# Gas-Liquid Systems

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.

##### DEFINITION

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

##### DEFINITION

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

##### DEFINITION

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

##### DEFINITION

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

##### DEFINITION

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

##### DEFINITION

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.)

## Raoult's Law

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):

yiP = pi* = pi

##### NOTE

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).

## Will the real Raoult's Law please stand up....

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)

##### NOTE

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: yiP = xipi*(T)
(Useful when xi ~ 1 ... see our example above)
• Henry's Law: yiP = xiHi(T)
(Useful when xi ~ 0)

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

##### Outcome:

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)

##### Test Yourself

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 % N2 and 99.7% water in equilibrium with water vapor and N2 gas at 80C. (Note that the N2 is considered a condensable component for this problem.)

##### NOTE

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 xi must sum up to one (for dew-point calculations) or that the partial pressures must sum to the total pressure (bubble-point calculation).