Kinetic Molecular Theory of Gases and the Gas Laws Mr. Nelson Chemistry
Mar 31, 2015
Kinetic Molecular Theory of Gases and the Gas LawsMr. NelsonChemistry
Properties of GasesGases are fluids
◦Fluids are any substance that flowsGases are highly compressible
◦Example: Tire pressureGases completely fill containersGases 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/GasLaw/GLP.htm
Kinetic Molecular Theory of GasesAssumptions:
◦Gas molecules are in constant, random motion
◦Gas molecules are separated by large distances
◦Gas molecules have no attractive/repulsive forces
Temperature of GasesTemperature 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 GasesAt sea level, the standard gas
pressure is 1 atmospherePressure is the force exerted by
gas moleculesStandard 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
PascalPa (Usually, kPa)
To convert,
1 atm = 760 mm Hg
1 atm = 101.3 kPa
Converting Pressure ExampleConvert 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 LawStates that for a fixed amount of
gas at constant temperature the volume of the gas is inversely proportional to the pressure of a gas
2211 VPVP Pressur
e
Volume
Boyle’s LawExample 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 LawExample 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 LawStates that the volume of a gas is
directly proportional to the Kelvin temperature if the pressure remains constant
2
2
1
1
T
V
T
V
Volume
Temperature
Charles’s LawExample 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 LawExample 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 LawStates that the pressure of a gas
is directly proportional to the Kelvin temperature if the volume remains constant
2
2
1
1
T
P
T
PPressur
eTemperature
Gay-Lussac’s LawExample 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 LawExample 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 LawA single equation that combines
all the gas laws:
Combined Gas LawExample 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 LawRelates the gas laws and the
amount of gasRequires the gas constant, R
◦R can be a different number depending on the units
Kmol
LkPaR 31.8
Kmol
LatmR 08205.0
PV = nRTExample 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 LawExample 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 HypothesisEqual 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 acceptedWhy?
◦Tennis balls vs. Bowling balls
But its true!