Gases: Macroscopic Observation Gases fill the container into
which they are placed Gases are compressible Gases mix completely
and evenly when confined to the same container Gases have much
lower densities than solids or liquids (g/L)
Slide 6
Gases: Molecular View Fill space evenly and completely:
randomly, fast moving particles Low density and compressibility:
large distances between particles Idealized assumptions Gas
particles have no volume Gas particles have no interaction, so
identity of gas particle is inconsequential
Slide 7
Gases: Historical View Molecular basis Kinetic energy of
molecules much greater than intermolecular forces Historical
studies precede the atom First we will look at non-molecular
properties
Slide 8
Torricelli (1608-1647) 1 atm = 760 torr
Slide 9
Pressure Velocity = distance / time (m/s) Acceleration = change
in velocity / time (m/s 2 ) Force = mass x acceleration (kg m/s 2 =
N) Pressure is the force of the gas pressing on a given area P =
F/A (N/m 2 = Pa) Ability to cut with a knife doesnt depend simply
on amount of force
Slide 10
Test the concept
Slide 11
Pressure Pressure = Force/Area Force = mass acceleration
Acceleration = g = pull of gravity mass = V = h A where =density of
Hg, h= height of Hg, A = cross-sectional area of column Force = h A
g Pressure=( h A g)/A = h g P height and density If the density of
mercury is 13.6g/ml, what is the height of a column of water under
vacuum at atmospheric pressure? (76 cm =2.5 ft)
Experimenting with Gases As P (h) increases V decreases Robert
Boyle (1627-1691)
Slide 15
Plot of Pressure vs Volume
Slide 16
Boyles Law V =k/P
Slide 17
Boyles Law P 1/V, when one sample is kept at constant
temperature Acts as an Ideal Gas
Slide 18
Ideal Gas Pressure is inversely proportional to volume at a
range of constant temperatures and sample sizes k changes value at
different temperatures, but is constantwell, almost constant Also
notice that identity of gas matters little, and all approach same
ideal (all data from 1 mol samples at 0 o C)
Slide 19
Ideal Gas Molecular perspective Assumptions Molecules occupy no
space Molecules do not interact with each other Good
assumptions?
Slide 20
Test your Understanding When you blow up your tire, you
increase the pressure and volume simultaneously. According to
Boyle, pressure and volume are inversely proportional. What
gives?
Slide 21
Charless Law Jacque Charles (1746- 1823) Solo balloon flight At
constant pressure, volume increases linearly with temperature Write
Law
Slide 22
Charless Law (1783) V T T in Kelvin K = o C + 273 Absolute
zero
Slide 23
Pressure and Temperature Draw Pressure as a function of
Temperature at constant volume
Slide 24
Avagadros Law (1811) In light of Daltons Atomic Theory (1808)
Based on Gay-Lussac Law of combining volumes
Slide 25
Avogadros Law At constant P and T, the volume of a gas is
proportional to the amount of gas molar volume V m = V/n V n Little
known historical fact: Junior High nickname happened to be The
Mole
Slide 26
Combined Ideal Gas Law
Slide 27
Problem Types If three variables known, calculate fourth Some
conditions changehow does it affect others? Stoichiometry Determine
a molar mass
Slide 28
Molar Volume Molar Volume = V m Defined as the volume taken up
per mole of gas V m at STP = 22.41 L/mol Standard Pressure is 1 atm
What is standard temperature in Celcius?
Slide 29
A flask that can withstand an internal pressure of 2500 torr,
but no more, is filled with a gas at 21.0 o C and 758 torr and
heated. At what temperature will it burst? Strategy/Sketch: Answer:
7.0 x 10 2 o C
Slide 30
Change in State of Ideal Gas If the stopcock is opened, the
total pressure is 0.975 atm. What was the original pressure of the
red bulb? Strategy: Logic Check: 2.00L Ar at 360 torr 1.00 L Ar
unknown pressure Assumption Check: According to ideal gas, would
the total pressure change if the right bulb were filled with 1 L of
carbon dioxide? Answer: 1.50 x 10 3 torr
Slide 31
Gas Density
Slide 32
Experimental Importance
Slide 33
Daltons Law of Partial Pressures An example of early utility of
Daltons atomic theory
Slide 34
Mole Fraction
Slide 35
Slide 36
Collecting a Gas Over Water Gases collected by water
displacement are a mixture of the gas and water vapor. All liquids
have a certain amount in the gas phase. This is known as the Vapor
Pressure of the liquid. It is temperature dependent. P T = P gas +
P H 2 O
Kinetic Molecular Theory Describes gases at the molecular level
1. Gases consist of small particles separated by large distances
(assume no volume.) 2. Constant, random motion. Collisions with
wall cause pressure 3. Gas particles have no interaction with one
another (no intermolecular forces.) Collisions occur continuously
and are elastic (no gain/loss of KE). 4. KE T, average kinetic
energy only changes when temperature changes.
Slide 40
Slide 41
Ideal Gas Law from Theory: Qualitative
Slide 42
Is KMT consistent with Observation? Compressibility Boyle P and
V Charles V and T, P and T Avogadro V and n Daltons Partial
Pressures
Slide 43
Ideal Gas Law from Theory: Quantitative
Slide 44
Derivation of KMT See handout
Slide 45
Slide 46
Slide 47
The meaning of Temperature
Slide 48
Velocity of particles in Gas
Slide 49
Slide 50
Maxwell-Boltzmann Distribution How does this function form the
shape of the distribution? How does high mass shift curve? How does
high T shift curve?
Slide 51
Maxwell/Boltzmann Distribution
Slide 52
Typical Velocities at 298 K in m/s These gases are at the same
temperature, so they have the same __________ but they have
different average velocities because they have different
_________________.
Slide 53
Three ways to describe a typical velocity Most probable Average
RMS
Slide 54
Determination of RMS velocity
Slide 55
Root Mean Square Speed
Slide 56
Test your understanding
Slide 57
Diffusion Effusion Gas Motion on a Molecular Level
Slide 58
Diffusion and Effusion Diffusion mixing due to motion Effusion
passage of a gas through a small hole into an evacuated space Ratio
of effusion or diffusion rates depends on relative velocities of
gases
Slide 59
Real Gases At 200K Nitrogen gas
Slide 60
Real Gases: Check Assumptions 1. Gases consist of small
particles separated by large distances (assume no volume.) 2.
Constant, random motion. Collisions with wall cause pressure 3. Gas
particles have no interaction with one another (no intermolecular
forces.) Collisions occur continuously and are elastic (no
gain/loss of KE). 4. KE T, average kinetic energy only changes when
temperature changes.
Slide 61
Assumptions that Fail Gases have no contribution to volume. Is
this assumption equally valid at all states?
Slide 62
Assumptions that Fail Gases velocity is unaffected by
attraction to other particles.
Slide 63
When Is a Gas Most Ideal?
Slide 64
Make a Real Gas Law Points to consider Volume: must factor in
_________and __________ of particles Pressure: must factor in
___________ and ___________ of interaction
Slide 65
Van der Waals equation nonideal gas P + (V nb) = nRT an 2 V2V2
() } corrected pressure } corrected volume Does this experimental
data match theory?
