The Simplest Phase Equilibrium Examples and Some Simple Estimating Rules

Chapter 3

When is a system at equilibrium?

For a system to be at equilibrium there can be no spontaneous processes occurring within the system

1. Temperature

It must be at the same temperature as the surroundings

It must have a uniform temperature Steady state is not the same as

equilibrium

Steady State

0

x

T

0

t

T

At steady state different temperatures can exist at different points around the system, but the system does not change with time.

Equilibrium

0

x

T

0

t

T

At equilibrium the temperature is the same throughout the system, and the system does not change with time.

2. Energy

Mechanical Energy can be converted completely to some other form of mechanical energy

It can also be converted completely to heat by a frictional process

Heat can not be converted completely to energy by a frictional process

No moving parts

This means that a system at equilibrium can not have moving parts, because in real systems motion leads to friction – which is irreversible

Constant Pressure

In the absence of restraining gravity, spring, electrostatic, magnetic, osmotic, or surface forces, at equilibrium the system must be at uniform pressure

If it’s not, the pressure difference causes motion

3. No flow of electricity

Electricity flowing through a resistor causes the wire to heat up – the current is changed into heat, which is an irreversible process

Phase Equilibrium

First some definitions Gas – any substance in a gaseous state Vapor – a gas at a temperature below it’s

critical point That means it can condense if we raise the

pressure enough

Liquid-Vapor Phase Equilibrium Consider the liquid water – water

vapor equilibrium To be at equilibrium, the rate of water

molecules leaving the liquid must be the same as the rate of molecules returning to the liquid

Evaporation = condensation Vapor pressure of the liquid =

pressure of the vapor

If the system is not at equilibrium

The liquid either spontaneously boils to transfer mass into the vapor phase until equilibrium is attained, or…

The vapor condenses until the gas pressure equals the vapor pressure of the liquid.

Consider a more complicated system – where air is involved

Water + dissolved air

Air + water vapor

Frictionless piston

There is air dissolved in the water, and water vapor in the gas phase

Composition of Air and Water in Equilibrium at 20 0C and 1 atm

Gas Phase Liquid Phase

Mole fraction water

0.023 .999985

Mole fraction oxygen

0.205 5x10-6

Mole fraction nitrogen

0.772 10x10-6

Total 1.0 1.0The composition of the gas and liquid phases is different

What happens when you change the temperature?

More liquid evaporates, and goes into the vapor phase.

Less gas becomes soluble in the liquid phase

Increasing Complexity

When there is only one substance, the composition of both phases is the same (100%)

When we add additional components, the composition of each phase is different

Chemical Engineers use this fact in separation processes

It’s the basis of distillation columns, liquid extraction, drying operations and crystallization to name a few

How do you predict the composition in each phase of a multicomponent system?

Raoult’s law Henry’s law

Raoult’s Law – Partial Pressure

Pi is the partial pressure of component i

yi is the mole fraction of component i in the gas

P is the total gas pressure

PyP ii

Raoult’s Law – Partial Vapor Pressures

0iii PxP

Pi is the partial vapor pressure of component i

xi is the mole fraction of component i in the liquid

P0 is the pure component vapor pressure of component i

Pyi

Raoult’s Law

0iii PxPy

i

ii

y

PxP

0

And by extension

0 iiPxP

Fugacity

0iii PxPy

Partial Pressure Partial Vapor Pressure

Fugacity of the gas

For ideal gases and for ideal solutions

Fugacity of the liquid

Henry’s Law Used with gases above their critical

temperature For example, consider dissolving O2 in

water The O2 can’t exist as liquid at room

temperature, so we can’t use Raoult’s law

We don’t have a vapor pressure, so we use a “pseudo” vapor pressure called the Henry’s law constant

Henry’s Law

Henry’s Law is identical to Raoult’s law, except that the Henry’s law constant replaces the vapor pressure

iii HxPy

Which equation should I use?

Raoult’s Law deals with vapor-liquid equilibrium

Henry’s Law deals with gas-liquid equilibrium Gases usually do not dissolve in liquids

to any great extent

Problem Solving

Consider a system where water is in equilibrium at one atmosphere with air

0waterwaterwater PxPy

oxygenoxygenoxygen HxPy

nitrogennitrogennitrogen HxPy

We know P= 1 atm, the vapor pressure of water, and the Henry’s law constants for oxygen and nitrogen.

That gives us 3 equations and 6 unknowns!!!

Raoult’s law

Henry’s law

Henry’s law

But we know three more relationships We know that the sum

of the mole fractions in the liquid is 1

The sum of the mole fractions in the gas is 1

The ratio of oxygen gas to nitrogen gas

1 nitrogenoxygenwater yyy

1 nitrogenoxygenwater xxx

266.079.0

21.0

nitrogen

oxygen

y

y

There are lots of ways to solve these systems of equations

Spread Sheet MATLAB Calculator “solve” feature Paper, pencil and brain power

How do you find the vapor pressure and Henry’s law constant values?

Vapor Pressures Steam tables Antoine’s equation

Henry’s Law Constant Appendix A.3 Perry’s Handbook

Two Component Phase diagram

Liquid-Vapor Compositions of Benzene-Tolune at 1 atm

75

80

85

90

95

100

105

110

115

0 0.2 0.4 0.6 0.8 1

Mole fraction benzene

Te

mp

era

ture

, (C

)

Liquid

Vapor

2 phase

Liquid-Vapor Compositions of Benzene-Tolune at 1 atm

75

80

85

90

95

100

105

110

115

0 0.2 0.4 0.6 0.8 1

Mole fraction benzene

Te

mp

era

ture

, (C

)

A 40% benzene-60% toluene solution boils at 94 C, and is in equilibrium with a 64% benzene – 36% toluene vapor

Uses and Limits of Raoult’s and Henry’s Laws

1. In a dilute solution, Raoult’s law will probably apply to the solvent.

2. If the solvent and solute are chemically similar, Raoult’s law will probably apply to both, over the entire range of concentration.

3. If the solvent and solute interact chemically, Raoult’s law will probably do a poor job.

Uses and Limits of Raoult’s and Henry’s Laws

4. Henry’s law works well for most gases unless they interact chemically with the solvent.

5. Henry’s law works well for liquids that are immiscible in water, and only dissolve a small amount.

6. Henry’s law can be used for solvents besides water.

Uses and Limits of Raoult’s and Henry’s Laws

7. You can add a fudge factor, called the activity coefficient, to account for non-ideal behavior.