Transcript Gas Laws

Gas Laws
Real Gas Properties
• Compressible
• They have no constant volume.
*They fill the container they are placed in.
•
•
•
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They have mass.
They have high Kinetic energy (KE = ½ mv2)
Movement is random and rapid.
Gases exert pressure.
*They undergo thousands of collisions with each
other and with the container walls.
Kinetic Molecular Theory
1. All gases consist of very small particles with very
small (point) masses.
2. Large distances separate gas particles.
1.
The volume of the gas particles themselves is assumed to be
zero because it is negligible compared with the total volume
of the container.
3. Gas particles are in constant, rapid, linear motion.
4. Collisions within the container are perfectly elastic.
5. The average KE depends only on the temperature of
the gas.
6. Gas particles exert no force on one another.
1.
Attractive forces between gas particles are so weak that the
model assumes them to be zero.
Gas Forms
Monatomic
(Nobel Gases)
Diatomic
Molecules
(N2, O2, H2, F2,Cl2) (Compounds such as
CO2, H2O and NO2 )
Ideal Gas Properties
•Ideal gases are described by the kinetic-molecular theory postulates.
•Ideal gases are considered point masses with no volume.
•No attractive forces exist between gas particles.
Measuring Gases
Temperature (T):
The average kinetic energy of a system.
•Units: Celcius (°C) and convert to Kelvin (K)
K = °C + 273
•The Kelvin temperature scales is based on absolute zero.
•“0” K is equal to –273 °C.
•Absolute zero suggests that matter has no energy and all motion
has stopped.
Amount of Gas (n): “n” is the letter
designated to indicate moles of gas.
Recall:
1 mole of gas = 22.4 L at STP
STP = 0 °C and 1 atm
Volume (v): The volume of a
gas varies with container size.
Recall: 1 mL = 1 cm3
1 L = 1 dm3
Pressure (P): Force per unit area.
•Particles strike the container with a force relative to their velocity
(v) and rebound with an equal force in the opposite direction.
•With an abundance of collisions, the force per unit area becomes
constant.
•Atmospheric pressure results by air colliding with objects on
Earth and Earth itself.
•Standard Atmospheric pressure (at sea-level) is:
1 atm = 760 torr = 760 mm Hg = 101.325 kPa = 1 N/m2
Barometers measure atmospheric pressure.
Aneroid Barometers exist in a
metal can (aneroid) that contains
a near vacuum. The pressure is
measured relative to the changes
in the aneroid size.
Mercury Barometers
measure pressure by the
changes that occur in the
height of a column of Hg
supported by the atmosphere.
An instrument used to measure the pressure of enclosed gases
relative to the atmospheric pressure in a closed container.
A U-shaped glass tube is filled with mercury. One end of the
tube is open into the container in which the gas pressure is to
be measure while the other end of the tube is open to the
surrounding atmoshpere.
•If the gas pressure is greater it
will push the mercury away from
it.
•If the atmospheric pressure is
greater, it will push the mercury
down.
Pgas = Patm+ h
Pgas = Patm- h
At Sea-Level!
Manometer Sample problems
You have a closed container attached to a U-tube. The
mercury in the open-ended side of the tube is higher, the
difference between the heights of the mercury columns in
27 mm. You have measured the atmospheric pressure as
755 mm Hg. What is the pressure of the gas in the
container in atmospheres?
A balloon is attached to an open-ended manometer. The
mercury level in the manometer is 13 mm lower on the
side attached to the balloon than on the side open to the
atmosphere. The pressure of the atmosphere is measured
to be 755 mm Hg. What is the pressure of the balloon in
torr and kPa?
Boyle’s Law
Robert Boyle measured the volume (v) of the air
at different pressures (p) while keeping the
temperature constant.
PV = kb
where k is a constant
With this relationship, we can measure the pressure and volume
in the laboratory and then mathematically determine a second set
of data for the same substances.
P1V1 = kb = P2V2
P1V1 = P2V2
P1V1 = P2V2
•This suggests that pressure and volume are inversely proportional.
•Boyle’s Law is valid for real gases except at very low temperatures
and very high pressures.
Boyle’s Law
The curve is a hyperbola
indicating an inverse
relationship.
Gas Law Practice problems
#1
Charles Law
Jacque Charles measured the volume (v) of the
gases at different temperature (T) while keeping
the pressures constant.
V = k cT
where kc is a constant
With this relationship, we can measure the temperature and
volume in the laboratory and then mathematically determine a
second set of data for the same substances.
V1 = kc = V2
T1
T2
V1 =
T1
V2
T2
You must always put your
1
2
temperature in Kelvin for any
gas law calculation. (Remember,
1
2
you can’t divide by 0!)
•This suggests that Temperature and volume are directly proportions.
•Charles Law was used to estimate the point of absolute zero.
V =V
T
T
Charles Law
Gas Law Practice problems
#3
Avogadro’s Law
Equal volumes of gases at the same
temperature and pressure contain an
equal number of particles.
V = kan or
V = ka
n
Where V = volume, k3 = a constant, and n = mols
of gas
This law suggests:
 All gases show the same physical behavior.
 Gases with a larger volume must consist of a
greater number of particles.
 Volume is directly proportional to mols of gas
Remember!!!! 1 mol of gas at STP = 22.4 L
Dalton’s Law of Partial Pressure
The sum of the partial pressures of all the
components in a gas mixture is equal to the
total pressure of the gas mixture.
PT = Pa + Pb + Pc +…….Pn
What is the atmospheric pressure if the partial
pressure of nitrogen, oxygen, and argon are 604.5
mm Hg, 162.8 mm Hg and 0.5 mm Hg respectively?
PT = Pa + Pb + Pc
PT= 604.5 mm Hg + 162.8 mm Hg + 0.5 mm Hg
PT = 767.8 mm Hg
Gas Law Practice problems
#7
Combining Boyle’s & Charles’ Laws
P1V1 = P2V2
T1
T2
The combined gas law relates temperature,
pressure and volume of a gas.
•Temperature and volume are directly
proportional
•Temperature and Pressure are directly
proportional
•Pressure and volume are inversely proportional
Gas Law Practice problems
#6
Ideal Gas Law
PV = nRT
Where: P = pressure in “atm”, V = volume in “L”,
n = mols of gas T = temperature in Kelvin.
R = Ideal Gas Law Constant = 0.0821 atm•L/mol•K
How many moles of gas at 100.0°C does it take to fill a 1.00 L
flask to a pressure of 1.50 atm?
T = 100.0°C = 373.0 K
P = 1.50 atm
V =1.00 L
PV = nRT
PV = n
RT
n = (1.50 atm) (1.00 L) = 0.0490 mols
(0.0821 atm•L)(373 K)
mol•K
A camping stove uses a 5.00 L propane tank that holds 3.00 kg
of liquid C3H8. How large a container would be needed to
hold the same amount of propane as a gas at 25.0 °C and a
pressure of 303.975 kPa?
Givens:
V=?
= 298 K
T = 25.0 °C
P = 303.975 kPa = 3.00 atm
= 3000 g 1 mol C3H8 = 68.1 mols C3H3
m = 3.00 kg
44.03 g c3H8
PV = nRT
V = nRT
P
V = (68.1 mols)((0.0821 atm•L)(298 K)
mol•K
3.00 atm
= 555 L
Variations of the Ideal Gas Law
PV = nRT
Moles (n) = mass of given
FM or MM of given
So make a substitution
PV = mRT
(FM)
We also know, density = mass
volume
P = mRT
V (FM)
P = dRT
(FM)
Substitute d for m
V
Thus, you have three forms of the
Ideal Gas law!
Gas Diffusion
 The movement of a gas throughout an area.
 Diffusion is also dependent on how big the gas particle is.
Lighter gas particles diffuse faster than heavier particles because
the velocity of lighter particles is greater than those of
heavier
particles.
1.Explain how gas density is related to molar mass and
temperature.
Since there are the same number of gas particles in equal volumes at the same
temp and pressure (1 mol gas = 22.4 L at STP), the density of a gas is directly
proportional to the mass of its particles. Also since temperature increase causes
gas volume to increase, fewer particles in a unit of volume will exist thus causing
the density to decrease.
2. Describe two ways in which a balloon can get lift in air.
To achieve lift, the gas inside the balloon must be less dense than the air
outside. This can be done by either using a gas whose particles have a smaller
mass than the weighted average mass of the particle is air, or using hot gases
that have expanded enough to make them less dense than the surrounding air.
Gas Effusion
 The movement of a gas through a hole so tiny that they do
not stream through but instead pass through one particle at a
time.
 Effusion is dependent on how big the gas particle is. Lighter
gas particles effuse faster than heavier particles.
Ex… CO2, O3, C2H6, and SO3. Rank the gases in order
of increasing effusion rate.
**First find the molecular masses of each gas.
CO2=44 g/mol, O3=48 g/mol, C2H6=30 g/mol,
and SO3=80 g/mol
Thus, ranking from slow to fast…SO3, O3, CO2,and C2H6