Transcript States of Matter

Gas Laws
Remember that gas has mass
Pressure
• Pressure is the amount
of force applied to an
area.
F
P=
A
• Atmospheric pressure
is the weight of air per
unit of area.
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 level
1 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 a
gas 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 are
Inversely Proportional
Charles’ Law
Volume and
Temperature
are directly
proportional
V = bT
The temperature that
Volume = zero is
Absolute zero
Avogadro’s Law
• Volume of a gas is directly proportional to the
number of molecules
• V = na
 V = volume in liters
 n = number of moles
 a = proportionality constant
• Avogadro did not invent Avogadro’s number! It
was named after him 50 years after his death
Ideal Gas Law
• If
• And
• And
PV = k
V = bT
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 the
partial 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 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.
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 Temperature
Water Vapor Pressure
The Clausius-Clapeyron Equation
slope =
00.002720
- H vap
R
400.003260
Temperature
ºC
1/Kelvin temp
80 0.0037
100
Kinetic-Molecular Theory
Theory of moving molecules developed to explain gas
behavior.
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.
• Pressure of a gas results
from the number of
collisions per unit time on
the walls of container.
Kinetic-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 Theory
Boltzman Distribution
Colder gas
Warmer gas
Kinetic Molecular Theory
Kinetic Molecular Theory
Kinetic-Molecular Theory
• As kinetic energy increases, the velocity of the
gas molecules increases.
• Root mean square speed, u, 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:
2
KE = 1/2mu
Kinetic-Molecular Theory
Application to the Gas Laws
• As volume 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 decreases.
• If temperature increases at constant volume,
the average kinetic energy of the gas molecules
increases. Therefore, there are more collisions
with the container walls and the pressure
increases.
Molecular Effusion and Diffusion
If 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:
u
3 RT
M
The lower the molar mass, M, the higher the rms, u,
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 Diffusion
Molecular Effusion and Diffusion
Graham’s Law of Effusion
Molecular Effusion and Diffusion
Graham’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
3 RT
r1 u1
M2
M1



3 RT
r2 u2
M1
M2
Molecular Effusion and Diffusion
Diffusion 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 25C 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 Diffusion
Diffusion 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:
Deviations from Ideal Behavior
• From the ideal gas equation, we have
PV
n
RT
• 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.
Real Gases
• P= nRT
V
• P
• Pobs = P’ - factor
= P’ – a(n/V)2
• P
= nRT
V – nb
• The molecules
actually take up space
= 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.
2

n a
 P  2 V  nb  nRT
V 

Van der Waals equation
This equation is a modification of the ideal gas
relationship. It accounts for attractive forces
and molecular volume.
an2
P + 2 (V - nb) = nRT
V
(
)
Correction for
Molecular volume
Correction for attractive
forces 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
Molecular Comparison of Liquids & Solids
• Converting a gas into a liquid or solid requires
the molecules to get closer to each other:
– cool or compress.
• Converting a solid into a liquid or gas requires
the molecules to move further apart:
– heat or reduce pressure.
• The forces holding solids and liquids together
are called intermolecular forces.
Phase Changes
Energy Changes Accompanying Phase Changes
Molecular 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)
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.
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Pearson Education, Inc.
Chapter Eight
59
Dipoles line up
To minimize repulsion
And maximize attraction
The closer the molecules
The more important
Intermolecular 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.
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 weight
The 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?
London Dispersion Forces
• 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
London Dispersion Forces
Can be viewed as an “induced dipole”
Copyright © 2010
Pearson Education, Inc.
Chapter Eight
69
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
0
-50
-100
-150
-200
-250
-300
n
no
xe ton
yp
kr
n
go
ar
on
ne m
iu
l
he
– Have to move really slowly
to induce a dipole
Freezing Point
Van Der Waals Forces
Alkane Boiling Points
150
100
50
0
-50
-100
-150
-200
e
oc tan
ne
he pta
ne
he xa
ne
pe nta
e
butan
ane
prop
e
e than
ane
me th
• 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
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 Liquids
Viscosity
• 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 water
Cold oil vs hot oil
Surface Tension
• Bulk molecules (those in the liquid) are equally
attracted to their neighbors.
beads of water on a newly waxed car
meniscus in graduated cylinder
Some Properties of Liquids
Surface Tension
Some Properties of Liquids
Surface 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 liquids
Surface Tension
• Force in the surface of a liquid that makes
the area of the surface as small as possible.
Molecules at the
surface interact
only with neighbors
inside the liquid.
Properties of liquids
Capillary action
• It is the competition between two forces.
Cohesive forces
• The attractions between molecules of a
substance.
Adhesive forces
• Attractions between molecules of different
substances.
Properties of liquids
Capillary action
Capillary tube
meniscus
Mercury
Cohesive is larger
than adhesive.
Water
Adhesive is larger
than cohesive.
Some Properties of Liquids
Surface Tension
• Meniscus 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 liquids
Diffusion
• This takes place in both liquids and
gases. It is the spontaneous mixing of
materials that results from the random
motion of molecules.
Viscosity Properties
• Resistance to flow.
of liquids
• This increases with increased intermolecular
attractions.
CH3CH2CH2
OH
CH3CH CH2
OH OH
CH2CH CH2
OH OH OH
Increasing viscosity
• Also, liquids composed of long, flexible
molecules can entwine, resulting in increased
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 Solids
Unit Cells
• Crystalline 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 Solids
Unit Cells
Structures of Solids
Unit Cells
Three 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 Solids
Unit Cells
Space-Filling Cubic Cells
Crystal Lattice of NaCl
Unit Cell of NaCl
Structures of Solids
Crystal 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 Clions as Ca2+ ions.
Sample Unit Cells
Structures of Solids
Close 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 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 Very low MP
mp, hardness
Conductor
Soft,
Low MP
Insulator
Hard
High MP
Insulator
Example
Silver, iron
Ice,
Dry ice
NaCl
KF
Diamond
Argon
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 Compounds
have
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
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Pearson Education, Inc.
Chapter Eight
117
Phase Changes
Heating 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 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.
Phase Changes
Critical Temperature and Pressure
• Gases liquefied by increasing pressure at
some temperature.
• Critical temperature: the minimum
temperature for liquefaction of a gas using
pressure.
• Critical pressure: the minimum pressure
required for liquefaction at the critical
temperature.
Phase Diagram of Water
Pressure
Super critical fluid
Freezing
Melting
liquid
Evaporation
Condensation
gas
solid
Triple
Point
Sublimation
Deposition
Temperature
Phase Diagram of Water
Pressure
Super critical fluid
Pressure water changes
To solid.
Temperature
“Normal” Boiling and Melting
Point
1 atm
Pressure
100 C
0 C
Temperature
A solution
In 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.
• solvent - component in the greater concentration
• solute- 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 solutions
•
dental fillings, 14K gold, sterling silver
•
• Liquid solutions
•
saline, vodka, vinegar, sugar water
• Gas solutions
•
the atmosphere, anesthesia gases
Predicting Solubilites
“Like dissolves like.”
Materials with similar polarity are soluble in
each other. Dissimilar ones are not.
• Miscible - Liquids that are soluble in each
other in all proportions such as ethanol and
water.
• Immiscible - Liquids that are not soluble in
each other such as hexane and water.
Solubility
A measure of how much of a solute can be
dissolved in a solvent.
Common unit
- grams / 100 mL
Factors affecting solubility
Temperature
Pressure
Polarity
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 is
added to a supersaturated solution of sodium acetate.
130
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
Concentration Units
The concentration of a solution is the amount of solute
present in a given quantity of solvent or solution.
Percent by Mass
mass of solute
% by mass =
mass of solute + mass of solvent
x 100%
mass of solute x 100%
=
mass of solution
Mole Fraction (X)
moles of A
XA =
sum of moles of all components
132
Concentration Units Continued
Molarity (M)
moles of solute
M =
liters of solution
Molality (m)
m =
moles of solute
mass of solvent (kg)
133
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
0.500 L
0.500 L
[Ca+2] = 0.024 M
[Cl-1] = 2 x 0.024M = 0.048M
= .024 molar CaCl2
What is the molality of a 5.86 M ethanol (C2H5OH) solution whose
density is 0.927 g/mL?
moles of solute
moles of solute
m =
M =
mass of solvent (kg)
liters of solution
Assume 1 L of solution:
5.86 moles ethanol = 270 g ethanol
927 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
moles of solute
=
m =
mass of solvent (kg)
5.86 moles C2H5OH
= 8.92 m
0.657 kg solvent
135
What is the molality of a 5.86 M ethanol (C2H5OH) solution whose
density is 0.927 g/mL?
moles of solute
moles of solute
m =
M =
mass of solvent (kg)
liters of solution
Assume 1 L of solution:
5.86 moles ethanol = 270 g ethanol
927 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
moles of solute
=
m =
mass of solvent (kg)
5.86 moles C2H5OH
= 8.92 m
0.657 kg solvent
136
Calculate molarity, molality, mole fraction
Concentrated HCl has a density of 1.19 g/ml
and is 38% HCl in water (mass percent)
Molarity
1000 mL of solution has a mass of 1190 g
.38 x 1190 = 452.2 g HCl
452.2 g x
1 mole
= 12.4 moles
36.4 g HCl
12.4 moles in one liter = 12.4 molar
Molality In one liter
12.4 moles HCl in 737.8g
Or 0.7378 Kg of water
12.4mole = 16.8 m
.7378 Kg
Mole Fraction
In one liter of solution there is 452.2 g HCl = 12.4 moles
In one liter there is 1190 – 452.2g = 737.8 g water = 41.0 moles water
X HCl = 12.4 / (12.4 + 41.0) x 100 = 23.2 %
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
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
140
Heat of Solution
Exothermic
Endothermic
Heat of Solution Depends on…
P Solv
P Solu
P Solv
NP Solu
NP Solv
P Solu
NP Solv
NP Solu
H1
H2
H3
Hsol
Outcome
Large
Large
Small
Solution
forms
Small
Large
Large
Neg
Small
Large
Small
Small
Large
No
positive solution
Small
Small
Small
Small
Large
No
positive solution
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 nonpolar 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.
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 is the concentration (M) of the dissolved gas
c = kP
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
high P
low c
high c
147
Henry’s Law
• The partial pressure of a gas above a solution is
proportional to its concentration
P=kC
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
kCO2
=
5 atm
= 0.16 mol
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
Solubility (g solute/100g H2O)
Notice at 90 C there is
more solute than solvent!
There is almost no difference
In cold and hot solubility
This solid has a lower solubility
In hot water than cold
Temperature ºC
Temperature and Solubility
Solid solubility and temperature
solubility increases with
increasing temperature
solubility decreases with
increasing temperature
153
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
154
Solubility (g solute/100g H2O)
Gases
Warmer temperature means
Less 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 gases
cg = kpgas
This law is accurate to
within 1-3% for slightly
soluble gases and
pressures up to one
atmosphere.
Solubility
(g/100g water)
Henry’s Law
At constant temperature, the solubility of a
gas is directly proportional to the pressure of
the gas above the solution.
0.010
O2
0.005
N2
He
0.000
0
1
2
Pressure (atm)
Solubility of some substances
Substance
Temperature
oC
Solubility
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.
• Unsaturated - Can still dissolve more.
• Saturated - Have dissolved all you can.
• Supersaturated - Temporarily have
dissolved too much.
• Precipitate - 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 of aqueous solutions
• There are two general classes of solutes.
• Electrolytic
• ionic compounds in polar solvents
• dissociate in solution to make ions
• conduct electricity
• may be strong (100% dissociation) or weak (less
than 10%, )
• Nonelectrolytic
• 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 properties
• vapor pressure lowering
• freezing point depression
• boiling point elevation
• osmotic pressure
Colligative Properties
Lowering the Vapor Pressure
Vapor pressure lowering
The 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.
Colligative Properties
Raoult’s Law
The 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.
PA   A PA 
Recall Dalton’s Law:
PA   A Ptotal
Colligative Properties
Solute’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.
Tbp = Kbp x molality
• The boiling point will continue to be elevated
as you add more solute until you reach
saturation.
Freezing point depression
• When you add a solute to a solvent, the
freezing point goes down.
Tfp = Kfp x molality
• The more you add, the lower it gets.
• This will only work until you reach
saturation.
Examples “Salting” roads in winter
Making ice cream
Ionic vs. covalent substances
Ionic 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!
Tbp or fp = iKbp or fp x molality
Where i is the van’t Hoff factor that compares the
measured ∆Tbp or fp / calculated ∆Tbp or fp as nonelectrolyte
Ionic vs. covalent substances
The ideal van’t Hoff factor for NaCl is 2,
because it consists of 1 mole Na1+ ions and 1
1- ions.
mole
Cl
Oppositely charged ions in solution collide
and briefly stick together as one particle.
This lowers the ideal van’t Hoff factor.
compound
sucrose
NaCl
K2SO4
MgSO4
0.100 m
1.00
1.87
2.32
1.21
0.0100 m
1.00
1.94
2.70
1.53
0.00100 m
1.00
1.97
2.84
1.84
Ideal value
1.00
2.00
3.00
2.00
The more dilute a solution is and the lower the
charges of the ions formed, the closer the value
of 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 membranes, such as cell
walls, only allow small molecules and ions
to go through.
Osmosis
Eventually the pressure difference between the arms
stops osmosis.
Osmotic pressure
The pressure required to stop
osmosis.
osmotic pressure (  ) = iMRT
i = 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
n R T form of
the gas law equation. V
Osmotic Pressure
Three conditions can exist for living cells.
Concentration is the same on both sides.
–
isotonic
Concentration is greater on the inside.
–
–
hypertonic cell
hypotonic solution
Concentration is greater on the outside.
–
–
hypotonic cell
hypertonic solution
Cell in isotonic solution
A red blood cell and
plasma have the same
osmotic pressure.
Cells in hypertonic solution
If the level of salt in
the plasma is too high,
the cell collapses.
Crenation - water is
drawn out of the cell.
Cells in hypotonic solution
If the level of salt
in the plasma is
too low, the cell
swells and ruptures.
Hemolysis - water is
drawn 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:
diffusion
osmosis
ultrafiltration
Dialysis
By passing large amounts of a pure solvent
past the membrane, we can flush out all but
the largest components.
pure
water in
water, ions
and small
molecule
out
Colloids
Homogeneous mixtures of two or more substances
which are not solutions.
The substances are present as larger particles
than those found in solution.
Dispersing medium - The substance in a
colloid found in the greater extent.
Dispersed 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.
Dispersing
medium
Types
of colloids
Dispersed
phase
Name
Example
Gas
Gas
Liquid
Solid
Aerosol
Aerosol
Fog
Smoke
Liquid
Liquid
Liquid
Gas
Liquid
Solid
Foam
Emulsion
Sol
Whipped cream
Milk, mayo
Paint, ink
Solid
Solid
Solid
Gas
Liquid
Solid
Solid foam
Emulsion
Marshmallow
Butter
Pearls, opals
Colloids
• Tyndall effect - the ability of a colloid to
scatter light. A beam of light can be seen
passing through a colloid.
Tyndall Effect
Light is scattered by the colloidal-sized particles.
Colloids
• 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.
Colloids
• Hydrophilic 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.
Colloids
• Hydrophilic and Hydrophobic Colloids
Colloids
• Hydrophilic and Hydrophobic Colloids
• 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.
Colloids
• Hydrophilic and Hydrophobic Colloids
• 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.
Colloids
• Hydrophilic and Hydrophobic Colloids
Colloids
• Hydrophilic 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.
Colloids
• Hydrophilic and Hydrophobic Colloids
Colloids
• Hydrophilic and Hydrophobic Colloids
• 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.
Colloids
• Removal 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.
Colloids
• Removal 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
Motion.
• 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.