Change in Standard State from Pure Component to the 1 wt%
in Solution

The one weight percent standard
state in designed for convenience when computing the amount of a component in
present in a molten solution. For example, when using the normal pure component
as the standard state, the computation of the amount of Si in molten steel
would proceed as follows:

SiO2 + 2C     = 2CO + Si(l)       (1)

When the1 wt % ss is used, the
standard state of Si is changed from the pure liquid to the 1 wt % ss so that
the computed activity of Si is essentially in wt %.  The activity is given the symbol hSi.  The computation proceeds as follows
where the under score denotes the1 wt % standard state:

SiO2
+ 2C     = 2CO + Si(l)                                                                                                  (1)

Si(l)                =
Si                                                                                                              (2)

______________________

SiO2
+ 2C = 2CO + Si                                                                                                        (3)

where fSi ≈ 1.

Clearly, this is a more convenient method of performing
computations when weight percents are needed.  The need, then, is how to determine the
standard Gibbs energy for the change in standard state for the reaction
(2).  That is now shown.

For the reaction

Si(l)
=   Si                                                                                                              (2)

Starting with the identity for chemical potential and
substituting the standard Gibb’s energies and the definitions of
activities for the two different standard states, gives for the standard
Gibb’s energy change for reaction (2)

Now the value of this Gibb’s Energy can be computed
from any pair of ai and hi that correspond to an
equilibrium condition as required by equating their two chemical
potentials.  There are infinite such
pairs since the equilibrium condition is satisfied by using the same
composition when computing the two activities.  Therefore, one should choose a pair that
is easy to compute.  One such pair
is when hi = 1.  In this
case

The activity coefficient at infinite dilution is used here
rather than the value at 1 weight percent for convenience.  That means that the 1 wt percent
standard state is really

The hypothetical 1 wt% i solution behaving as the infinitely dilute
solution

Some minor adjustment for real solution behavior will be
needed and is shown later.  However,
the adjustment will be small since there is very little difference in the
infinitely dilute solution and the 1 wt% solution.

The mole fraction is fairly precisely approximated as

Therefore

The adjustment in from the ideal solution, which behaves as
the infinitely dilute solution and the real solution is handled using an
activity coefficient fi.

The ideal lines always run through (0, 0) to (1, 1)

This is not unlike the definition of the activity
coefficient when the pure component is the standard state:

The ideal lines always run through (0,0) to (1,1)

The value of fi is always close to unity since
dilute solutions depart little from infinite dilution behavior.  It is recommended not to exceed a
percent, or 2 at most.

ai =1

Figure 1 Relative positions and values of pure and 1 wt%
Standard States