Transcript Pre-AP_Gas_Properties_and_Laws.ppt

Kinetic Theory of Gases
1. Gas is composed of small particles that are far
apart. No attractive or repulsive forces exist.
2. Particles move rapidly in constant random
motion. They travel in straight lines and change
path only when they rebound after a collision.
– Gas fills their container regardless of shape
and volume gas not contained diffuse into
space without limit.
3. All collisions are perfectly elastic…there is no
loss of energy during contact…so the total
Kinetic Energy remains the same.
Kinetic Theory in Review
• Gases expand to fill any container.
• Gases are fluids (like liquids).
• Gases have very low densities.
• Gases can be compressed.
• Gases undergo diffusion.
– Diffusion is the spreading of gas
molecules throughout a container until
evenly distributed.
Nature of Gases
• Gas Pressure is the force exerted by a
gas per unit surface area of an object.
• Vacuum is an empty space with no
particles and no pressure.
Gas Pressure
• What causes gas pressure?
– Result of billions of collisions of the
gas particles with the sides of its
container.
– Collisions are elastic.
– Kinetic Theory – particles are in constant
random motions.
• ↑ temp ↑ motion ↑ energy
Atmospheric Pressure
• Results from collisions of air molecules
with objects.
• Atmospheric pressure decreases as you
climb a mountain the air layer around the
earth thins out as elevation increases.
Atmospheric Pressure
• Barometers are devices used to measure
atm. Weather forecasts are determined by
pressure.
• The SI unit of pressure is pascal (Pa).
• Older units are millimeters of mercury
(mmHg) and atomospheres (atm)
• Conversion Factor:
– 1 atm = 760 mm Hg = 101.3 kPa = 760 torr
Atmospheric Pressure
Conversions
• A gas is at a pressure of 1.5 atm.
Convert this pressure to kilopascals.
• What pressure, in atmospheres, does a
gas exert 385 mm Hg?
• The pressure at the top of Mt. Everest is
33.7 kPa. What is the pressure in mm
Hg?
Factors that Affect Gases
1.
2.
3.
4.
Amount of gas present
Volume
Temperature
Pressure
Factor: Amount of Gas
• What happens if you increase the number
of gas particles present in a fixed size
container?
• If you increase the number of gas particles
present, how does that affect the number of
collisions that are occurring?
• More collisions equals more pressure.
Factor: Volume of a Gas
• What happens to the pressure of a gas if
you change its volume?
– If you decrease the volume, the
pressure will increase. If you increase
the volume, the pressure will decrease.
Factor: Temperature of a Gas
• What will happen if you increase the
temperature of a gas?
– The particles gain kinetic energy.
– Therefore they move faster (collide
more often and with more force).
– The pressure will increase.
Factor: Pressure of a Gas
• What will happen if you change the
external pressure acting on a gas?
– If you increase the external pressure,
the volume of the gas will decrease.
– If you decrease the external pressure,
the volume of the gas will increase.
Boyle’s Law
Pressure-Volume Relationship
• The pressure of a gas in inversely
proportional to the volume of the gas if its
temperature is held constant.
P1V1 = P2V2
Boyle’s Law Examples
1. John fills a balloon with 30-L of Helium gas at
1.00-atm. What is the new volume when the
balloon gets away from him and rises to an
altitude where the pressure is only 0.25-atm?
2. A gas occupies 100-mL at 150-kPa. Find its
volume at 200-kPa.
3. A sample of helium gas in a balloon is
compressed from 4.0-L to 2.5-L at a constant
temperature. If the pressure of the gas in the
4.0-L volume is 210 kPa, what will the
pressure be at 2.5-L?
Charles’s Law
Temperature-Volume Relationship
• The volume of a gas is directly
proportional to its Kelvin temperature if
the pressure is held constant (K = C
+273).
V1 = V2
T1
T2
Charles’ Law Examples
1. A gas occupies 473 cm3 at 36°C. Find its
volume at 94°C.
2. Andy inflates a balloon for a party. He is in an
air-conditioned room at 27°C, and the balloon
has a volume of 4.0L. He heats the balloon to
a temperature of 57°C. What is the new
volume of the balloon if the pressure remains
constant?
3. A gas sample at 40⁰C occupies a volume of
2.32-L. If the temperature is raised to 75 ⁰ C,
what will the volume be, assuming the
pressure remains constant?
Gay-Lussac’s Law
Temperature-Pressure Relationship
• The pressure of a gas is directly
proportional to its Kelvin temperature if
the volume is held constant.
P1
T1
=
P2
T2
Gay-Lussac’s Law Examples
1. An unopened coke was sitting in a car during
the afternoon. The can’s temperature was
20°C and the gas inside had a pressure of 2.0atm. The can was left in the car, and the
temperature escalated to 70°C. What was the
pressure in the can just before it exploded?
2. The pressure of a gas in a tank is 3.20-atm at
22⁰C. If the temperature rises to 60.0 ⁰C, what
will be the gas pressure in the tank?
3. The pressure in a car tire is 1.88-atm at 25⁰C.
What will be the pressure if the temperature
warms up to 37⁰C?
Combined Gas Law
• Combined Gas Law - P1V1
T1
=
P2V2
T2
Combined Gas Law Examples
1. Andrea takes a trip in a hot air balloon from the Rocky
Mountains. At her launch site, the temperature is 5°C, the
atmospheric pressure is 0.50-atm, and the volume of the air
in the balloon is 120-L. When she lands in Dallas, the
temperature is 28°C and the atmospheric pressure is 1-atm.
What is the new volume of the air in the balloon?
2. A sample of air in a syringe exerts a pressure of 1.02-atm at
a temperature of 22ºC. The syringe is placed a hot water
bath at 100ºC. The pressure of the air increases to 1.23atm by pushing the plunger in, which reduces the volume to
0.224-mL. What was the original volume of the air?
3. A 0ºC and 1-atm pressure, a sample of gas occupies 30-L.
If the temperature is increased to 30ºC and the entire gas
sample is transferred to a 20-L container, what will be the
gas pressure inside the container?
Ideal Gas Law
• Ideal Gas Law considers the amount of gas
or moles of gas
• Formula:
PV = nRT
– R = ideal gas constant = 8.31 L x kPa/K x mol
– P = pressure
– V = volume
– n = number of moles
– T = temperature (in Kelvin)
• K = ºC + 273
Ideal Gas Law Examples
1. Calculate the pressure in atmospheres of
0.412 mol of Helium at 289 K & occupying
3.25 L.
2. Determine the temperature required for
0.0470 mol of gas to fill a balloon to 1.2-L
under 0.988-atm pressure.
3. A rigid steel cylinder with a volume of
20.0L is filled with nitrogen gas to a final
pressure of 200-atm at 27°C. How many
moles of gas does the cylinder hold?
Dalton’s Law of Partial Pressures
• Dalton’s Law of Partial Pressures – at
constant volume and pressure, the total
pressure exerted by a mixture of gases is
equal to the sum of the partial components.
• When a gas is collected by water
displacement, the gas in the collection
bottle is actually a mixture of the gas and
water vapor.
• Formula: Ptotal = P1 + P2 + P3…
Dalton’s Law Examples
1. A mixture of oxygen (O2), carbon dioxide (CO2),
and nitrogen (N2) has a total pressure of 0.97atm. What is the partial pressure of O2, if the
partial pressures of CO2 is 0.70-atm and N2 is
0.12-atm?
2. What is the partial pressure of hydrogen gas in
a mixture of hydrogen and helium if the total
pressure is 600-mm Hg and the partial pressure
of helium is 439-mm Hg?
3. Find the total pressure for a mixture that
contains four gases with partial pressures of
5.00-kPa, 4.56-kPa, 3.02-kPa, and 1.20-kPa.
Real Gases vs. Ideal Gases
• Particles in a REAL gas:
– have their own volume
– attract each other
• Particles in an IDEAL Gas:
– Conform precisely to the assumptions of
kinetic theory
– All gas law calculations completed assume the
gases were ideal gases.
Graham’s Law
• Diffusion
– Spreading of gas molecules throughout a container
until evenly distributed.
• Effusion
– Passing of gas molecules through a tiny opening in
a container
• Speed of diffusion/effusion
– Kinetic energy is determined by the temperature of
the gas.
– At the same temp & KE, heavier molecules move
more slowly.
• Larger m  smaller v