Like the simple example of boiling a pot of water, there are many processes which may contain a substance capable of being both a liquid and a vapor at the operating conditions:

- evaporation
- drying
- (de)humidification
- condensation

In this course, we will not deal with mass transfer operations
(you will learn that in a year or two), so we will not discuss how
a system actually *gets* to equilibrium or how *fast* it
gets there, but we will simply accept the fact that it is or is not
at equilibrium.

There are a number of important definitions that will help us clearly discuss vapor-liquid systems in equilibrium.

A vapor in equilibrium with a liquid is said to be
**saturated**.

A vapor which has a partial pressure less than the saturation
value is **superheated**.

The **dew point** is the temperature at which saturation will
occur in the gas phase (for a given pressure).

The **bubble point** is the temperature at which saturation
will occur in the liquid phase (for a given pressure).

**Degrees of superheat** refers to the difference in
temperature between the actual temperature and the dew point.

If we have a two component mixture which has one of its
components in both the liquid and vapor phase (let's consider air
and water):

Gibbs: DF = 2+2-2=2

Therefore fixing two intrinsic variables will fix the thermodynamic state of the system! (i.e., tell me the temperature and the pressure, or the pressure and the composition, etc.)

If we continue with our water/air mixture, we could calculate the composition if we fixed the temperature and pressure (since we only had two degrees of freedom).

At equilibrium, this system would obey Raoult's Law (for a
single condensable species):

y_{i}P = p_{i}^{*} = p_{i}

Raoult's Law looks very much like our ideal gas expression for
partial pressures, except that the partial pressure is **equal**
to the vapor pressure (since we are at equilibrium).

The above example was a simple one: air and water. Why?

In real multi-phase, multi-component processes it is often the
case that we have multiple components in **both** the liquid and
gas phases. This makes the problem of using physical laws to
determine these compositions more difficult. (But the Gibbs Phase
Rule still applies for determining just *how much* we can
theoretically calculate)

Just like in the last chapter with the gas phase,
multi-component, multi-phase systems **also** may behave as
*ideal* and *non-ideal*; however, you will take a course
(the Thermodynamics Pillar) that will help you to determine the
non-ideal ones, so for the most part (see Txy and relative
volatility), in this class, we will assume that the solution is
ideal.

With ideal solutions in gas-liquid equilibrium, we have two options:

- Raoult's Law: y
_{i}P = x_{i}p_{i}^{*}(T)

(Useful when x_{i}~ 1 ... see our example above) - Henry's Law: y
_{i}P = x_{i}H_{i}(T)

(Useful when x_{i}~ 0)

NOTE: The (T)'s are simply a reminder that the vapor pressure (and Henry's constant) are functions of T only.

Use ideal solution expressions to determine the composition of liquids and their corresponding vapors (Distinguish between when Henry's Law and Raoult's Law would be applicable)

Let's look at an example:

Using Raoult's or Henry's Law for each substance, calculate
the pressure and gas-phase composition in a system containing a
liquid that is 0.3 mole % N_{2} and 99.7% water in
equilibrium with water vapor and N_{2} gas at 80C. (Note
that the N_{2} is considered a condensable component for
this problem.)

**Bubble** (composition of the liquid is given) and
**Dew** (composition of the gas is given) point temperature
calculations are obtained by iteratively solving for the
temperatures, using one of our partial pressure equations and
either x_{i} must sum up to one (for dew-point
calculations) or that the partial pressures must sum to the total
pressure (bubble-point calculation).