Gas Laws Remember that gas has mass Pressure Pressure is the amount of force applied to an area. Atmospheric pressure is the weight of air per unit of

Gas Laws

Remember that gas has mass

Pressure• Pressure is the amount

of force applied to an area.

• Atmospheric pressure is the weight of air per unit of area.

P =FA

Pressure• What is pressure?

– Accumulated force of the collisions of atoms• Pascals (Pa) or kilopascals (kPa)

– 1 Pa = 1 newton/square meter = 1 N/m2

• Bar– 1 bar = 105 Pa = 100 kPa

• mm Hg or torr– These units are literally the difference in the height

measured in mm of a mercury barometer. Atmospheres (atm)

– Average value of atmospheric pressure at sea level1 atm = 760 torr = 101.325 kPa

How is Pressure Measured• Barometers and manometers

– Use pressure to elevate a liquid• An open-end manometer is used to measure the difference between atmospheric pressure and that of agas in a vessel.• A closed-end manometer will only measure the pressure of the gas inside the vessel.• Piezoelectric chips

Pressure Conversions• Normal atmospheric pressure at sea level and room

temperature is referred to as standard temperature and pressure, or STP.

• 1 atm = 760 torr = 760 mmHg = 14.7 psi• 1 atm = 101,325 Pa (use kPa)

• Temperature– 25 ºC = 298 Kelvin USE KELVIN! ALL THE

TIME!Kelvin = Celsius + 273 REMEMBER ME!

Gas Laws• There are three gas laws discovered

independently that tell us how gases behave when certain variables are changed.

• Boyle’s• Charles’• Avogadro’s

Boyles Law

PV=k (constant)

V = 1/P x k

Pressure and Volume areInversely Proportional

Charles’ LawVolume and Temperature are directly proportional

V = bT

The temperature that Volume = zero isAbsolute zero

Avogadro’s Law

• Volume of a gas is directly proportional to the number of molecules

• V = naV = volume in litersn = number of molesa = proportionality constant

• Avogadro did not invent Avogadro’s number! It was named after him 50 years after his death

Ideal Gas Law• If PV = k

• And V = bT

• And V = an

• Then PV = nT x constant

• PV = nRT

Ideal Gas Law• Ideal Gas Law is an Equation of State

– Given any three, you can determine the fourth– It is empirically derived

• It expresses what REAL gases approach– At low pressure– High temperature– Using KMT :

• Why is low pressure and high temp conditions required for a gas to approach ideal conditions?

Gas Law Problems

• Use the equation for all problems.

• R = PV nT

• What is constant in the problem?

• Derive the equation and solve.

A 125.01 L balloon is at 250.0K It is heated to 350.0K. What is the volume?

• R = PV nT

• What is constant?• Moles and pressure.• R = V1 = V2

T1 T2

• 175.0 L

Gas Stoichiometry

• One mole of any gas at STP (273K, 1 atm) is 22.4 liters.

• True for Ideal Gases.

• R = PV nT

• P = 1 atm, V = 22.4L, T = 273.15K, and moles (n) = 1.0, then

R = 0.0821 L atm / mol K

Units of R

• There are two common “R”’s– Besides the pirates “rrrrrr”

• 0.0821 L atm /mol k– Used in gas problems

And

• 8.3145 L Kpa / mol K – used in thermo problems, whenever the answer is

in joules

15.0 TL (teraliter) of hydrogen gas at 450 K and 1488 torr was reacted with 273 Tg (teragram) of

iron (III) oxide.

• What is the reaction?

• What is the limiting reactant?

• How much iron will be formed?

• What is the pressure of the water assuming the reaction tank is at the same conditions (temperature and volume) as the reactants?

Gas and Molar Mass

• Whenever moles are used in a relationship– Like the ideal gas law

• It can be thought of as“grams divided by molar mass” – Or– g

molar mass (M)

Molar Mass of Gas

• PV = nRT • P = nRT = (m/M) R T

V V• P = (m)(RT) = d R T

V M M

m = mass, d = density (units = g/L)

Rearrange the Equation

• P = d R T M

• Molar mass = d R T P

• m = mass, d = density (units g/L)

Dalton’s Law

The total pressure of a gas mixture is the sum of thepartial pressures of the gases if they were alone.

Ptotal = P1 + P2 + P3 +…..

Dalton’s Law

• The pressure is a combination of all partial pressures

• It assumes gases have no influence on each other

• Under what conditions do gases act ideally?

Mole Fraction

• Mole Fraction is the fraction of the moles of one substance in a mixture compared to the total number of moles

• Mole fraction

• X1 = n1 = n1 ntotal n1+ n2+ n3+ ……

• If V and T are constant

X1 = P1 or P1 = X1 • Ptotal

Ptotal

Gas Collected Over Water

Gases collected over water always have some water vapor included due to evaporation. (Vapor pressure)If the water level in the flask is equal to the surrounding water, than the inside pressure is equal to the outside pressure. Pin = PO2 + PH2O = P atmospheric

Vapor Pressure

Explaining Vapor Pressure on a Molecular LevelExplaining Vapor Pressure on a Molecular Level• Some of the molecules on the surface of a liquid have

enough energy to escape the attraction of the bulk liquid.

• These molecules move into the gas phase.• As the number of molecules in the gas phase

increases, some of the gas phase molecules strike the surface and return to the liquid.

• After some time the pressure of the gas will be constant at the vapor pressure.

Explaining Vapor Pressure on the Molecular Level

• Dynamic Equilibrium: the point when as many molecules escape the surface as strike the surface.

• Vapor pressure is the pressure exerted when the liquid and vapor are in dynamic equilibrium.

Vapor Pressure

Volatility, Vapor Pressure, and TemperatureVolatility, Vapor Pressure, and Temperature

Vapor Pressure

The Clausius-Clapeyron EquationThe Clausius-Clapeyron EquationWater Vapor Pressure

0 20 40 60 80 100 Temperature ºC

Pre

ssu r

e, k

Pa

0

20

40

6 0

8

0

100

ln P

3.

0

3 .

4

3.

8

4.

2

4

.6

R

H- = lope vap

s

0.0027 0.0032 0.0037 1/Kelvin temp

Kinetic-Molecular TheoryKinetic-Molecular TheoryTheory of moving molecules developed to explain gas

behavior.

Assumptions:Assumptions:

Gases consist of a large number of molecules in constant random motion.

Volume of individual molecules negligible compared to volume of container.

Intermolecular forces (forces between gas molecules) negligible.

Energy can be transferred between molecules, but total kinetic energy is constant at constant temperature.

Average kinetic energy of molecules is proportional to temperature.

Kinetic-Molecular Theory

• Kinetic molecular theory gives us an understanding of pressure and temperature on the molecular level.

• PressurePressure of a gas results results from the number of from the number of collisions per unit time on collisions per unit time on the walls of containerthe walls of container.

Kinetic-Molecular TheoryKinetic-Molecular Theory• Magnitude of pressure given by how often and how

hard the molecules strike. • Since the mass is small, the momentum of the atom is

really small, however there are a lot of atom• What ever increases the number of collisions will

increase the pressure (more atoms in the same space)• What ever increases the kinetic energy of the particle

will increase the pressure (Temperature increase)• Gas molecules have an average kinetic energy but each

molecule has a different energy within a certain range.

• As the temperature increases, the average kinetic energy of the gas molecules increases.

Kinetic-Molecular TheoryKinetic-Molecular Theory

Boltzman DistributionColder gas

Warmer gas

Kinetic Molecular Theory

Kinetic Molecular Theory

• As kinetic energy increases, the velocity of the gas molecules increases.

• Root mean square speedRoot mean square speed, uu, is the speed of a gas molecule having average kinetic energy. It is calculated by taking the square root of the average of the squared speeds of the gas molecules in a gas sample.

• Average kinetic energy, KE, is related to root mean square speed and the molar mass of the gas:

Kinetic-Molecular TheoryKinetic-Molecular Theory

KE = 1/2mKE = 1/2muu22

Application to the Gas LawsApplication to the Gas LawsKinetic-Molecular TheoryKinetic-Molecular Theory

• AsAs volume increases at constant temperaturevolume increases at constant temperature, the average kinetic of the gas remains constant. Therefore, u is constant. However, volume increases so the gas molecules have to travel further to hit the walls of the container. Therefore, pressure decreasespressure decreases.

• If temperature increases at constant volumeIf temperature increases at constant volume, the average kinetic energy of the gas molecules increases. Therefore, there are more collisions more collisions with the container walls and the pressure with the container walls and the pressure increasesincreases.

Molecular Effusion and DiffusionMolecular Effusion and DiffusionIf one particle has more mass than the other, it must be moving slower since they have the same KEavg!

Different gases at the same temperature have different average speeds. The bigger particles are moving slower.

Mathematically:Mathematically:

MRT

u3

The lower the molar mass, M, the higher the rms, uu, for that gas at a constant temperature.

Using Equation• Velocity of a gas particle can be calculated• In AP exam, you will be given the equation:

• urms= (3RT)1/2

M• R is 8.3145 J/k •mol (from KE)• M is in Kg/mol ( molar mass x 10-3)• Derivation on Pg 216

Molecular Effusion and DiffusionMolecular Effusion and Diffusion

Molecular Effusion and DiffusionMolecular Effusion and DiffusionGraham’s Law of EffusionGraham’s Law of Effusion

Molecular Effusion and DiffusionMolecular Effusion and DiffusionGraham’s Law of EffusionGraham’s Law of Effusion• Only those molecules that hit the small hole will

escape through it.• Therefore, the higher the rms the more likelihood of a

gas molecule hitting the hole.• We can show

1

23

3

2

1

2

1

2

1MM

M

M RT

RT

uu

rr

Molecular Effusion and DiffusionMolecular Effusion and DiffusionDiffusion and Mean Free PathDiffusion and Mean Free Path• Diffusion of a gas is the spread of the gas through

space.• Diffusion is faster for light gas molecules.• Diffusion is significantly slower than rms speed

(consider someone opening a perfume bottle: it takes while to detect the odor but rms speed at 25C is about 1150 mi/hr).

• Diffusion is slowed by gas molecules colliding with each other.

• Average distance of a gas molecule between collisions is called mean free path.

Molecular Effusion and DiffusionMolecular Effusion and DiffusionDiffusion and Mean Free PathDiffusion and Mean Free Path• At sea level, mean free path is about 6 10-6 cm.

Ideal vs Real Gases

• Size of atom doesn’t count

• Molecules do not interact

• Kinetic energy (velocity) is directly proportional to temperature

• Size of atom does• Molecules do interact• Even non-polar

molecules interact!• Velocity is not directly

proportional (close but no cigar)

Real Gases: Real Gases: Deviations from Ideal BehaviorDeviations from Ideal Behavior• From the ideal gas equation, we have

• For 1 mol of gas, PV/RT = 1 for all pressures.• In a real gas, PV/RT varies from 1 significantly.• The higher the pressure the more the deviation from

ideal behavior.

nRTPV

Real Gases

• P= nRT V

• Pobs = P’ - factor = P’ – a(n/V)2

• P = nRT V – nb

• The molecules actually take up space

• P = nRT – a(n/V)2 V – nb

• Molecules attract

Van der Waals Equation

• Corrected version of the ideal gas law.

• Uses two constants: a and b – which are experimentally determined and will be given for real gas calculations.

• These constants “correct” the pressure and volume from ideal to real.

nRTnbVV

anP

2

2

Van der Waals equationThis equation is a modification of the ideal gas

relationship. It accounts for attractive forces and molecular volume.

P +an2

V2 (V - nb) = nRT( )Correction for Molecular volume

Correction for attractiveforces between molecules

Clearly, not all gases behave ideal.

Even the same gas acts differently at different temperatures.

Real Gases

• The assumptions of the kinetic-molecular theory break down at low temperature and high pressure.

• Increased collisions between particles change the ideal behavior.

Values for a,b

Gas a (atm ∙L2)/mol2 b (L/mol)

He 0.0341 0.0237

Ne 0.211 0.0171

Kr 2.32 0.0398

Xe 4.19 0.0511

CO2 3.59 0.0427

CH4 2.25 0.0428

NH3 4.17 0.0371

H2O 5.46 0.0305

Van der Waals Equation

• If 1.000 mol of an ideal gas were confined to 22.41 L at 0.0 ºC, it would exert a pressure of 1.000 atm. Use the van der Waals equation and the values of a and b for Cl2 to estimate the pressure exerted by 1.000 mol of Cl2 in 22.41 L at 0.0 ºC.

• a = 6.49 L2-atm/mol2

• b = 0.0562 L/mol

• Converting a gas into a liquid or solid requires Converting a gas into a liquid or solid requires the molecules to get closer to each other:the molecules to get closer to each other:

– cool or compress.cool or compress.

• Converting a solid into a liquid or gas requires Converting a solid into a liquid or gas requires the molecules to move further apart: the molecules to move further apart:

– heat or reduce pressure.heat or reduce pressure.

• The forces holding solids and liquids together The forces holding solids and liquids together are called are called intermolecular forcesintermolecular forces..

Molecular Comparison of Liquids & SolidsMolecular Comparison of Liquids & Solids

Phase ChangesPhase Changes

Energy Changes Accompanying Phase ChangesEnergy Changes Accompanying Phase Changes

Molecular Comparison of Liquids & SolidsMolecular Comparison of Liquids & Solids

• Solid - the attractive forces are stronger than the kinetic energy of the particles– The particles are held in position

• Gas - the attractive forces are weak compared to their kinetic energy– particles move freely, are far apart, and have almost no influence

on one another.• Liquid - the attractive forces between particles pull the particles

close together– The particles have considerable freedom to move about.

Why Aren’t All Substances Gases?

• Democritus’ theory of atoms was dismissed because why don’t all these particles fall apart like sand?

• Why don’t all these particles fall apart like sand?

• If there is nothing holding molecules together, then they should be free to go where ever. Just like an ideal gas.

Dipole-Dipole

• Why does a molecule have a dipole?

• When two molecules approach one another– Positive and negative sides are attracted– This attraction restricts the movement

or– it takes more energy to be a gas

(break the attractive force)

Copyright © 2010 Pearson Education, Inc.

Chapter Eight 59

Dipole–dipole forces: • The positive and negative ends of polar molecules

– are attracted to one another by dipole–dipole forces.– molecules have higher boiling points than nonpolar

molecules of similar size.

Dipoles line up

To minimize repulsion

And maximize attraction

The closer the molecules The more importantIntermolecular forces

Hydrogen Bond

• Hydrogen make particularly strong dipoles– It is a very small atom so it can get real close

• Relatively strong intermolecular force

• The unusual properties of water are due to hydrogen bonding

Hydrogen bond

• O, N, or F atom and a positively polarized hydrogen atom bonded to another electronegative O, N, or F.

• An interaction between an unshared electron pair and the polarized hydrogen

• Hydrogen bonds occur in both water and ammonia.

O

HH O

H

HO

HH

O

HH

O

H

H

Intermolecular bonds are responsible for the “condensed states

Boiling Points

Smaller atoms are more electronegative, so they have more polar bonds. H – bonding is more effective so they have higher boiling points

The higher the molecular weightThe higher the boiling point.Ask why!

London Dispersion Forces

• Why does a noble gas condense into a liquid?– It has no polarity– It is not reactive– What attracts one atom to another?


• On average, the electron distribution in a nonpolar molecule is symmetrical.

• At any instant, it may be unsymmetrical, resulting in a temporary polarity that can attract neighboring molecules.

• All molecules, regardless of structure, experience London dispersion forces.– Only polar molecules experience dipole-dipole


Chapter Eight 69


Can be viewed as an “induced dipole”

Induced Dipoles

• When non-polar molecules approach – The negative electron

clouds repel

– Inducing a dipole

– Which allows the molecules to interact

• Helium freezes at 3K– Have to move really slowly

to induce a dipole

-300

-250

-200

-150

-100

-50

0

Freezing Point

Van Der Waals Forces

• The longer the chain, the higher the boiling point

• The chains get tangled like spaghetti

• Takes more energy to break intermolecular tangles

or in other words

• It has a higher boiling point

-200-150-100

-500

50100150

methane

ethanepropanebutanepentanehexaneheptaneoctane

Alkane Boiling Points

Which has the higher boiling point, melting point and why?

• Heptane or Octane• 1-Decanol or 1- octanol

• Ammonia or methyl amine (NH2CH3)

• Hydrogen sulfide or hydrogen oxide• Hydrogen selenide or hydrogen telluride• Decane or 2,3 diethyl hexane (isomer of decane)• Xenon or krypton

Liquids

• Physical properties of liquids are determined mainly by the nature of their intermolecular forces

Some Properties of LiquidsSome Properties of Liquids

ViscosityViscosity• Viscosity is the resistance of a liquid to flow.• A liquid flows by sliding molecules over each other.• The stronger the intermolecular forces, the higher the

viscosity.Karo syrup vs waterCold oil vs hot oil

Surface TensionSurface Tension• Bulk molecules (those in the liquid) are equally

attracted to their neighbors.beads of water on a newly waxed carmeniscus in graduated cylinder


Surface TensionSurface Tension


Surface TensionSurface Tension• Surface molecules are only attracted inwards towards

the bulk molecules.– Therefore, surface molecules are packed more closely than

bulk molecules.

• Surface tension is the amount of energy required to increase the surface area of a liquid.

• Cohesive forces bind molecules to each other.• Adhesive forces bind molecules to a surface.

Properties of liquidsSurface TensionSurface Tension• Force in the surface of a liquid that makes

the area of the surface as small as possible.

Molecules at thesurface interactonly with neighborsinside the liquid.

Molecules at thesurface interactonly with neighborsinside the liquid.

Properties of liquidsCapillary actionCapillary action

• It is the competition between two forces.

Cohesive forcesCohesive forces

• The attractions between molecules of a substance.

Adhesive forcesAdhesive forces

• Attractions between molecules of different substances.

Properties of liquidsCapillary actionCapillary action

MercuryCohesive is largerthan adhesive.

WaterAdhesive is largerthan cohesive.

Capillary tube

meniscus


Surface TensionSurface Tension• MeniscusMeniscus is the shape of the liquid surface.

– If adhesive forces are greater than cohesive forces, the liquid surface is attracted to its container more than the bulk molecules. Therefore, the meniscus is U-shaped (e.g. water in glass).

– If cohesive forces are greater than adhesive forces, the meniscus is curved downwards.

• Capillary Action: When a narrow glass tube is placed in water, the meniscus pulls the water up the tube.

Properties of liquidsDiffusionDiffusion• This takes place in both liquids and

gases. It is the spontaneous mixing of materials that results from the random motion of molecules.

ViscosityViscosity

• Resistance to flow.

• This increases with increased intermolecular attractions.

• Also, liquids composed of long, flexible molecules can entwine, resulting in increased viscosity - motor oil.

Properties of liquids

CH3CH2CH2

OH

CH3CH CH2

OHOH

CH2CH CH2

OHOHOH

Increasing viscosity

Water is Weird• Most abundant substance on earth’s surface• You are 60% water• High heat capacity• High boiling point• Lower density solid than liquid• High surface tension• High heat of vaporization • Universal solvent

Structures of SolidsStructures of SolidsUnit CellsUnit Cells

• Crystalline solidCrystalline solid: well-ordered, definite arrangements of molecules, atoms or ions.

• Crystals have an ordered, repeated structure.

• The smallest repeating unit in a crystal is a unit cell.

• Unit cell is the smallest unit with all the symmetry of the entire crystal.

• Three-dimensional stacking of unit cells is the crystal lattice.

Hydrogen Bonds in H2O

snowflake

Structures of SolidsUnit CellsUnit Cells

Structures of SolidsUnit CellsUnit CellsThree common types of unit cell.

• Primitive(simple) cubic, atoms at the corners of a simple cube– each atom shared by 8 unit cells;

• Body-centered cubic(bcc), atoms at the corners of a cube plus one in the center of the body of the cube– corner atoms shared by 8 unit cells, center atom completely

enclosed in one unit cell;

• Face-centered cubic(fcc), atoms at the corners of a cube plus one atom in the center of each face of the cube– corner atoms shared by 8 unit cells, face atoms shared by 2

unit cells.

Structures of SolidsStructures of SolidsUnit CellsUnit Cells

Space-Filling Cubic Cells

Crystal Lattice of NaCl

Unit Cell of NaCl

Structures of SolidsStructures of SolidsCrystal Structure of Sodium ChlorideCrystal Structure of Sodium Chloride• Face-centered cubic lattice.• Two equivalent ways of defining unit cell:

– Cl- (larger) ions at the corners of the cell, or

– Na+ (smaller) ions at the corners of the cell.

• The cation to anion ratio in a unit cell is the same for the crystal. In NaCl each unit cell contains same number of Na+ and Cl- ions.

• Note the unit cell for CaCl2 needs twice as many Cl- ions as Ca2+ ions.

Sample Unit Cells

Structures of SolidsStructures of SolidsClose Packing of SpheresClose Packing of Spheres

• Solids have maximum intermolecular forces.• Molecules, atoms or ions can be modeled by spheres.• Crystals are formed by close packing of the

molecules, atoms or ions.• We rationalize maximum intermolecular force in a

crystal by the close packing of spheres.• When spheres are packed as closely as possible,

there are small spaces between adjacent spheres. The spaces are called interstitial holesinterstitial holes.

• Other atoms can sometimes fit into these holes.

Hexagonal Close Packed Spheres

X-Ray Crystallography

Types of Solids

Diamond and Graphite

Cross Section of a Metal

Solids

• Amorphous solids– “super cooled” liquids– glass, rubber, many plastics– gets softer and softer as heated

Solids

• Metallic solids - gold, silver

• Molecular solids - wax, rubber, plastic

• Ionic Solids - sodium chloride

• Covalent-network solids - diamond, graphite

Types and Properties of Solids

Type Network Metallic Group 18 Molecular Ionic

Structure Atom Atom Atom Molecule Ion

Type

of

Bond

Directional

Covalent

Bonds

Nondir.

Delocalized elctrons

London

Dispersion

Forces

Dipole

LD

Van dWaals

Ionic

Properties Hard

High MP

Insulator

Wide range of mp, hardness

Conductor

Very low MP Soft,

Low MP

Insulator

Hard

High MP

Insulator

Example Diamond Silver, iron Argon Ice,

Dry ice

NaCl

KF

Metal Alloys

• Alloy is a mixture of elements with metallic properties

• Substitutional – replaces one element with the other in the structure of the solid– High grade steel – replace some irons with

chromium, vanadium, titanium, etc• Interstitial – fits inside the structure of the solid

– Steel – carbon fits inside of iron atoms

Semiconductors

• Silicon and germanium most common

• Doping – add elements (like an alloy) to change the conductivity

• n-type semiconductor – has more conductivity

• p-type semiconductor – has less conductivity

• p-n junction and transitiors

Vapor Pressure

• What does it mean when something evaporates?

• What does it mean when something boils?

• What is vapor pressure again?

Rate of Escape = Rate of Return

Equilibrium

----time-

What is Vapor Pressure?

• Gas has mass lab– Water has a vapor pressure of 17.2 mmHg@20C

• Pressure is the accumulated collisions– More molecules mean more collisions

• The warmer the water– The higher the vapor pressure

Different Compoundshave

Different Vapor Pressures

• Why?

• How could you test?– Qualitative– Quantitative

Evaporation

• In order for one molecule to escape– It has to break the intermolecular attractions– It has to have enough kinetic energy to leave– Why does one molecule have enough energy to

leave and another does not?• It has to do with the concept of average

Temperature and Kinetic Energy

• Particles with KE greater that Emin can

evaporate. • More particles can

evaporate at higher temperatures(red and blue areas) than at low temperatures (Blue)

Boiling

• Higher temps = higher kinetic energy– More escaping molecules– When the pressure of the escaping molecules

exceeds atmospheric pressure– The solution is said to boil– Vapor pressure = atmospheric pressure

Atmosphere is exerting pressure or colliding with particles.

When the vapor pressure exceeds atmospheric pressure, it boils

What is Boiling, Condensing, Melting, Freezing?

• Heat of Vaporization kJ/mol to go from liquid to gas– Energy to overcome all intermolecular

interactions

• Heat of Fusion kJ/mol to go from liquid to solid– Energy to be able to move past your neighbor


Chapter Eight 117


Heating CurvesHeating Curves

Heating Curve• Energy is exchanged

– Explain the heating curve in terms of the KMT– What happens during the flat parts of the

curve?

Temp

Time

Phase DiagramsPhase Diagrams• Phase diagram: plot of pressure vs. Temperature

summarizing all equilibria between phases.• Given a temperature and pressure, phase diagrams

tell us which phase will exist.• Features of a phase diagram:

– Triple point: temperature and pressure at which all three phases are in equilibrium.

– Vapor-pressure curve: generally as pressure increases, temperature increases.

– Critical point: critical temperature and pressure for the gas.

– Melting point curve: as pressure increases, the solid phase is favored if the solid is more dense than the liquid.

– Normal melting point: melting point at 1 atm.

Phase Diagrams• Any temperature and pressure combination not on a

curve represents a single phase.

Critical Temperature and PressureCritical Temperature and Pressure

• Gases liquefied by increasing pressure at some temperature.

• Critical temperatureCritical temperature: the minimum temperature for liquefaction of a gas using pressure.

• Critical pressureCritical pressure: the minimum pressure required for liquefaction at the critical temperature.


Phase Diagram of Water

Temperature

Pre

ssu

re

solid

gas

liquid

SublimationDeposition

FreezingMelting

EvaporationCondensation

Super critical fluid

Triple Point

Phase Diagram of Water

Temperature

Pre

ssu

re

Super critical fluid

Pressure water changesTo solid.

“Normal” Boiling and Melting Point

1 atm

Pre

ssu

re

Temperature

0 C

100 C

A solutionIn a solution

• The solute can’t be filtered out.• The solute always stays mixed.• Particles are always in motion.• Volumes may not be additive.• A solution will have different properties than the solvent

• A solution consists of two component types.

• solventsolvent - component in the greater concentration

• solutesolute- component in the lesser amount(You may have more than one.)

Physical states of solutions• Solutions can be made that exist in any of the

three states.

• Solid solutionsSolid solutions• dental fillings, 14K gold, sterling silver•

• Liquid solutionsLiquid solutions• saline, vodka, vinegar, sugar water

• Gas solutionsGas solutions• the atmosphere, anesthesia gases

Predicting Solubilites““Like dissolves like.”Like dissolves like.”

Materials with similar polarity are soluble in each other. Dissimilar ones are not.

• MiscibleMiscible - Liquids that are soluble in each other in all proportions such as ethanol and water.

• ImmiscibleImmiscible - Liquids that are not soluble in each other such as hexane and water.

SolubilityA measure of how much of a solute can be

dissolved in a solvent.

Common unit- grams / 100 mL

Factors affecting solubilityFactors affecting solubilityTemperaturePressurePolarity

130

A saturated solution contains the maximum amount of a solute that will dissolve in a given solvent at a specific temperature.

An unsaturated solution contains less solute than the solvent has the capacity to dissolve at a specific temperature.

A supersaturated solution contains more solute than is present in a saturated solution at a specific temperature.

Sodium acetate crystals rapidly form when a seed crystal isadded to a supersaturated solution of sodium acetate.

How much stuff is in a mixture?

• Molarity (M) moles per liter solution

• Normality (N) equivalents per liter solution– 1M H2SO4 has 2X the H+ than 1M HCl

– It has a normality of 2N vs 1N for 1M HCL

• Molality (m) moles per kilogram solvent

• Mole Fraction (X) is ratio of moles to total moles

132

Concentration UnitsThe concentration of a solution is the amount of solute present in a given quantity of solvent or solution.

Percent by Mass

% by mass = x 100%mass of solutemass of solute + mass of solvent

= x 100%mass of solutemass of solution

Mole Fraction (X)

XA = moles of A

sum of moles of all components

133

Concentration Units Continued

M =moles of solute

liters of solution

Molarity (M)

Molality (m)

m =moles of solute

mass of solvent (kg)

In practice we often make a “stock” solution of a chemical and dilute it to a desired level

A solution is prepared by diluting 30.00 mL of a 0.400 M solution of CaCl2 to a final volume of 0.500L.

What is the final concentration of [CaCl2] in this solution?What is the final concentration of [Ca+2]?What is the final concentration of [Cl-1]?

.0300L x 0.400M = .012 moles = .024 molar CaCl2

0.500 L 0.500 L[Ca+2] = 0.024 M[Cl-1] = 2 x 0.024M = 0.048M

135

What is the molality of a 5.86 M ethanol (C2H5OH) solution whose density is 0.927 g/mL?

m =moles of solute

mass of solvent (kg)M =

moles of solute

liters of solution

Assume 1 L of solution:5.86 moles ethanol = 270 g ethanol927 g of solution (1000 mL x 0.927 g/mL)

mass of solvent = mass of solution – mass of solute

= 927 g – 270 g = 657 g = 0.657 kg

m =moles of solute

mass of solvent (kg)=

5.86 moles C2H5OH

0.657 kg solvent= 8.92 m

136

What is the molality of a 5.86 M ethanol (C2H5OH) solution whose density is 0.927 g/mL?

m =moles of solute

mass of solvent (kg)M =

moles of solute

liters of solution

Assume 1 L of solution:5.86 moles ethanol = 270 g ethanol927 g of solution (1000 mL x 0.927 g/mL)

mass of solvent = mass of solution – mass of solute

= 927 g – 270 g = 657 g = 0.657 kg

m =moles of solute

mass of solvent (kg)=

5.86 moles C2H5OH

0.657 kg solvent= 8.92 m

Calculate molarity, molality, mole fraction

Concentrated HCl has a density of 1.19 g/ml and is 38% HCl in water (mass percent)

Molarity1000 mL of solution has a mass of 1190 g.38 x 1190 = 452.2 g HCl452.2 g x 1 mole = 12.4 moles

36.4 g HCl12.4 moles in one liter = 12.4 molar

Mole FractionIn one liter of solution there is 452.2 g HCl = 12.4 molesIn one liter there is 1190 – 452.2g = 737.8 g water = 41.0 moles waterX HCl = 12.4 / (12.4 + 41.0) x 100 = 23.2 %

Molality In one liter12.4 moles HCl in 737.8gOr 0.7378 Kg of water

12.4mole = 16.8 m .7378 Kg

Energy of Solutions

• Remember lattice energies? What are they?E = k (Q1Q2)

r

• When an ionic solid dissolves in water, the lattice energy is overcome. How?– The water surrounds the ions and hydrates them– The water has to get in between the ions or– The ions have to get in between the water molecules

Three Steps to Dissolution

• Step 1– Separate the solute into individual components

– Expanding the solute

• Step 2– Overcoming the intermolecular forces in the solvent to make

room for the solute

– Expanding the solvent

• Step 3– Allowing the solute and solvent to interact to form the solution

140

Three types of interactions in the solution process:• solvent-solvent interaction• solute-solute interaction• solvent-solute interaction

Molecular view of the formation of solution

Hsoln = H1 + H2 + H3

Heat of Solution

ExothermicEndothermic

Heat of Solution Depends on…H1 H2 H3 Hsol Outcome

P Solv

P Solu

Large Large Large

Neg

Small Solution forms

P Solv

NP Solu

Small Large Small Large positive

No solution

NP Solv

P Solu

Large Small Small Large positive

No solution

NP Solv

NP Solu

Small Small Small Small Solution forms

Factors Affecting Solubility

• The structure of a compound determines what it will dissolve

• If it is non-polar, lots of C – H bonds, then it will dissolve in non-polar solvents.

• If it is polar or ionic, it will dissolve in polar solvents

• The polarity of solvent can be measured by its dielectric constant. The higher the constant the more polar it is

Fat Soluble Chemicals• Fat soluble vitamins A,D,E and K. These are non-polar

structures. They can be stored in fat, because fat is non-polar.– If you eat too much of these, you can get sick because they

accumulate in fatty tissue.

• DDT, the insecticide, is fat soluble. It is in all our bodies, even if it has not been sprayed in the US since the 70’s.– DDT bioacculmulates. As you move up the food chain, the

animals store the DDT in their fat. When they are eaten, all the DDT goes to the predator, who then stores it in his fat. As you move up the food chain, there is a greater accumulation of DDT.

Water Soluble Vitamins

• Some vitamins are water soluble. – They are excreted. – If we do not replenish them, they lower their

concentration quickly.

• Vitamin C is a good example– British navy called Limies because they brought

limes– Without the water soluble vitamin C, they were

prone to getting scurvy.

Why did the white bear dissolve in water?

Because it was polar.

147

Pressure and Solubility of Gases

The solubility of a gas in a liquid is proportional to the pressure of the gas over the solution (Henry’s law).

c = kP

c is the concentration (M) of the dissolved gas

P is the pressure of the gas over the solution

k is a constant for each gas (mol/L•atm) that depends only on temperature

low P

low c

high P

high c

Henry’s Law

• The partial pressure of a gas above a solution is proportional to its concentration

P = k C

P = partial pressure in atm

k = constant = L • atm

mol

C = molarity of solution (moles/liter)• Explain using KMT

What is concentration of CO2 in a soda if the partial pressure of above the soda is CO2 is 5.0 atm?

• CCO2 = PCO2 = 5 atm = 0.16 mol kCO2 32 L atm/mol L

Temperature Effects• Solids

– Dissolve faster at higher temperatures– Many solids have a higher solubility at higher

temperatures• Not all. Many sulfates do not

• The only way to find out is to measure/experiment

• Gases– Less soluble at higher temps– Explain use KMT

Water

• As the temperature increases, the levels of dissolved gases lowers

• Oxygen is an important gas for aquatic life– Dissolved oxygen (DO) can be measured– Warmer water holds less oxygen– Fish need the oxygen– Warm water kills certain types of fish

Sol

ubil

ity

(g s

olut

e/10

0g H

2O)

Notice at 90 C there is more solute than solvent!

This solid has a lower solubilityIn hot water than cold

There is almost no differenceIn cold and hot solubility

Temperature ºC

153

Temperature and Solubility

Solid solubility and temperature

solubility increases with increasing temperature

solubility decreases with increasing temperature

154

Fractional crystallization is the separation of a mixture of substances into pure components on the basis of their differing solubilities.

Suppose you have 90 g KNO3 contaminated with 10 g NaCl.

Fractional crystallization:

1. Dissolve sample in 100 mL of water at 600C

2. Cool solution to 00C

3. All NaCl will stay in solution (s = 34.2g/100g)

4. 78 g of PURE KNO3 will precipitate (s = 12 g/100g). 90 g – 12 g = 78 g

GasesS

olub

ilit

y (g

sol

ute/

100g

H2O

)

Warmer temperature meansLess DO (dissolved oxygen)

Poor fishies

Pressure and solubility of gases• Increasing the pressure of a gas above a liquid

increases the concentration of the gas.

• This shifts the equilibrium, driving more gas into the liquid.

Pressure and solubility of gasesHenry’s LawHenry’s Law

At constant temperature, the solubility of a gas is directly proportional to the pressure of the gas above the solution.

cg = kpgas

This law is accurate to

within 1-3% for slightly

soluble gases and

pressures up to one

atmosphere.0 1 2 Pressure (atm)

Solu

bili

ty(g

/10

0g

wate

r)

0.010

0.005

0.000

O2

N2

He

Solubility of some substances Temperature Solubility

Substance oC g/100 mL water

NaCl (s) 100 39.12

PbCl2 (s) 100 3.34

AgCl (s) 100 0.00021

CH3CH2OH (l) 0 -100 infinity

CH3CH2OCH2CH3 (l) 15 8.43

O2 (g) 60 0.0023

CO2 (g) 40 0.097

SO2 (g) 40 5.41

Saturation• When a solution contains as much solute as it

can at a given temperature.

• UnsaturatedUnsaturated - Can still dissolve more.

• SaturatedSaturated - Have dissolved all you can.

• SupersaturatedSupersaturated - Temporarily have dissolved too much.

• PrecipitatePrecipitate - Excess solute that falls out of solution.

Saturated Solutions• At saturation, the solute is in dynamic

equilibrium. The concentration is constant.

• Solute species are• constantly in• motion, moving• in and out of • solution.

Properties ofaqueous solutions• There are two general classes of solutes.

• ElectrolyticElectrolytic• ionic compounds in polar solvents

• dissociate in solution to make ions

• conduct electricity

• may be strong (100% dissociation) or weak (less than 10%, )

• NonelectrolyticNonelectrolytic• do not conduct electricity

• solute is dispersed but does not dissociate

Colligative properties“Bulk” properties that change when you add a

solute to make a solution.

• Based on how much you add but not what the solute is.

• Effect of electrolytes is based on number of ions produced.

Colligative propertiesColligative properties• vapor pressure lowering• freezing point depression• boiling point elevation• osmotic pressure

Colligative PropertiesColligative Properties

Lowering the Vapor PressureLowering the Vapor Pressure

Vapor pressure loweringThe introduction of a nonvolatile solute will reduce

the vapor pressure of the solvent in the resulting solution.

• The vapor pressure of a nonvolatile component is essentially zero.

• It does not contribute to the vapor pressure of the solution.

• However, the solution’s vapor pressure is dependent on the solute mole fraction.


Raoult’s LawRaoult’s LawThe partial pressure exerted by solvent vapor above a

solution, PA, equals the mole fraction of the solvent in the solution, A , times the vapor pressure of the pure solvent, PA.

Recall Dalton’s Law:

AAA PP

totalAA PP


Solute’s Effect on Phase DiagramSolute’s Effect on Phase Diagram

Boiling point elevation• When you add a nonvolatile solute to a solvent, the

boiling point goes up. This is because the vapor pressure has been lowered.

bp = Kbp x molality

• The boiling point will continue to be elevated as you add more solute until you reach saturation.

ExamplesExamples Cooking pasta in salt water Antifreeze

Freezing point depression• When you add a solute to a solvent, the freezing

point goes down.

fp = Kfp x molality• The more you add, the lower it gets.

• This will only work until you reach saturation.

ExamplesExamples “Salting” roads in winter Making ice cream

antifreeze

Ionic vs. covalent substancesIonic substances have a greater effect per mole than

covalent.

• 1 mol/kg of water for glucose = 1 molal

• 1 mol/kg of water for NaCl = 2 molal ions

• 1 mol/kg of water for CaCl2 = 3 molal ions

Effects are based on the number of particles!Effects are based on the number of particles!

bp or fp = iiKbp or fp x molality

Where ii is the van’t Hoff factor that compares the

measured ∆Tmeasured ∆Tbpbp or fp or fp / calculated ∆T/ calculated ∆Tbpbp or fp or fp as nonelectrolyteas nonelectrolyte

Ionic vs. covalent substancesThe ideal van’t Hoff factor for NaCl is 2, because it

consists of 1 mole Na1+ ions and 1 mole Cl1- ions.

Oppositely charged ions in solution collide Oppositely charged ions in solution collide and briefly stick together as one particle. and briefly stick together as one particle. This lowers the ideal van’t Hoff factor.This lowers the ideal van’t Hoff factor.

compound 0.100 m 0.0100 m 0.00100 m Ideal valuesucrose 1.00 1.00 1.00 1.00NaCl 1.87 1.94 1.97 2.00

K2SO4 2.32 2.70 2.84 3.00MgSO4 1.21 1.53 1.84 2.00

The more dilute a solution is and the lower the charges of the ions formed, the closer the value of i i is to the ideal van’t Hoff factor.

Osmosis• The movement of a solvent through a semipermeable membrane from a dilute solution to a more concentrated one.

• Semipermeable membranesSemipermeable membranes, such as cell walls, only allow small molecules and ions to go through.

OsmosisOsmosisEventually the pressure difference between the arms

stops osmosis.

Osmotic pressureThe pressure required to stop osmosis.

osmotic pressure ( osmotic pressure ( ) = ) = iMRTiMRT

ii = van’t Hoff factor

M = molar concentration

T = temperature in Kelvin

R = gas law constant

Since molarity is moles/liter, this equation is just a modified form of the gas law equation.

P = n R TV

Osmotic PressureThree conditions can exist for living cells.

Concentration is the same on both sides.

– isotonicisotonic

Concentration is greater on the inside.

– hypertonic cellhypertonic cell– hypotonic solutionhypotonic solution

Concentration is greater on the outside.

– hypotonic cellhypotonic cell– hypertonic solutionhypertonic solution

Cell in isotonic solution

A red blood cell andplasma have the sameosmotic pressure.

Cells in hypertonic solution

If the level of salt inthe plasma is too high,the cell collapses.

CrenationCrenation - water isdrawn out of the cell.

Cells in hypotonic solution

If the level of saltin the plasma istoo low, the cellswells and ruptures.

HemolysisHemolysis - water isdrawn into the cell.

Dialysis• The process where solvent and other small molecules can pass through a membrane.

• Similar to osmosis but the ‘holes’ in the membrane are larger. As a result, even hydrated ions can pass through.

• The method relies on:

diffusiondiffusion

osmosisosmosis

ultrafiltrationultrafiltration

Dialysis

By passing large amounts of a pure solvent past the membrane, we can flush out all but the largest components.

purewater in

water, ions and small molecule

out

ColloidsHomogeneous mixtures of two or more substances Homogeneous mixtures of two or more substances

which are not solutions.which are not solutions.

The substances are present as larger particles than those found in solution.

Dispersing mediumDispersing medium - The substance in a colloid found in the greater extent.

Dispersed phaseDispersed phase - The substance found

in the lesser extent.

Colloids• For solutions, ions and molecules have a size

of about 10-7 cm.

• In colloids, the particles are larger, with sizes from 10-7 to 10-5 cm.

• The colloidal particles are still too small to settle out of solution due to gravity.

• There are several types of colloids depending on the physical state of the dispersing medium and the dispersed phase.

Types of colloidsDispersingDispersing DispersedDispersed

medium medium phasephase NameName ExampleExample

Gas Liquid Aerosol Fog

Gas Solid Aerosol Smoke

Liquid Gas Foam Whipped cream

Liquid Liquid Emulsion Milk, mayo

Liquid Solid Sol Paint, ink

Solid Gas Solid foam Marshmallow

Solid Liquid Emulsion Butter

Solid Solid Pearls, opals

ColloidsColloids• Tyndall effectTyndall effect - the ability of a colloid to

scatter light. A beam of light can be seen passing through a colloid.

Tyndall EffectLight is scattered by the colloidal-sized particles.

ColloidsColloids• Hydrophilic and Hydrophobic Colloids

• Many times water is the dispersing medium in colloids. The dispersed phase can be either:

• “Water loving” colloids: hydrophilic.•

• “Water hating” colloids: hydrophobic.

ColloidsColloids• Hydrophilic and Hydrophobic ColloidsHydrophilic and Hydrophobic Colloids

• Molecules arrange themselves so that hydrophobic portions are oriented towards each other.

• If a large hydrophobic macromolecule (giant molecule) needs to exist in water (ex. proteins), hydrophobic portions embed themselves into the macromolecule leaving the hydrophilic ends to interact with water.



• Typical hydrophilic groups are polar (containing C-O, O-H, N-H bonds) or charged.

• Hydrophobic colloids need to be stabilized in water by adding a surfactant that reduces the water’s surface tension and permits mixing to occur.


• Adsorption: when something sticks to a surface we say that it is adsorbed.

• If ions are adsorbed onto the surface of a colloid, the colloids appears hydrophilic and is stabilized in water.

• Consider a small drop of oil in water.

• Add to the water sodium stearate.

ColloidsColloids

• Hydrophilic and Hydrophobic ColloidsHydrophilic and Hydrophobic Colloids


• Sodium stearate has a long hydrophobic tail (CH3(CH2)16-) and a small hydrophobic head (-CO2

-Na+).

• The hydrophobic tail can be absorbed into the oil drop, leaving the hydrophilic head on the surface.

• The hydrophilic heads then interact with the water and the oil drop is stabilized in water.



• Most dirt stains on people and clothing are oil-based. Soaps are molecules with long hydrophobic tails and hydrophilic heads that remove dirt by stabilizing the colloid in water.

• Bile excretes substances like sodium stereate that forms an emulsion with fats in our small intestine.

• Emulsifying agents help form an emulsion.

ColloidsColloids• Removal of Colloidal ParticlesRemoval of Colloidal Particles

• Colloid particles are too small to be separated by physical means (e.g. filtration).

• Colloid particles are coagulated (enlarged) until they can be removed by filtration.

ColloidsColloids• Removal of Colloidal ParticlesRemoval of Colloidal Particles

• Methods of coagulation:– heating (colloid particles move and are attracted

to each other when they collide);– adding an electrolyte (neutralize the surface

charges on the colloid particles).

• Dialysis: using a semipermeable membranes separate ions from colloidal particles.

Suspension

• In a suspension, the particles temporarily remain mixed because of collisions with the much smaller particles of the solvent. They appear to move in a zig-zag pattern, called Brownian Brownian MotionMotion.

• In suspensions, the particles are larger than 10-4 cm, which can be viewed under a microscope.

• The suspended particles will eventually settle out of the mixture due to gravity.

Documents

Gas Laws Remember that gas has mass Pressure Pressure is the amount of force applied to an area. Atmospheric pressure is the weight of air per unit of