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

Equilibrium 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 0 C and 1 atm Gas PhaseLiquid Phase Mole fraction water Mole fraction oxygen x10 -6 Mole fraction nitrogen x10 -6 Total1.0 The 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 P i is the partial pressure of component i y i is the mole fraction of component i in the gas P is the total gas pressure

Raoult’s Law – Partial Vapor Pressures P i is the partial vapor pressure of component i x i is the mole fraction of component i in the liquid P 0 is the pure component vapor pressure of component i

Raoult’s Law And by extension

Fugacity 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 O 2 in water The O 2 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

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 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

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

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 2 phase

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.