A respectively, in Eq.(6.27) they signify relative to the infinitely dilute, atom fraction standard state, while in Eq.(6.30) they are relative to the infinitely dilute, weight percent standard state. 

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