Transcript Ch._12_Behavior_of_Gases_ppt.ppt

Gases
The Kinetic Theory of Gases
Makes three assumptions about gases:
 A Gas is composed of particles
 usually molecules or atoms
 Considered to be hard spheres far
enough apart that we can ignore their
volume.
 Between the molecules is empty space.
The particles are in constant random
motion.
Move in straight lines until they bounce off
each other or the walls.
All collisions are perfectly elastic
• The Average speed of an oxygen
molecule is 1660 km/hr at 20ºC
• The molecules don’t travel very far
without hitting each other, so they move
in random directions.
Gas Pressure
• Pressure is the result of collisions of the
molecules with the sides of a container
• A vacuum is completely empty space no particles, no pressure!
• Pressure measured in units of
atmospheres (atm) (SI = pascal)
• Measuring device = barometer
Mercury barometer
1 atm
Pressure
• At one atmosphere
pressure, a column of
mercury = 760 mm
high.
Column of Mercury
Dish of Mercury
Mercury Barometer
1 atm
Pressure
• At one atmosphere
pressure, a column of
760 mm
mercury = 760 mm
high.
• Thus, another unit of
pressure is mm Hg
• 1 atm = 760 mm Hg
and also = 101.3 kPa
Kinetic Energy and Temperature
• Temperature is a measure of the
average kinetic energy (K.E.) of the
molecules of a substance.
• Higher temperature = faster molecule
movement
• At absolute zero (0 K), all molecular
motion would theoretically stop.
Temperature
• The average kinetic energy is directly
proportional to the temperature, in
Kelvin
• If you double the temperature (in
Kelvin) you double the average kinetic
energy.
• If you change the temperature from 300
K to 600 K, the kinetic energy doubles.
Temperature
• If you change the temperature from
300 ºC to 600 ºC the kinetic energy
doesn’t double.
– Because 873 K is not twice 573 K
Variables that describe a Gas
• The four variables and their common
units:
1. pressure (P) in kilopascals
2. volume (V) in Liters
3. temperature (T) in Kelvin
4. number of moles (n)
1. Amount of Gas
• When we inflate a balloon, we are
adding gas molecules.
• Increasing the number of gas particles
increases the number of collisions
– thus, the pressure increases
• If temp. is constant- doubling the number of
particles doubles pressure
Pressure and the number of
molecules are directly related
• More molecules means more collisions.
• Fewer molecules means fewer collisions.
• Gases naturally move from areas of high
pressure to low pressure because there is
empty space to move in - spray can is
example.
1. Volume of Gas
• In a smaller container, molecules have less
room to move.
• Hit the sides of the container more often.
• As volume decreases, pressure increases.
(think of a syringe)
2. Temperature of Gas
• Raising the temperature of a gas increases
the pressure, if the volume is held constant.
• The molecules hit the walls harder, and
more frequently!
• The only way to increase the temperature at
constant pressure is to increase the volume.
The Gas Laws
• These will describe HOW gases
behave.
• Can be predicted by the theory.
• Amount of change can be calculated
with mathematical equations.
1. Boyle’s Law
• At a constant temperature, gas pressure
and volume are inversely related.
– As one goes up the other goes down
• Formula to use: P1 x V1= P2 x V2
Examples
• A balloon is filled with 25 L of air at 1.0 atm
pressure. If the pressure is changed to 1.5
atm what is the new volume?
• A balloon is filled with 73 L of air at 1.3 atm
pressure. What pressure is needed to change
the volume to 43 L?
2. Charles’s Law
• The volume of a gas is directly
proportional to the Kelvin temperature,
if the pressure is held constant.
• Formula to use: V1/T1 = V2/T2
Examples
• What is the temperature of a gas
expanded from 2.5 L at 25 ºC to 4.1L at
constant pressure?
• What is the final volume of a gas that
starts at 8.3 L and 17 ºC, and is heated to
96 ºC?
3. Gay-Lussac’s Law
• The temperature and the pressure of
a gas are directly related, at
constant volume.
• Formula to use: P1/T1 = P2/T2
Examples
• What is the pressure inside a 0.250 L can of
deodorant that starts at 25 ºC and 1.2 atm if
the temperature is raised to 100 ºC?
• At what temperature will the can above
have a pressure of 2.2 atm?
4. Combined Gas Law
• The Combined Gas Law deals with the
situation where only the number of
molecules stays constant.
• Formula: (P1 x V1)/T1= (P2 x V2)/T2
• This lets us figure out one thing when
two of the others change.
Examples
• A 15 L cylinder of gas at 4.8 atm pressure and
25 ºC is heated to 75 ºC and compressed to 17
atm. What is the new volume?
• If 6.2 L of gas at 723 mm Hg and 21 ºC is
compressed to 2.2 L at 4117 mm Hg, what is
the final temperature of the gas?
Ideal Gases
• We are going to assume the gases behave “ideally”obeys the Gas Laws under all temp. and pres.
• An ideal gas does not really exist, but it makes the
math easier and is a close approximation.
• Particles have no volume.
• No attractive forces.
Ideal Gases
• There are no gases for which this is
true; however,
• Real gases behave this way at high
temperature and low pressure.
5. The Ideal Gas Law #1
• Equation: PV = nR T
• Pressure times Volume equals the number
of moles times the Ideal Gas Constant (R)
times the temperature in Kelvin.
• This time R does not depend on anything, it
is really constant
• R = 8.31 (L x kPa) / (mol x K)
The Ideal Gas Law
• We now have a new way to count moles
(amount of matter), by measuring T, P, and
V. We aren’t restricted to STP conditions
n = PV
RT
Real Gases behave like Ideal
Gases...
• When the molecules
are far apart
• The molecules do not
take up as big a
percentage of the
space
• We can ignore their
volume.
• This is at low pressure
Real Gases behave like Ideal gases
when...
• When molecules are moving fast
– = high temperature
• Collisions are harder and faster.
• Molecules are not next to each other
very long.
• Attractive forces can’t play a role.
Avogadro’s Hypothesis
• Avogadro’s Hypothesis: Equal volumes of
gases at the same temp. and pressure
contain equal numbers of particles.
– Saying that two rooms of the same size could
be filled with the same number of objects,
whether they were marbles or baseballs.
7. Dalton’s Law of Partial
Pressures
• The total pressure inside a container is equal
to the partial pressure due to each gas.
• The partial pressure is the contribution by
that gas.
PTotal = P1 + P2 + P3
• We can find out the pressure in the fourth
container.
• By adding up the pressure in the first 3.
2 atm
+ 1 atm
+ 3 atm
= 6 atm
Diffusion
Molecules moving from areas of high
concentration to low concentration.
 Example: perfume molecules spreading
across the room.

• Effusion: Gas escaping through a tiny hole in a
container.
• Depends on the speed of the molecule.
8. Graham’s Law
RateA
RateB
=
 MassB
 MassA
• The rate of effusion and diffusion is inversely
proportional to the square root of the molar mass of
the molecules.
• Kinetic energy = 1/2 mv2
• m is the mass v is the velocity.
Graham’s Law
• Heavier molecules move slower at the
same temp. (by Square root)
• Heavier molecules effuse and diffuse
slower
• Helium effuses and diffuses faster than
air - escapes from balloon.