The Kinetic Molecular Theory of Gases (KMT)

What are the 5 distinguishing properties of Gases?

1. they are easy to compress

2. they expand as temperature increases if pressure remains constant. they expand to fill their container

3. they have very low viscosity. They can flow more freely through pipes than liquids and able to escape quickly from opening in containers

4. they occupy far more space and have lower densities than liquids and solids

5. they are miscible

What is an ideal gas?

a hypothetical gas whose molecules occupy negligible space and have no interactions, and which consequently obeys the gas laws exactly

What is KMT?

• Kinetic Molecular Theory of Gases

• fundamental model for ideal gases

• based on 6 assumptions

Assumption 1 of KMT

Gasses are composed of a large number of particles that behave like hard spherical objects in a state of constant random motion

Assumption 2 of KMT

• These particles move in a straight line until they collide with another particle or the walls of the container

• An ideal gas has high translational kinetic energy

Assumption 3 of KMT (4)

• Individual gas particles are considered point masses (a mass w/o volume)

• these particles are much smaller in volume than the distance between particles

• Most of the volume of a gas is therefore empty space

• The volume of the gas particles is considered negligible compared to the container

Assumption 4 of KMT

There is no force of attraction between gas particles or between the particles and the walls of the container

Assumption 5 of KMT

Collisions between gas particles or collisions with the walls of the container are perfectly elastic

None of the energy of the gas particles is lost when it collides with the walls of the container

Assumption 6 of KMT

The average kinetic energy of a collection of gas particles depends on the temperature of the gas and nothing else

What is temperature?

• the average kinetic energy

• measured in Kelvin (always convert to Kelvin for calculations)

  • Kelvin = Celsius + 273.15

• absolute zero is the temperature at which all movement of all particles stop (0 K = -273.15°C)

What is pressure?

• the # of collisions made with a container

• force per unit area

• the push of the molecules on the surface of the container

how is pressure measured?

1 atm =

• 101.3 kPa (NIST) or 100 (IUPAC)

• 760 mm Hg

• 760 torr

• 1.013 bar

• 14.69 psi (don’t use this!)

Atmospheric pressure equals the weight of air above a point, measured at sea level as 1 atmosphere (atm)

What is STP?

aka Standard Temperature and Pressure

• T = 0°C = 273.15 K

• P = 100 kPa or 101.3 kPa

(used in lab conditions)

What is SATP?

aka Standard Ambient temperature and pressure

• T = 25°C = 298.15 K

• P = 100 kPa or 101.2 kPa

(used in naturalistic conditions)

Ideal Gas Law

Helps us understand how gases behave

PV = n RT

• P = pressure (kpa/ atm)

• V = volume (L)

• n = moles (mol)

• R = universal constant 8.314 L kPa/ mol K

• T = temperature (K)

Boyle’s Law

For a fixed mass of gas at a constant temperature, pressure and volume are inversely proportional

• Increase the pressure of a gas its volume will decrease (vise versa)

• P₁V₁ = P₂V₂

Charles’ Law

For a fixed amount of gas at a constant pressure, volume is directly proportional to its absolute temperature (K)

• If you increase temperature (heat up) of a gas, it expands

• V₁/T₁ = V₂/T₂

Gay-Lussac’s Law

For a fixed amount of gas in a constant volume, the pressure is directly proportional to its absolute temperature (K)

• If you heat up gas in a rigid container the gas particles move faster and hit the container’s wall harder, increasing the pressure

• P₁/T₁ = P₂/T₂

Combined Gas Law

Describes the relationship between pressures, volume, and absolute temperature of a fixed amount of gas

• P₁V₁/T₁ = P₂V₂/T₂