SiO2 + 2C

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

The one weight percent stan= dard 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 compo= nent as the standard state, the computation of the amount of Si in molten steel would proceed as follows:

SiO₂ + 2C =3D 2CO + Si_{(l) &n=
bsp; (1)}

_<=
/sub>

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

&= nbsp; SiO₂ + 2C =3D 2CO + Si= _(l) &n= bsp; = ; &n= bsp; = ; &n= bsp; = ; &n= bsp; = ; (1)

&= nbsp; Si_(l) =3D &nbs= p; Si &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; (2)

= ______________________

&= nbsp; SiO₂ + 2C =3D 2CO + Si &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; (3)

_<=
/sub>

where f_Si ≈ 1.

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

For the reaction

&= nbsp; Si_(l) = =3D Si &n= bsp; = ; &n= bsp; = ; &n= bsp; = ; &n= bsp; = ; &n= bsp; (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)

_<=
/sub>

Now the value of this Gibb’s Energy can be compu= ted from any pair of a_i and h_i that correspond to an equilibrium condition as required by equating their two chemical potentials. There are infinit= e such pairs since the equilibrium condition is satisfied by using the same composition when computing the two activities. Therefore, one should choose a pai= r that is easy to compute. One such = pair is when h_i =3D 1. = In this case

&nbs= p; _<=
/sub>

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. Ho= wever, 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 =

&nbs= p; _<=
/sub>

Therefore

_<=
/sub>

The adjustment in from the ideal solution, which behav= es as the infinitely dilute solution and the real solution is handled using an activity coefficient f_i.

_{<=
/sub> =

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:

_{<=
/sub> =}

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

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

a_i =3D1

Figure 1 Relative positions and values of pure and 1 w= t% Standard States