Download Document

1) Spherical molecules in constant, random
straight-line motion
2) “Elastic” collisions
3) Point masses
4) No interactions
5) Avg. KE of gas molecules  Temperature
5 Postulates of
Kinetic Theory
The gas particles move in
straight lines between collisions.
Recall: straight-line motion
implies that no forces are acting
on the particle.
Random, straight-line motion?
Total KE is conserved.
Total KE before collision
=
Total KE after collision.
BUT KE may be TRANSFERRED!
Elastic Collisions
Kinetic energy may be transferred
between particles.
Elastic Collisions
Kinetic Energy is NOT
conserved!
Inelastic Collision
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).
Point Mass
Tgas  KEavg
So all gases at the same T have the
same average kinetic energy.
Recall that KE = ½ mv2.
Temperature of a gas
He
Ne
Ar
Kr
Xe
Lightest is fastest!
At the same temperature,
which of the following gases
diffuses most rapidly?
He
Ne
Ar
Kr
Xe
Heaviest is slowest!
At the same temperature,
which of the following gases
diffuses most slowly?
KE = ½ mv2
Lighter gas particles have higher
average speeds than heavier gas
particles at the same temperature.
For gases at the same
Temperature
Gas that obeys all 5 assumptions of
the kinetic theory all of the time.
It doesn’t exist. It’s a model.
Ideal Gas
Most real gases obey the kinetic
theory most of the time.
Real Gas
Spherical molecules in random,
straight-line motion
2. “Elastic” collisions
1.
Which assumptions of the
kinetic theory hold up?
1. Point masses
2. No interactions
Which assumptions of the
kinetic theory break down?
When the gas molecules are
close to each other.
When do the assumptions
of the kinetic theory break
down?
At high pressure & low
temperature.
When are the gas molecules
close to each other?
At low pressure & high
temperature.
When are the gas molecules
far apart from each other?
Good!
How do the gas molecules
act when they are far apart
from each other?
Molecules are always attracted to one
another, even if just weakly.
Molecules take up space.
Real Gases
1. Have mass
2. Take the shape & volume of their
container
3. Compressible
4. Flow
5. Diffuse
6. Exert Pressure
What are the properties
of gases?
Force/Area
Pressure
Collisions of the gas molecules
with the walls of the container.
Pressure results from?
With a Barometer!
P = DHggh
but since DHg & g don’t change,
we just report h.
How do you measure air
pressure?
Closed-ended
manometer
With a manometer!
A closed ended manometer:
h is directly proportional
to the pressure of the
confined gas.
Pgas = DHggh but we just
say h most of the time.
To
vacuum
pump
Attach gas bulb here
How do you measure the
pressure of a confined gas?
22
A
222222
A
A
A
Pgas < Patm
Pgas = Patm - h
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
Pgas > Patm
Pgas = Patm + h measure Patm.
How do you measure the
pressure of a confined gas?
# of impacts per unit time and
force of each impact
Pressure depends on?
(microscopically)
# of gas molecules per unit volume
And
temperature
Pressure depends on?
(macroscopically)
•
•
•
•
•
•
1 atm =
760 torr =
760 mm Hg =
101.3 kPa =
101,325 Pa =
14.7 lb / in2 or psi
Pressure Units
A measure of the avg. kinetic
energy of the particles of a
substance.
Temperature
1.Temperature
2.Pressure
3.Volume
4.# of moles
4 variables needed to
completely describe a gasphase system?
Can change size:
balloons or
cylinders with pistons
Elastic containers
Walls are fixed.
Size does not change.
Rigid Containers
Standard Temperature & Pressure
1 atm or 101.3 kPa or 760 torr
0C or 273K
STP
For a fixed mass and temperature,
the pressure-volume product is a
constant.
Boyle’s Law
PV = k where k = a constant
Boyle’s Law
Constant T, n
P1V1 = P2V2
Boyle’s Law
Hyperbola – it’s an inverse
relationship!
Graph of Boyle’s Law
Graph of Boyle’s Law,
Pressure vs. Volume
Volume goes to ½ the original
volume
Double the pressure
Volume goes to 1/3 the original
volume
Triple the pressure
Volume goes to 2 X the original
volume
Halve the pressure
Volume goes to 1/4 of the original
volume
Quadruple the pressure
What does the graph of a
direct relationship look
like?
Kelvin: 0 K means 0 speed.
Which temperature
scale has a direct
relationship to molecular
velocity?
The top graph!
Which graph shows the
relationship between average KE
and Kelvin temperature?
It’s a direct
relationship.
Graph of Volume vs.
Kelvin Temperature
V1/T1 = V2/T2
Charles’ Law
Math expression of
Volume & Kelvin
Temperature
Constant P, n
The volume doubles!
What happens to the
volume when the Kelvin
temperature is doubled?
The volume triples!
What happens to the
volume when the Kelvin
temperature is tripled?
The volume is halved!
What happens to the
volume when the Kelvin
temperature is halved?
It’s halved!
What happens to the Kelvin
temperature when the volume
is halved?
It’s a direct
relationship.
Graph of Pressure vs.
Kelvin Temperature
Constant V, n
P1/T1 = P2/T2
Gay-Lussac’s Law
Math expression for
pressure & temperature.
The pressure is doubled.
What happens to the
pressure when the Kelvin
temperature is doubled?
The pressure is halved.
What happens to the
pressure when the Kelvin
temperature is halved?
The pressure is tripled.
What happens to the
pressure when the Kelvin
temperature is tripled?
The Kelvin temperature is
doubled.
What happens to the Kelvin
temperature when the
pressure is doubled?
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.
Combined Gas Law
V = kn
The volume of a gas is directly proportional
to the # of moles.
At STP, k = 22.4 liters/mole
Avogadro’s Law
Constant T, P
Equal volumes of gases at
the same temperature &
pressure have equal numbers
of molecules.
What is another way to
state Avogadro’s Law?
He
N2
These 2 boxes have the same:
a) Mass
b) Density
c) # of molecules
d) # of atoms
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 Literatm
moleK
Ideal Gas Law
Governed by R. If R = 0.0821 Latm then
moleK
P in atm
V in liters
T in Kelvins
n in moles
PV = nRT
Ideal Gas Law units
• From Table T:
# of moles = given mass
gram-formula mass
moles & mass
Use it to find molar mass, M
mass
PV = nRT =
RT
M
Rearrange:
M = massRT
PV
Ideal Gas Law Extension #1
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
Ideal Gas Law Extension #2
Only at STP:
Density of a gas = Molar Mass (grams/mol)
22.4 (Liters/mol)
Density of a gas at STP
Gas phase of a substance that is
normally a liquid at room
temperature (298C).
Vapor
Closed container, at equilibrium
(both liquid & gas phases present)
Manometer!
http://www.chemteam.info/GasLaw/VaporPressureImage.GIF
How do you measure vapor
pressure?
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.
Vapor pressure depends on?
It can be tabulated! You
don’t have to measure it
every time you do an
experiment!
Handy result: since vapor pressure
only depends on the temperature
of the liquid phase …
Ptot = P1 + P2 + P3 + P4 + …
What is Dalton’s Law of
Partial Pressures?
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.
When the water levels
inside and outside line up,
then the gas pressure + the
water vapor pressure is
equal to the air pressure!
http://crescentok.com/staff/jaskew/isr/tigerchem/gas_laws/dalton2.gif
Gas Collection over Water
Pinside = Patm when levels align
N2(g) + H2O(g) = Pgas
Patm = PN2 + PH2O
But since it’s water
vapor, we can look up
PH2O in a table.
N2
http://abetterchemtext.com/gases/images/over_water.png
PN2 = Patm – PH2O
Gas Collection over Water
You need a barometer to measure Patm.
450.0 mLs of a gas is collected over water at
23C. 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.
Correction
ratios!
V2 = V1 X P X T
P
T
Dry volume of a gas at STP
Spontaneous mixing of two
substances caused by their
random motion. The two gases
move through each other.
Diffusion
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
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
½ m1v1
2
= ½ m2v2
2
m1 / m2 = v22 / v12
Graham’s Law of Effusion
Estimate the molar mass of a gas that effuses
at 1.6 times the effusion rate of CO2.
Graham’s Law – general.
Stick in the labels for
this problem
= 1.6
mCO2/munk = 2.56 or 44/x = 2.56
X = 17
Graham’s Law of Effusion