5 postulates of kinetic theory 1) spherical molecules in constant, random straight-line motion 2)...
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5 Postulates of Kinetic Theory
1) Spherical molecules in constant, random straight-line motion
2) “Elastic” collisions3) Point masses4) No interactions5) Avg. KE of gas molecules
Temperature
Random, straight-line motion?
The gas particles move in straight lines between
collisions.
Recall: straight-line motion implies that no forces are
acting on the particle.
Total KE is conserved.Total KE before collision
=Total KE after collision.
BUT KE may be TRANSFERRED!
Elastic Collisions
Elastic Collisions
Kinetic energy may be transferred between particles.
Inelastic Collision
Kinetic Energy is NOT conserved!
Point Mass
The volume of the gas molecule itself is tiny compared to the distance between
gas molecules. In other words, the distance between the molecules is more important than
their actual size. We say the volume of each molecule is
insignificant; but they need to be a point so we can locate them in space (give
them coordinates).
Temperature of a gas
Tgas KEavg
So all gases at the same T have the same average kinetic energy.
Recall that KE = ½ mv2.
At the same temperature, which of the following gases diffuses most
rapidly?
He Ne Ar Kr Xe
Lightest is fastest!
At the same temperature, which of the following gases diffuses most
slowly?
He Ne Ar Kr Xe
Heaviest is slowest!
For gases at the same Temperature
KE = ½ mv2
Lighter gas particles have higher average speeds than heavier gas
particles at the same temperature.
Ideal Gas
Gas that obeys all 5 assumptions of the kinetic theory all of the time. It doesn’t exist. It’s a model.
Real Gas
Most real gases obey the kinetic theory most of the time.
Which assumptions of the kinetic theory hold up?
1. Spherical molecules in random, straight-line motion
2. “Elastic” collisions
Which assumptions of the kinetic theory break
down?
1. Point masses2. No interactions
When do the assumptions of the kinetic theory
break down?
When the gas molecules are close to each other.
When are the gas molecules close to each
other?
At high pressure & low temperature.
When are the gas molecules far apart from
each other?
At low pressure & high temperature.
How do the gas molecules act when they are far apart from each
other?
Good!
Real Gases
Molecules are always attracted to one another, even if just weakly.
Molecules take up space.
What are the properties of gases?
1. Have mass2. Take the shape & volume of their
container3. Compressible4. Flow5. Diffuse6. Exert Pressure
Pressure
Force/Area
Pressure results from?
Collisions of the gas molecules with the walls of the
container.
With a Barometer!
P = DHggh
but since DHg & g don’t change, we just report h.
How do you measure air pressure?
How do you measure the pressure of a confined gas?
With a manometer!
Attach gas bulb here
To vacuumpump
Closed-ended manometer
A closed ended manometer:
h is directly proportional to the pressure of the confined gas.Pgas = DHggh but we just say h most of the time.
How do you measure the pressure of a confined gas?
With a manometer!An open ended manometer:
h tells you how far away the gas pressure is from the air pressure. So you also need a barometer to measure Patm.
AAAA
22222222
Pgas > Patm
Pgas = Patm + h
Pgas < Patm
Pgas = Patm - h
Pressure depends on?(microscopically)
# of impacts per unit time and force of each impact
Pressure depends on?(macroscopically)
# of gas molecules per unit volumeAnd
temperature
Pressure Units
• 1 atm = • 760 torr = • 760 mm Hg =• 101.3 kPa =• 101,325 Pa =• 14.7 lb / in2 or psi
Temperature
A measure of the avg. kinetic energy of the particles of a
substance.
4 variables needed to completely describe a
gas-phase system?
1.Temperature2.Pressure3.Volume4.# of moles
Can change size:
balloons orcylinders with pistons
Elastic containers
Walls are fixed.Size does not change.
Rigid Containers
STP
Standard Temperature & Pressure1 atm or 101.3 kPa or 760 torr
0C or 273K
Boyle’s Law
For a fixed mass and temperature, the pressure-
volume product is a constant.
Boyle’s Law
PV = k where k = a constant
Constant T, n
Boyle’s Law
P1V1 = P2V2
Graph of Boyle’s Law
Hyperbola – it’s an inverse relationship!
Graph of Boyle’s Law, Pressure vs. Volume
Double the pressure
Volume goes to ½ the original volume
Triple the pressure
Volume goes to 1/3 the original volume
Halve the pressure
Volume goes to 2 X the original volume
Quadruple the pressure
Volume goes to 1/4 of the original volume
What does the graph of a direct relationship look
like?
Which temperature scale has a direct
relationship to molecular velocity?
Kelvin: 0 K means 0 speed.
Which graph shows the relationship between average KE
and Kelvin temperature?
The top graph!
Graph of Volume vs. Kelvin Temperature
It’s a direct relationship.
Math expression of Volume & Kelvin
Temperature
V1/T1 = V2/T2
Charles’ Law
Constant P, n
What happens to the volume when the Kelvin temperature is doubled?
The volume doubles!
What happens to the volume when the Kelvin temperature is tripled?
The volume triples!
What happens to the volume when the Kelvin temperature is halved?
The volume is halved!
What happens to the Kelvin temperature when the
volume is halved?
It’s halved!
Graph of Pressure vs. Kelvin Temperature
It’s a direct relationship.
Constant V, n
Math expression for pressure &
temperature.
P1/T1 = P2/T2
Gay-Lussac’s Law
What happens to the pressure when the Kelvin temperature is doubled?
The pressure is doubled.
What happens to the pressure when the Kelvin temperature is halved?
The pressure is halved.
What happens to the pressure when the Kelvin temperature is tripled?
The pressure is tripled.
What happens to the Kelvin temperature when the pressure is doubled?
The Kelvin temperature is doubled.
Combined Gas Law
For constant n:
P1V1 = P2V2
T1 T2
If they do NOT mention a variable, it’s constant. Constant variables are the same on both sides, so you can neglect them.
V = knThe volume of a gas is directly proportional to the # of moles.
At STP, k = 22.4 liters/mole
Avogadro’s Law
Constant T, P
What is another way to state Avogadro’s Law?
Equal volumes of gases at the same temperature & pressure have equal numbers of molecules.
These 2 boxes have the same:
a) Mass c) # of molecules
b) Density d) # of atoms
He N2
Ideal Gas Law
Equation of state for a gas. Relates the macroscopic variables that describe the system.
PV = nRT
R = gas law constant. In US, we use R = 0.0821 Literatm
moleK
Ideal Gas Law units
Governed by R. If R = 0.0821 Latm then mole
KP in atmV in litersT in Kelvinsn in moles
PV = nRT
moles & mass
• From Table T:
# of moles = given massgram-formula mass
Ideal Gas Law Extension #1
Use it to find molar mass, M
PV = nRT = RTmass
M
Rearrange: M = massRTPV
Ideal Gas Law Extension #2
Use it to find the density of a gas:
PV = nRT = mRT where m = mass M
Density = m/V so MP = D or M = DRT RT P
Density of a gas at STP
Only at STP:
Density of a gas = Molar Mass (grams/mol)
22.4 (Liters/mol)
Vapor
Gas phase of a substance that is normally a liquid at room
temperature (298C).
How do you measure vapor pressure?
Closed container, at equilibrium (both liquid & gas phases
present)
http://www.chemteam.info/GasLaw/VaporPressureImage.GIF
Manometer!
Vapor pressure depends on?
Temperature of the liquid phase ONLY!
BOTH phases MUST be present for it to be a vapor. If no liquid is
present, it’s a gas.
Handy result: since vapor pressure only depends on the
temperature of the liquid phase …
It can be tabulated! You don’t have to
measure it every time you do an experiment!
What is Dalton’s Law of Partial Pressures?
Ptot = P1 + P2 + P3 + P4 + …
Gas Collection over Water
The test tube was full of water at the beginning. As the reaction proceeds, the gas displaces the water. There is
also some water vapor up there.
http://crescentok.com/staff/jaskew/isr/tigerchem/gas_laws/dalton2.gif
When the water levels inside and outside line up, then the gas pressure + the water vapor pressure is equal to the air pressure!
Gas Collection over Water
Pinside = Patm when levels align
http://abetterchemtext.com/gases/images/over_water.png
N2
N2(g) + H2O(g) = Pgas
Patm = PN2 + PH2O
But since it’s water vapor, we can look up PH2O in a table.
PN2 = Patm – PH2O
You need a barometer to measure Patm.
Dry volume of a gas at STP
450.0 mLs of a gas is collected over water at 23C. Patm = 748.0 torr. Find the
volume of the dry gas at STP.
1. Look up the vapor pressure of water at 23 C. It’s 21.1 torr.
2. Find the pressure of the gas alone. Pgas = Patm - PH2O = 748.0 - 21.1 = 726.9 torr
3. Use combined gas law to find volume of the gas at STP.
V2 = V1 X P X TP T
Correction ratios!
Diffusion
Spontaneous mixing of two substances caused by their random motion. The two gases move through each
other.
Effusion
Process by which gas particles pass through a tiny
opening.
http://chemwiki.ucdavis.edu/@api/deki/files/8671/e2.JPG?size=bestfit&width=350&height=209&revision=1
Graham’s Law of Effusion
The rates of effusion of gases at the same temperature and
pressure are inversely proportional to the square roots
of their molar masses.
Another way to find the molar mass of a substance!
Graham’s Law of Effusion
KE1 = ½ m1v12 and
KE2 = ½ m2v22
At the sa
me
temperature, these
two
gases h
ave the sa
me
average KE!
½ m1v12 = ½
m2v22
m1 / m2 = v2
2 / v12
Take the sq
uare
root o
f both
sides.
Graham’s Law of Effusion
Estimate the molar mass of a gas that effuses at 1.6 times the effusion rate of CO2.
= 1.6Squar
e bot
h sides
!
mCO2/munk = 2.56 or 44/x = 2.56X = 17
Graham’s Law – general. Stick in the labels for this problem