Kinetic Molecular Theory of Gases and the Gas Laws
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Transcript Kinetic Molecular Theory of Gases and the Gas Laws
Kinetic Molecular Theory of
Gases and the Gas Laws
Mr. Nelson
Chemistry
Properties of Gases
Gases
are fluids
◦ Fluids are any substance that flows
Gases
are highly compressible
◦ Example: Tire pressure
Gases
completely fill containers
Gases have lower densities than
liquids and solids
Kinetic Molecular Theory
KMT
describes the motion of
the particles
◦ Particles have the same motion
as billiard balls
http://intro.chem.okstate.edu/NSFCCLI/GasLa
w/GLP.htm
Kinetic Molecular Theory of Gases
Assumptions:
◦ Gas molecules are in constant,
random motion
◦ Gas molecules are separated by
large distances
◦ Gas molecules have no
attractive/repulsive forces
Temperature of Gases
Temperature and energy of gases are
directly proportional
◦ As the temperature increases, kinetic energy
of the molecules increases
◦ As temperature decreases, kinetic energy will
also decrease
Pressure of Gases
At sea level, the standard gas pressure is 1
atmosphere
Pressure is the force exerted by gas
molecules
Standard Temperature and Pressure (STP)
is equal to 1 atm and 0 °C
Different Units of Pressure
Unit
Abbreviation
Atmosphere
atm
Millimeter of
mercury
mm Hg
Pascal
Pa
(Usually, kPa)
To convert,
1
atm = 760 mm Hg
1 atm = 101.3 kPa
Converting Pressure Example
Convert 72.7 atmospheres (atm) into
kilopascals (kPa)
The Gas Laws
Variables
in Gas Equations:
◦ P = Pressure (kPa or atm)
◦ V = Volume (L)
◦ T = Temperature (K)
◦ n = amount of gas (moles)
Boyle’s Law
States that for a fixed amount of gas at
constant temperature the volume of the
gas is inversely proportional to the
pressure of a gas
P1V 1 P2V 2
Boyle’s Law
Example Problem
◦ The pressure on 2.50 L of anesthetic gas
changes from 105 kPa to 40.5 kPa. What will
be the new volume if the temperature
remains constant?
Boyle’s Law
Example Problem
◦ A high-altitude balloon contains 30.0 L of
helium gas at 103 kPa. As the balloon rises,
you record a new volume of 35.0 L. What is
the atmospheric pressure in kPa? (Assume
constant temperature)
Charles’s Law
States that the volume of a gas is directly
proportional to the Kelvin temperature if
the pressure remains constant
V1
T1
V2
T2
Charles’s Law
Example Problem
◦ The air in a hot air balloon has a volume of
400.0 L at 30.0°C (303 K). What will the
volume be if the temperature is raised to
120.0 °C (393 K)?
Charles’s Law
Example Problem
◦ An aerosol can has a volume of 3.00 x 102 mL
at 150.0°C is heated until its volume is 6.00 x
102 mL.What is the new temperature (in K)
of the gas if pressure remains constant?
Gay-Lussac’s Law
States that the pressure of a gas is directly
proportional to the Kelvin temperature if
the volume remains constant
Temperature
Pressure
P1
T1
P2
T2
Gay-Lussac’s Law
Example Problem
◦ The gas left in a used aerosol can is at a
pressure of 103 kPa at 25 °C. If this can is
thrown onto a fire, what is the pressure of
the gas when its temperature reaches 928 °C?
Gay-Lussac’s Law
Example Problem
◦ A sealed cylinder of gas contains nitrogen gas
at 1.00 x 103 kPa pressure and a temperature
of 20.0 °C. The cylinder is left in the sun, and
the temperature of the gas increases to 50.0
°C. What is the new pressure in the cylinder?
Combined Gas Law
A single equation that combines all the
gas laws:
Combined Gas Law
Example Problem
◦ A gas takes up a volume of 17 liters, has a
pressure of 2.3 atm, and a temperature of 299
K. If I raise the temperature to 350 K and
lower the pressure to 1.5 atm, what is the
new volume of the gas?
Ideal Gas Law
Relates the gas laws and the amount of
gas
Requires the gas constant, R
◦ R can be a different number depending on the
units
R 8 . 31
kPa L
mol K
R 0 . 08205
atm L
mol K
PV = nRT
Example Problem
◦ A container of 3.0 L of nitrogen (N2) is at a
pressure of 4.5 x 102 kPa and a temperature
of 39 °C. How many grams of N2 are in the
container?
Ideal Gas Law
Example Problem
◦ What pressure will be exerted by 0.450 mol
of a gas at 25.0 °C if it is contained in a 0.650
L vessel?
Avogadro’s Hypothesis
Equal
volumes of gases at the same
temperature and pressure contain
equal numbers of particles
Due mainly to the large amount of
empty space between particles
◦ From this, scientists have determined
that 1 mol = 22.4 L at STP
This was not well accepted
Why?
◦ Tennis balls vs. Bowling balls
But its true!