### Reaction Equilibrium in the Solid and Liquid Phases

Again, we start with the general expression for reactive
equilibrium:

$K = \Pi_i \left [\frac{\hat f_i}{f_i^o} \right ]^{\nu_i}
$

Here, the $f_i^o$ value is the fugacity of species $i$ at the
reference pressure of 1 bar.

As with liquids and solids in the phase equilibrium sections of
the course, we will consider this reference value to be the
*pure species fugacity* ($f_i$), but now it will be
specifically at the reference pressure of 1 bar ($f_i^o$).

If we expand our expression for the mixture fugacity (numerator)
in terms of activity coefficients, we get:

$K = \Pi_i \left [\frac{\hat f_i}{f_i^o} \right ]^{\nu_i}
= \Pi_i \left [\gamma_i x_i \frac{f_i}{f_i^o} \right
]^{\nu_i}$

##### Note:

Since liquids and solids are essentially incompressible, the
pure species fugacity at any pressur is typically very close to the
same as the pure species fugacity at 1 bar. This is why we would
typically choose the **saturation fugacity** ($f_i =
P_i^{sat}$) to be the "correct" value of pure species fugacity.

##### Definition:

If we have very high pressure reactions, we must use the
**Poynting correction** that states:

$\frac{f_i}{f_i^o} = exp \left [\frac{1}{RT}\int_{P^o}^P v_i
dP\right ]$

For most problems, we can still assume the liquid/solid to be
incompressible (so $v_i$ is constant), so that this reduces to

$\frac{f_i}{f_i^o} = exp \left [\frac{v_i}{RT}(P-P^o)\right
]$

Combining these we get:

$K = \Pi_i \left [\gamma_i x_i exp \left
[\frac{v_i}{RT}(P-P^o)\right ] \right ]^{\nu_i}$

which at low pressures gives us:

$K = \Pi_i \left [\gamma_i x_i \right ]^{\nu_i}$

which at low pressures and for an ideal solution gives us:

$K = \Pi_i \left [ x_i \right ]^{\nu_i}$

##### Note:

This last form is what you may be familiar with from Chemistry
classes and is typically called the **law of mass
action**. Remember that it assumes that the fugacity is
independent of pressure and that the solution is ideal!

##### Outcome:

Determine the equilibrium composition for a single-phase,
single-reaction system in liquid phase reactions