Transcript Gases - Dr. VanderVeen

Gases
GASES
manometers
Kinetic theory of gases
pressure
Units of pressure
Behavior of gases
Pressure vs.
volume
Pressure vs.
temperature
Combined gas law
Ideal gas law
Temperature vs.
volume
Partial pressure
of a gas
Diffusion/effusion
Properties of Gases
• Very low density
• Low freezing points
• Low boiling points
• Can diffuse (rapidly and
spontaneously spread out and mix)
• Flow
• Expand to fill container
• Compressible
Kinetic Molecular Theory of
Gases
• Particles move non-stop, in straight lines.
• Particles have negligible volume (treat as
points)
• Particles have no attractions to each other
(no repulsions, either).
• Collisions between particles are “elastic”
(no gain or loss of energy)
• Particles exert pressure on the container
by colliding with the container walls.
Kinetic Energy
• Energy due to motion
• KE = ½ mv2
Temperature
• Temperature is a measure of average
kinetic energy.
– Temperature measures how quickly the
particles are moving. (Heat IS NOT the
same as temperature!)
– If temperature increases, kinetic energy
increases.
• Which has greater kinetic energy: a 25
g sample of water at 25oC or a 25 g
sample of water at -15oC?
Why use the Kelvin scale?
• In the Kelvin scale, there is an
absolute correlation between
temperature and kinetic energy.
– As temperature in Kelvin increases,
kinetic energy increases.
• Absolute zero: All molecular motion
ceases. There is no kinetic energy.
–0 K
Kelvin-Celsius Conversions
• K = oC + 273.15
• oC = K – 273.15
Kelvin-Celsius conversions
• The temperature of liquid nitrogen is
-196oC. What is this temperature in
Kelvin?
• Convert 872 Kelvin to Celsius
temperature.
Pressure
• Pressure = force/area
• Atmospheric pressure
– Because air molecules collide with
objects
• More collisions  greater pressure
Pressure Units
• Atmosphere
• Pounds per square inch (psi)
• mm Hg
• Torr
• Pascal (Pa) or kilopascal (kPa)
1 atm = 14.7 psi = 760 mm Hg = 760
torr = 101.3 kPa
Barometer
• Torricelli-1643
• Air molecules collide
with liquid mercury in
open dish
• This holds the column
up!
• Column height is an
indirect measure of
atmospheric pressure
Manometer
• Two types: open
and closed
• Use to measure the
pressure exerted
by a confined gas
Chapter 15 Wrapup
(Honors)
• At the same temperature, smaller
molecules (i.e., molecules with lower
gfm) have faster average velocity.
• Energy flows from warmer objects to
cooler objects.
• Plasma
– High energy state consisting of cations
and electrons
• Found in sun, fluorescent lights
Boyle’s Law
• Pressure-volume
relationships
• For a sample of a
gas at constant
temperature,
pressure and
volume are
inversely related.
• Equation form:
P 1 V1 = P 2 V 2
Charles’ Law
V1 V2

T1 T2
• Volume-temperature
relationships
• For a sample of a gas
at constant pressure,
volume and
temperature are
directly related.
• Equation form:
V1 V2

T1 T2
Guy-Lussac’s Law
• Pressure
temperature
relationships
• For a sample of a
confined gas at
constant volume,
temperature and
pressure are
directly related.
P1 P2

T1 T2
Combined Gas Law
• Sometimes, all three variables change
simultaneously
• This single equation takes care of the
other three gas laws!
P1V1 P2V2

T1
T2
Dalton’s Law of Partial
Pressures
• For a mixture of
(nonreacting)
gases, the total
pressure exerted
by the mixture is
equal to the sum of
the pressures
exerted by the
individual gases.
Ptot  P1  P2  ...
Collecting a sample of gas
“over water”
• Gas samples are
sometimes
collected by
bubbling the gas
through water
Ptot  Pgas  PH 2O
• If a question asks
about something
relating to a “dry
gas”, Dalton’s Law
must be used to
correct for the
vapor pressure of
water!
Ptot  Pgas  PH 2O
Table: Vapor Pressure of Water
Ideal Gas Law
• The number of
moles of gas
affects pressure
and volume, also!
– n, number of moles
•
•
•
•
•
nV
nP
P  1/V
PT
VT
PV  nRT
Where R is the universal gas constant
R = 0.0821 L●atm/mol●K
Ideal vs. Real Gases
• Ideal gas: completely obeys all
statements of kinetic molecular
theory
• Real gas: when one or more
statements of KMT don’t apply
– Real molecules do have volume, and
there are attractions between molecules
When to expect ideal
behavior?
• Gases are most likely to exhibit ideal
behavior at…
– High temperatures
– Low pressures
• Gases are most likely to exhibit real
(i.e., non-ideal) behavior at…
– Low temperatures
– High pressures
Diffusion and Effusion
• Diffusion
– The gradual mixing of 2 gases due to
random spontaneous motion
• Effusion
– When molecules of a confined gas
escape through a tiny opening in a
container
Graham’s Law
• Thomas Graham (1805-1869)
• Do all gases diffuse at the same
rate?
• Graham’s law discusses this quantitatively.
• Technically, this law only applies to gases
effusing into a vacuum or into each other.
Graham’s Law
• Conceptual:
– At the same temperature, molecules
with a smaller gfm travel at a faster
speed than molecules with a larger gfm.
• As gfm , v 
• Consider H2 vs. Cl2
Which would diffuse at the greater velocity?
Graham’s Law
• The relative rates of diffusion of two
gases vary inversely with the square
roots of the gram formula masses.
• Mathematically:
rate1

rate 2
gfm 2
gfm1
Graham’s Law Problem
• A helium atom travels an average
1000. m/s at 250oC. How fast would
an atom of radon travel at the same
temperature?
• Solution:
– Let rate1 = x
rate2 = 1000. m/s
– Gfm1 = radon 222 g/mol
– Gfm2 = helium = 4.00 g/mol
Solution (cont.)
• Rearrange:
x

rate 2
gfm 2
gfm1
x  rate2
gfm2
gfm1
• Substitute and evaluate:
x  1000.
m
s
4.00g / mol
 134 m / s
222g / mol
Applications of Graham’s
Law
• Separation of uranium isotopes
– 235U
– Simple, inexpensive technique
– Used in Iraq in early 1990’s as part of
nuclear weapons development program
• Identifying unknowns
– Use relative rates to find gfm
Problem 2
• An unknown gas effuses through an
opening at a rate 3.16 times slower
than that of helium gas. What is the
gfm of this unknown gas?
Solution
• Let gfm2 = x rate2 = 1
gfm1 = 4.00 rate1 = 3.16
• From Graham’s Law,
 rate1

 rate2
• Rearrange:
2

gfm2
 
gfm1

(rate1 ) 2
 gfm1  gfm2
2
(rate2 )
Solution, cont.
• Substitute and evaluate:
(3.16) 2
 4  39.9 g / m ol
2
1