### Reaction Equilibrium in the Vapor Phase

In general, we have determined that for reactive equilibrium we
have:

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

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

For a vapor-phase reaction, we will assume that the vapor **at
the reference state** behaves ideally, so that the value of
$f_i^o$ = 1 bar.

##### Note:

Just because the reference state behaves ideally, does
**not** mean that the material itself behaves ideally under the
reaction conditions.

with this in mind, we can write our general expression for vapor
phase reaction as

$K = \Pi_i \left [\hat f_i [bar] \right ]^{\nu_i} = \Pi_i
\left [y_i\hat \phi_i P_{tot}[bar] \right ]^{\nu_i}}$

where $\hat f_i^o$ and $P_{tot}$ are in units of bar.

##### Note:

This means that there will be an explicit pressure dependence of
the equilibrium whenever the $\nu_i$ do not cancel!

Recall that, for the special case of an ideal gas mixture, the
term $\hat \phi_i = 1$.

##### Outcome:

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

##### Outcome:

Relate extent of reaction expressions to the equilibrium
constant(s)

##### Test Yourself:

Write an expression for the equilibrium constant in terms of the
initial composition and the reaction coordinate, for the following
vapor-phase reaction (assuming ideal gas behavior):

$C_2H_4(g)+H_2O(g) \Longleftrightarrow C_2H_5OH(g)$