# Kinetic Molecular Theory of Gases and the Gas Laws

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Kinetic Molecular Theory of Gases and the Gas Laws
Mr. Nelson Chemistry

Properties of Gases Gases are fluids Gases are highly compressible
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

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
Abbreviation Atmosphere atm Millimeter of mercury mm Hg Pascal Pa (Usually, kPa)

To convert, 1 atm = 760 mm Hg 1 atm = kPa

Converting Pressure Example
Convert 72.7 atmospheres (atm) into kilopascals (kPa)

Variables in Gas Equations:
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 Pressure Volume

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 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 Temperature Volume

Charles’s Law Example Problem
The air in a hot air balloon has a volume of L at 30.0°C (303 K). What will the volume be if the temperature is raised to °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

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 °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

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 mol of a gas at 25.0 °C if it is contained in a L vessel?

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!