# CRE: Vapor-Phase Reaction Equilibrium

### 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):

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