Kinetic Molecular Theory of Gases and the Gas LawsChemistryMs. Piela

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 TheoryKMT 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 AbbreviationAtmosphere atmMillimeter of mercury mm Hg

Pascal Pa (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 LawsVariables 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 Pressu

re

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?

6.48 L

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)

88.3 kPa

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

TV

TV

Temperature

Volume

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)?

519 L

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?

846 K

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

TP

TP

Pressure

Temperature

Gay-Lussac’s LawExample Problem

◦The gas left in a used aerosol can is at a pressure of 103 kilopascals at 25.0 °C. If this can is thrown onto a fire, what is the pressure of the gas when its temperature reaches 928 °C?

415 kPa

Gay-Lussac’s LawExample Problem

◦A sealed cylinder of gas contains nitrogen gas at 2.50 atm 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?

2.76 atm

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?

30.5 L

Combined Gas LawExample ProblemA gas has a temperature of 14.0°C,

and a volume of 4.50 liters. If the temperature is raised to 29.0°C and the pressure is not changed, what is the new volume of the gas?

4.74 L

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

KmolLkPaR 31.8

KmolLatmR 0821.0

PV = nRTExample Problem

◦A container of 3.00 L of nitrogen (N2) is at a pressure of 4.50 x 102 kPa and a temperature of 39.0 °C. How many grams of N2 are in the container?

0.52 mol N2, 14.5 g N2

Ideal Gas LawExample Problem

◦What volume will 0.450 mol of a gas occupy at STP?

10.1 L

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!